diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,26 @@ +# Changelog for `gongju` + +All notable changes to the `gongju` package will be documented in this file. + +The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), +and this project adheres to the Haskell Package Versioning Policy (PVP). + +## [0.1.0.0] — 2026-10-24 + +### Added +- **`Gongju.Peano`**: Inductive Peano type kind (`Peano`, `'Z`, `'S`), compile-time natural bridge (`ToPeano`, `FromPeano`), and reflection typeclasses. +- **`Gongju.Composition`**: Variadic function composition (`compN @n`, `ComposeN`) and nested functor mapping (`fmapN @n`, `FmapN`) with bidirectional functional dependencies. +- **`Gongju.Positional`**: In-place curried arrow combinators without heap allocation: + - `slipr @n` (`Yank`): Pull the $n$-th argument to position 0. + - `slipl @n` (`Shove`): Push argument 0 deeper to position $n$. + - `twist @n` (`Twist`): Swap adjacent arguments at depth $n$ and $n + 1$. +- **`Gongju.Permute`**: Arbitrary curried function argument permutation (`permute @indices`, `Permute`) via iterated `Yank` and index adjustment (`Adjust`, `MapAdjust`), with full support for duplicate argument types. +- **`Gongju.Indexed`**: Indexed monads, indexed applicatives, and indexed comonads (`IxFunctor`, `IxApplicative`, `IxMonad`, `IxComonad`). +- **`Gongju.Comonad`**: Canonical comonad and distributive integrations (`Comonad`, `Distributive`, `Representable`, `W`, `PullDist`). +- **`Gongju.Adjunction`**: Categorical adjunctions and dual pairing annihilation (`Adjunction`, `zapLR`, `zapRL`, `AdjU`, `AdjC`). +- **`Gongju.Kan`**: Right and Left Kan extensions, Yoneda and Coyoneda $O(1)$ fusion, and Codensity CPS monad optimization (`Ran`, `Lan`, `Yoneda`, `Coyoneda`, `Codensity`, `Density`). +- **`Gongju.Profunctor`**: Profunctor mapping grids (`dimap`, `lmap`, `rmap`), Curried category arrow permutation (`CurriedCat`, `yankCat`, `permuteCat`), right-nested tuple spine arrow permutations (`yankTuple`, `permuteTuple`), and profunctor strand input/output reordering (`permuteInputs`, `permuteOutputs`, `permuteHandler`). +- **`Gongju.Contravariant`**: Contravariant syntax grids: positional pre-composition (`precomposeAt @n`, `(-.)`, `(-.*)`, `(-.**)`), 2D function splicing (`spliceAt @n @m`), and nested contravariant functor mapping with alternating parity (`contramapN @n`, `(<-$>)`, `(<-$$>)`, `(<-$$$>)`). +- **`Gongju.Monad`**: Two-phase positional monadic binding (`bindPos @before @after`, `bindAt @n`, `(==<<)`, `(=.=<<)`, `(===<<)`), multi-slot monadic lifting masks (`liftMask @'[MArg, PArg, MArg]`), and arity-indexed Kleisli composition (`liftPureN @n`, `bindKleisliN @n`, `(<=<.)`, `(.>=>)`). +- **`Gongju.Core`**: Top-level re-exports and Grand Unified Open-World Tape Engine (`withOps`, `(.@)`). +- **Core Inspection Test Suite**: Automated verification harness ensuring zero residual dictionaries and complete inlining under GHC `-O2`. diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,189 @@ +EUROPEAN UNION PUBLIC LICENCE v. 1.2 +EUPL © the European Union 2007, 2016 + +This European Union Public Licence (the ‘EUPL’) applies to the Work (as defined below) which is provided under the +terms of this Licence. 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`slipr @n` (`Yank`): Pull the $n$-th argument to position 0. + - `slipl @n` (`Shove`): Push argument 0 deeper to position $n$. + - `twist @n` (`Twist`): Swap adjacent arguments at depth $n$ and $n + 1$. +- **[`Gongju.Permute`](src/Gongju/Permute.hs)** — Arbitrary argument permutation (`permute @'[2, 0, 1]`, `Permute`) with full disambiguation of duplicate argument types. +- **[`Gongju.Indexed`](src/Gongju/Indexed.hs)** — Indexed monads, indexed applicatives, and indexed comonads (`IxFunctor`, `IxApplicative`, `IxMonad`, `IxComonad`). +- **[`Gongju.Comonad`](src/Gongju/Comonad.hs)** — Integrations with `comonad` and `distributive` (`W`, `PullDist`, `Representable`). +- **[`Gongju.Adjunction`](src/Gongju/Adjunction.hs)** — Categorical adjunctions and dual pairing annihilation (`zapLR`, `zapRL`, `AdjU`, `AdjC`). +- **[`Gongju.Kan`](src/Gongju/Kan.hs)** — Kan extensions, Yoneda and Coyoneda $O(1)$ fusion, and Codensity CPS monad optimization (`Ran`, `Lan`, `Yoneda`, `Codensity`). +- **[`Gongju.Profunctor`](src/Gongju/Profunctor.hs)** — Profunctor mapping grids (`dimap`), Curried category arrow permutation (`CurriedCat`, `yankCat`, `permuteCat`), right-nested tuple spine arrow permutations (`yankTuple`, `permuteTuple`), and profunctor strand input/output reordering (`permuteInputs`, `permuteOutputs`, `permuteHandler`). +- **[`Gongju.Contravariant`](src/Gongju/Contravariant.hs)** — Contravariant syntax grids: positional pre-composition (`precomposeAt @n`, `(-.)`, `(-.*)`), 2D function splicing (`spliceAt @n @m`), and nested contravariant functor mapping with alternating parity (`contramapN @n`, `(<-$>)`, `(<-$$>)`). +- **[`Gongju.Monad`](src/Gongju/Monad.hs)** — Two-phase positional monadic binding (`bindPos @before @after`, `bindAt @n`, `(==<<)`, `(=.=<<)`), multi-slot monadic lifting masks (`liftMask @'[MArg, PArg, MArg]`), and arity-indexed Kleisli composition (`liftPureN @n`, `bindKleisliN @n`, `(<=<.)`, `(.>=>)`). + +--- + +## Quick Start + +```haskell +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE TypeApplications #-} + +import Gongju.Core + +main :: IO () +main = do + -- 1. Variadic composition over a 3-argument function: + let add3 x y z = (x + y + z :: Int) + print (compN @3 (* 2) add3 1 2 3) -- Prints 12 + + -- 2. Permuting arguments of a function: + let f x y z = (x, y, z) + print (permute @'[2, 0, 1] f True 10 "gongju") -- Prints (10, "gongju", True) + + -- 3. Tape-driven composition: + let comp = ((+ 1) .@ [P, P]) (+) + print (comp 5 10) -- Prints 16 +``` + +--- + +## Zero-Cost Guarantee + +Under GHC `-O2`, all combinators inline and simplify into primitive lambda applications with zero residual typeclass dictionaries, verified mechanically by `bin/gongju-inspect-core`. + +--- + +## License + +Licensed under the European Union Public Licence (EUPL-1.2) or Apache License 2.0. diff --git a/gongju.cabal b/gongju.cabal new file mode 100644 --- /dev/null +++ b/gongju.cabal @@ -0,0 +1,85 @@ +cabal-version: 3.0 +name: gongju +version: 0.1.0.0 +synopsis: Pure type-level utility functions, arity composition, and curried combinators +description: + Gongju (공구 / 工具, tools/implement) provides inductive Peano type-level + utility functions in pure Haskell, replacing Template Haskell arity splices + (e.g. composition-extra) and finite tuple generics (e.g. tuple-sop) with + zero-overhead typeclass induction, bidirectional functional dependencies, + and TypeApplications-friendly GHC.TypeLits.Nat wrappers. + +license: EUPL-1.2 OR Apache-2.0 +license-files: LICENSE +author: Nadia Yvette Chambers +maintainer: nadia.yvette.chambers@ik.me +homepage: https://github.com/NadiaYvette/gongju +bug-reports: https://github.com/NadiaYvette/gongju/issues +category: Types, Functional, Combinators +build-type: Simple +extra-doc-files: + README.md + , CHANGELOG.md + , LICENSE + +tested-with: + GHC == 9.10.3 + , GHC == 9.12.4 + , GHC == 9.14.1 + +source-repository head + type: git + location: https://github.com/NadiaYvette/gongju.git + subdir: packages/gongju + +common commons + default-language: Haskell2010 + ghc-options: + -Wall + -Wcompat + -Wredundant-constraints + +library + import: commons + hs-source-dirs: src + exposed-modules: + Gongju.Core + Gongju.Peano + Gongju.Composition + Gongju.Positional + Gongju.Permute + Gongju.Indexed + Gongju.Comonad + Gongju.Adjunction + Gongju.Kan + Gongju.Profunctor + Gongju.Contravariant + Gongju.Monad + build-depends: + base >= 4.20 && < 5 + , adjunctions >= 4.4 && < 5 + , comonad >= 5 && < 6 + , distributive >= 0.6 && < 1 + , indexed >= 0.1 && < 1 + , indexed-profunctors >= 0.1 && < 1 + , kan-extensions >= 5.2 && < 6 + , profunctors >= 5.6 && < 6 + , contravariant >= 1.5 && < 2 + +test-suite gongju-test + import: commons + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Main.hs + other-modules: CoreInspection + build-depends: + base >= 4.20 && < 5 + , adjunctions >= 4.4 && < 5 + , comonad >= 5 && < 6 + , contravariant >= 1.5 && < 2 + , distributive >= 0.6 && < 1 + , gongju + , hspec >= 2.11 && < 3 + , indexed >= 0.1 && < 1 + , kan-extensions >= 5.2 && < 6 + , profunctors >= 5.6 && < 6 diff --git a/src/Gongju/Adjunction.hs b/src/Gongju/Adjunction.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Adjunction.hs @@ -0,0 +1,173 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Adjunction +-- Description: Adjunction transitions and dual-functor annihilation for Gongju +-- +-- Plugs functor adjunctions ('Adjunction', @l ⊣ r@) from 'Data.Functor.Adjunction' +-- into Gongju's open tape composition engine without modifying Core. +-- +-- Provides: +-- * Adjunction unit (@η : Id ⇒ R ∘ L@) and counit (@ε : L ∘ R ⇒ Id@) stack rewrites. +-- * Day-adjoint pairing ('zapLR', 'zapRL') that annihilates dual adjoint functor +-- contexts (1 + 1 → 0 active layers). +-- * Hom-set adjunct lifting ('leftAdjunct', 'rightAdjunct'). +module Gongju.Adjunction + ( -- * Re-exported Canonical Adjunction Class + Adjunction(..) + , zapWithAdjunction + , indexAdjunction + , tabulateAdjunction + -- * Dual Annihilation Workers + , zapLR + , zapRL + -- * Open Adjunction Tags + , PAdjU + , PAdjC + , PZapLR + , PZapRL + , PAdjL + -- * Ergonomic Aliases + , AdjU + , AdjC + , ZapLR + , ZapRL + , AdjL + ) where + +import Data.Functor.Adjunction + ( Adjunction (..) + , indexAdjunction + , tabulateAdjunction + , zapWithAdjunction + ) +import Gongju.Composition + ( F + , InOrder + , MapPath (..) + , StepPathMask (..) + , StepRole (..) + ) +import Gongju.Peano (Append, Init) + +-- --------------------------------------------------------------------------- +-- 1. Dual Adjoint Pairing Workers +-- --------------------------------------------------------------------------- + +-- | Annihilate left adjoint context @l (a -> b)@ and right adjoint context @r a@ into @b@. +zapLR :: Adjunction l r => l (a -> b) -> r a -> b +zapLR lab ra = counit (fmap (<$> ra) lab) +{-# INLINE zapLR #-} + +-- | Dual annihilation: @r (a -> b)@ and @l a@ into @b@. +zapRL :: Adjunction l r => r (a -> b) -> l a -> b +zapRL rab la = counit (fmap (\a -> fmap ($ a) rab) la) +{-# INLINE zapRL #-} + +-- --------------------------------------------------------------------------- +-- 2. Open Mode Tags & Aliases +-- --------------------------------------------------------------------------- + +-- | Tag for inserting an adjunction unit: @a -> r (l a)@. +data PAdjU + +-- | Tag for applying an adjunction counit: @l (r a) -> a@. +data PAdjC + +-- | Tag for pairing active left-adjoint @l (a -> b)@ against caller @r a@ (annihilating both). +data PZapLR + +-- | Tag for pairing active right-adjoint @r (a -> b)@ against caller @l a@ (annihilating both). +data PZapRL + +-- | Tag for applying 'leftAdjunct': turns expectation of @l a@ into caller passing pure @a@. +data PAdjL + +-- | In-order adjunction unit alias. +type AdjU = InOrder PAdjU + +-- | In-order adjunction counit alias. +type AdjC = InOrder PAdjC + +-- | In-order Day-adjoint pairing alias (left active, right caller). +type ZapLR = InOrder PZapLR + +-- | In-order Day-adjoint pairing alias (right active, left caller). +type ZapRL = InOrder PZapRL + +-- | In-order hom-set adjunct alias. +type AdjL = InOrder PAdjL + +-- --------------------------------------------------------------------------- +-- 3. StepRole Instances (Adjunction Transitions) +-- --------------------------------------------------------------------------- + +-- | Adjunction unit: expands inner tip to @r (l inner)@. +instance forall base active ms m t3 acc acc' out l r inner. + ( Adjunction l r + , MapPath (Init active) inner (r (l inner)) acc acc' + , StepPathMask base (Append active '[ F, F ]) ms m t3 acc' out + ) => StepRole PAdjU base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Append active '[ F, F ]) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @inner @(r (l inner)) unit acc) + {-# INLINE stepRole #-} + +-- | Adjunction counit: collapses @l (r inner)@ at the tip down to @inner@. +instance forall base active ms m t3 acc acc' out l r inner. + ( Adjunction l r + , MapPath (Init (Init active)) (l (r inner)) inner acc acc' + , StepPathMask base (Init (Init active)) ms m t3 acc' out + ) => StepRole PAdjC base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Init (Init active)) @ms @m @t3 @acc' @out f + (mapPath @(Init (Init active)) @(l (r inner)) @inner counit acc) + {-# INLINE stepRole #-} + +-- | ZapLR: Annihilates active left-adjoint layer with caller right-adjoint argument. +instance forall base active ms m t3 acc acc' out' l r a rem ra. + ( Adjunction l r + , ra ~ r a + , MapPath (Init active) (l (a -> rem)) rem acc acc' + , StepPathMask base (Init active) ms m t3 acc' out' + ) => StepRole PZapLR base active ms m t3 acc (ra -> out') where + stepRole f acc ra = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out' f + (mapPath @(Init active) @(l (a -> rem)) @rem (`zapLR` ra) acc) + {-# INLINE stepRole #-} + +-- | ZapRL: Annihilates active right-adjoint layer with caller left-adjoint argument. +instance forall base active ms m t3 acc acc' out' l r a rem la. + ( Adjunction l r + , la ~ l a + , MapPath (Init active) (r (a -> rem)) rem acc acc' + , StepPathMask base (Init active) ms m t3 acc' out' + ) => StepRole PZapRL base active ms m t3 acc (la -> out') where + stepRole f acc la = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out' f + (mapPath @(Init active) @(r (a -> rem)) @rem (`zapRL` la) acc) + {-# INLINE stepRole #-} + +-- | AdjL: Turns @l a -> rem@ in the accumulator into @a -> r rem@. +instance forall base active ms m t3 acc acc' out' l r a rem. + ( Adjunction l r + , MapPath active (l a -> rem) (r rem) acc acc' + , StepPathMask base (Append active '[ F ]) ms m t3 acc' out' + ) => StepRole PAdjL base active ms m t3 acc (a -> out') where + stepRole f acc a = + stepPathMask @base @(Append active '[ F ]) @ms @m @t3 @acc' @out' f + (mapPath @active @(l a -> rem) @(r rem) (`leftAdjunct` a) acc) + {-# INLINE stepRole #-} diff --git a/src/Gongju/Comonad.hs b/src/Gongju/Comonad.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Comonad.hs @@ -0,0 +1,149 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Comonad +-- Description: Comonads, Distributive, and Representable Functors for Gongju +-- +-- Plugs comonadic and distributive functor structures ('Comonad', 'Distributive', +-- 'Representable') into Gongju's open tape composition engine without modifying Core. +-- Allows non-Traversable comonads (such as Streams or Store) to commute with +-- Representable functors via distributive laws. +module Gongju.Comonad + ( -- * Categorical Classes + Comonad(..) + , Distributive(..) + , Representable(..) + -- * Open Tags + , PW + , PWL + , Dup + , Ex + , Dist + -- * Ergonomic Aliases + , W + , WL + , PullDist + ) where + +import Control.Comonad (Comonad (..)) +import Data.Distributive (Distributive (..)) +import Data.Functor.Rep (Representable (..)) +import Gongju.Composition + ( ApPath (..) + , ApStep (..) + , CommutePair (..) + , F + , InOrder + , MapPath (..) + , MapStep (..) + , PullRet + , StepPathMask (..) + , StepRole (..) + ) +import Gongju.Peano (Append, Init) +import Gongju.Positional (ExpectArrow) + +-- --------------------------------------------------------------------------- +-- 2. Open Mode & Layer Tags +-- --------------------------------------------------------------------------- + +-- | Tag for lockstep Cokleisli argument consumption ('extend' / 'duplicate'). +data PW + +-- | Tag for layered Cokleisli argument consumption ('extend' adds an active layer). +data PWL + +-- | Tag for Comonad context duplication ('duplicate'). +data Dup + +-- | Tag for Comonad focal value extraction ('extract'). +data Ex + +-- | Tag for Distributive and Representable functor layers. +data Dist + +-- | In-order unindexed comonadic cokleisli alias. +type W = InOrder PW + +-- | In-order unindexed layered comonadic cokleisli alias. +type WL = InOrder PWL + +-- | Commute a 'Dist' layer outward past all active layers. +type PullDist = PullRet '[Dist] + +-- --------------------------------------------------------------------------- +-- 3. Mapping, Zipping, and Commuting Instances +-- --------------------------------------------------------------------------- + +instance (Distributive g, s ~ g s', t ~ g t', MapPath ls a b s' t') + => MapStep Dist ls a b s t where + mapStep f = fmap (mapPath @ls f) + {-# INLINE mapStep #-} + +instance (Representable g, fab ~ g fab', fa ~ g fa', fb ~ g fb', ApPath ls fab' fa' fb') + => ApStep Dist ls fab fa fb where + apStep fab fa = tabulate (\i -> apPath @ls (index fab i) (index fa i)) + {-# INLINE apStep #-} + +-- | Right-driven Distributive law: commutes 'Dist' outside ANY 'Functor φ'. +instance (Functor φ, Distributive g, s ~ φ (g inner), t ~ g (φ inner)) + => CommutePair F Dist s t where + commutePair = distribute + {-# INLINE commutePair #-} + +instance (Traversable g, Applicative φ, s ~ g (φ inner), t ~ φ (g inner)) + => CommutePair Dist F s t where + commutePair = sequenceA + {-# INLINE commutePair #-} + +-- --------------------------------------------------------------------------- +-- 4. StepRole Instances (Comonad Transitions) +-- --------------------------------------------------------------------------- + +instance (Comonad φ, ExpectArrow "StepRole PW" acc (φ a) rTail, wa ~ φ a, StepPathMask base '[ F ] ms m t3 (φ rTail) out') + => StepRole PW base '[] ms m t3 acc (wa -> out') where + stepRole f acc wa = stepPathMask @base @'[ F ] @ms f (extend acc wa) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out' φ a rTail wa. + ( Comonad φ, wa ~ φ a + , MapPath active (φ a -> rTail) (φ rTail) acc acc' + , StepPathMask base (Append active '[ F ]) ms m t3 acc' out' + ) => StepRole PWL base active ms m t3 acc (wa -> out') where + stepRole f acc wa = + stepPathMask @base @(Append active '[ F ]) @ms @m @t3 @acc' @out' f + (mapPath @active @(φ a -> rTail) @(φ rTail) (`extend` wa) acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out φ inner. + ( Comonad φ + , MapPath (Init active) (φ inner) (φ (φ inner)) acc acc' + , StepPathMask base (Append active '[ F ]) ms m t3 acc' out + ) => StepRole Dup base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Append active '[ F ]) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(φ inner) @(φ (φ inner)) duplicate acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out φ inner. + ( Comonad φ + , MapPath (Init active) (φ inner) inner acc acc' + , StepPathMask base (Init active) ms m t3 acc' out + ) => StepRole Ex base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(φ inner) @inner extract acc) + {-# INLINE stepRole #-} diff --git a/src/Gongju/Composition.hs b/src/Gongju/Composition.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Composition.hs @@ -0,0 +1,577 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE RequiredTypeArguments #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeAbstractions #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Composition +-- Description: The Grand Unified Open-World Tape Engine and Variadic Composition +-- +-- Provides the open tag-driven state machine ('StepPathMask', 'StepRole') for multi-stage +-- functor and arrow composition, arbitrary argument permutation ('Permute'), lax monoidal +-- zipping ('ApPath'), distributive laws ('CommutePast', 'PullPath'), and ergonomic +-- visible-forall entry points ('composeUnifiedV', 'withOps', 'infixr 9 .@'). +-- +-- Also preserves legacy inductive Peano arity composition ('ComposeN', 'compN') and +-- nested functor mapping ('FmapN', 'fmapN') with bidirectional functional dependencies. +module Gongju.Composition + ( -- * Open Layer Tags + F + , C + , B1 + , B2 + , BB + , Fn + -- * Open Mapping Primitives + , MapStep(..) + , MapPath(..) + -- * Open Zipping Primitives + , ApStep(..) + , ApPath(..) + -- * Distributive Laws & Commuting + , CommutePair(..) + , CommutePast(..) + , PullPath(..) + -- * Open State Machine & Spec Tags + , StepRole(..) + , StepPathMask(..) + , type (#) + , InOrder + , PP + , PZ + , PL + , PM + , J + , CS + , SwapAt + , PullRet + -- * Ergonomic Unindexed Aliases + , P + , Z + , M + , L + , LF + , PullF + -- * Type Families for Index & Mode Extraction + , UnwrapMode + , OpModes + , HasExplicitIndex + , OpIndices + , OpIndicesIf + , TakePeano + , AtPeano + , SwapAtPeano + -- * Visible Forall & Infix Entry Points + , composeUnifiedV + , withOps + , (.@) + -- * Backward-Compatible Variadic Combinators + , ComposeN(..) + , compN + , FmapN(..) + , fmapN + ) where + +import Control.Monad (join) +import Data.Bifunctor (Bifunctor (bimap, first, second)) +import Data.Bitraversable (Bitraversable (bitraverse), bisequenceA) +import Data.Functor.Contravariant (Contravariant (contramap)) +import Data.Kind (Type) +import GHC.TypeLits (Nat) +import Gongju.Peano + ( Append + , Init + , Peano (..) + , Replicate + , ToPeano + ) +import Gongju.Permute (Permute (..)) +import Gongju.Positional (ExpectArrow) + +{- Note [Variadic Composition Bidirectional Fundeps] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-variadic-composition-fundeps] +Template Haskell composition libraries (such as 'composition-extra') generate static +operators for fixed arities ((.:), (..:), (...:)). Beyond bloating code size, Template +Haskell splices cannot be abstracted over dynamically in type-level pipelines. + +Gongju replaces these splices with an open tag-driven execution engine ('StepPathMask') +and inductive arity composition ('ComposeN'), indexed by Peano depth or tape masks. + +Crucially, bidirectional functional dependencies are maintained across the engine: + - @n b c g -> f@: Propagates input function types forward to determine composite function type. + - @n f -> c@: Propagates expected output type backward into the composite structure. + - @n f b -> g@: Infers intermediate argument shapes under polymorphic unification. +-} + +-- --------------------------------------------------------------------------- +-- 1. Open Layer Tags (Extensible by Downstream Modules Without Orphans) +-- --------------------------------------------------------------------------- + +-- | Covariant Functor layer tag. +data F + +-- | Contravariant Functor layer tag. +data C + +-- | Bifunctor first slot tag. +data B1 + +-- | Bifunctor second slot tag. +data B2 + +-- | Bifunctor diagonal tag (both slots). +data BB + +-- | Replicate @n@ covariant 'F' functor layers. +type Fn (n :: Nat) = Replicate n F + +-- --------------------------------------------------------------------------- +-- 2. Open Primitive 1: MapStep & MapPath +-- --------------------------------------------------------------------------- + +-- | 1-step mapping class dispatched on the head tag of kind 'Type'. +class MapStep (tag :: Type) (rest :: [Type]) a b s t where + mapStep :: (a -> b) -> s -> t + +-- | Sequential path mapping through a type-level stack of functor layers. +class MapPath (ls :: [Type]) a b s t where + mapPath :: (a -> b) -> s -> t + +instance (s ~ a, t ~ b) => MapPath '[] a b s t where + mapPath f = f + {-# INLINE mapPath #-} + +instance MapStep tag ls a b s t => MapPath (tag ': ls) a b s t where + mapPath = mapStep @tag @ls + {-# INLINE mapPath #-} + +instance (Functor φ, s ~ φ s', t ~ φ t', MapPath ls a b s' t') + => MapStep F ls a b s t where + mapStep f = fmap (mapPath @ls f) + {-# INLINE mapStep #-} + +instance (Contravariant φ, s ~ φ s', t ~ φ t', MapPath ls a b t' s') + => MapStep C ls a b s t where + mapStep f = contramap (mapPath @ls f) + {-# INLINE mapStep #-} + +instance (Bifunctor p, s ~ p s' c, t ~ p t' c, MapPath ls a b s' t') + => MapStep B1 ls a b s t where + mapStep f = first (mapPath @ls f) + {-# INLINE mapStep #-} + +instance (Bifunctor p, s ~ p c s', t ~ p c t', MapPath ls a b s' t') + => MapStep B2 ls a b s t where + mapStep f = second (mapPath @ls f) + {-# INLINE mapStep #-} + +instance (Bifunctor p, s ~ p s' s', t ~ p t' t', MapPath ls a b s' t') + => MapStep BB ls a b s t where + mapStep f = let g = mapPath @ls f in bimap g g + {-# INLINE mapStep #-} + +-- --------------------------------------------------------------------------- +-- 3. Open Primitive 2: ApStep & ApPath (Lax Monoidal Zipping) +-- --------------------------------------------------------------------------- + +-- | 1-step applicative zipping class dispatched on layer tag. +class ApStep (tag :: Type) (rest :: [Type]) fab fa fb where + apStep :: fab -> fa -> fb + +-- | Sequential applicative zipping along a stack of functor layers. +class ApPath (ls :: [Type]) fab fa fb where + apPath :: fab -> fa -> fb + +instance (fab ~ (fa -> fb)) => ApPath '[] fab fa fb where + apPath = id + {-# INLINE apPath #-} + +instance ApStep tag ls fab fa fb => ApPath (tag ': ls) fab fa fb where + apPath = apStep @tag @ls + {-# INLINE apPath #-} + +instance (Applicative φ, fab ~ φ fab', fa ~ φ fa', fb ~ φ fb', ApPath ls fab' fa' fb') + => ApStep F ls fab fa fb where + apStep = liftA2 (apPath @ls) + {-# INLINE apStep #-} + +instance (Applicative (p c), fab ~ p c fab', fa ~ p c fa', fb ~ p c fb', ApPath ls fab' fa' fb') + => ApStep B2 ls fab fa fb where + apStep = liftA2 (apPath @ls) + {-# INLINE apStep #-} + +-- --------------------------------------------------------------------------- +-- 4. Open Primitive 3: CommutePair & PullPath (Distributive Laws) +-- --------------------------------------------------------------------------- + +-- | Commute adjacent effect layers @l1@ and @l2@. +class CommutePair (l1 :: Type) (l2 :: Type) s t where + commutePair :: s -> t + +instance (Traversable φ, Applicative ψ, s ~ φ (ψ inner), t ~ ψ (φ inner)) + => CommutePair F F s t where + commutePair = sequenceA + {-# INLINE commutePair #-} + +instance (Bitraversable p, Applicative ψ, s ~ p c (ψ inner), t ~ ψ (p c inner)) + => CommutePair B2 F s t where + commutePair = bitraverse pure id + {-# INLINE commutePair #-} + +instance (Bitraversable p, Applicative ψ, s ~ p (ψ inner) c, t ~ ψ (p inner c)) + => CommutePair B1 F s t where + commutePair = bitraverse id pure + {-# INLINE commutePair #-} + +instance (Bitraversable p, Applicative ψ, s ~ p (ψ inner) (ψ inner), t ~ ψ (p inner inner)) + => CommutePair BB F s t where + commutePair = bisequenceA + {-# INLINE commutePair #-} + +-- | Bubble an inner layer @r@ outward past an entire @outer@ stack. +class CommutePast (outer :: [Type]) (r :: Type) s t where + commutePast :: s -> t + +instance (s ~ t) => CommutePast '[] r s t where + commutePast = id + {-# INLINE commutePast #-} + +instance forall l ls r s mid t subS subT. + ( CommutePast ls r subS subT + , MapPath '[ l ] subS subT s mid + , CommutePair l r mid t + ) => CommutePast (l ': ls) r s t where + commutePast = commutePair @l @r @mid @t . mapPath @'[ l ] @subS @subT @s @mid (commutePast @ls @r @subS @subT) + {-# INLINE commutePast #-} + +-- | Pull an entire @retPath@ stack outward past @outer@. +class PullPath (outer :: [Type]) (retPath :: [Type]) s t where + pullPath :: s -> t + +instance (s ~ t) => PullPath outer '[] s t where + pullPath = id + {-# INLINE pullPath #-} + +instance forall outer r rs s mid t subS subT. + ( CommutePast outer r s mid + , PullPath outer rs subS subT + , MapPath '[ r ] subS subT mid t + ) => PullPath outer (r ': rs) s t where + pullPath = mapPath @'[ r ] @subS @subT @mid @t (pullPath @outer @rs @subS @subT) . commutePast @outer @r @s @mid + {-# INLINE pullPath #-} + +-- --------------------------------------------------------------------------- +-- 5. Open Primitive 4: StepRole & StepPathMask (The Open State Machine) +-- --------------------------------------------------------------------------- + +-- | Individual operational step executing a transition on the accumulator. +class StepRole (op :: Type) (base :: [Type]) (active :: [Type]) (ms :: [Type]) m t3 acc out where + stepRole :: (m -> t3) -> acc -> out + +-- | Tape machine executing a list of operations @ms@ against the active functor stack. +class StepPathMask (base :: [Type]) (active :: [Type]) (ms :: [Type]) m t3 acc out where + stepPathMask :: (m -> t3) -> acc -> out + +instance (acc ~ m, out ~ t3) => StepPathMask base active '[] m t3 acc out where + stepPathMask f acc = f acc + {-# INLINE stepPathMask #-} + +instance StepRole op base active ms m t3 acc out + => StepPathMask base active (op ': ms) m t3 acc out where + stepPathMask = stepRole @op @base @active @ms + {-# INLINE stepPathMask #-} + +-- | Open spec tag pairing an explicit argument index with a mode. +infix 6 # +data (i :: Nat) # (mode :: Type) + +-- | Open spec tag for unindexed in-order arguments. +data InOrder (mode :: Type) + +-- | Pure argument mode tag. +data PP + +-- | Applicative zipped argument mode tag. +data PZ + +-- | Layered argument mode tag along sub-stack @sub@. +data PL (sub :: [Type]) + +-- | Monadic bind argument mode tag. +data PM + +-- | Monadic return join tag. +data J + +-- | Collapse 2 innermost monadic layers. +data CS + +-- | Swap active layers at depth @d@ and @d + 1@. +data SwapAt (d :: Nat) + +-- | Commute @retPath@ outward past @active@. +data PullRet (retPath :: [Type]) + +-- Ergonomic unindexed aliases: +type P = InOrder PP +type Z = InOrder PZ +type M = InOrder PM +type L (ls :: [Type]) = InOrder (PL ls) +type LF (n :: Nat) = InOrder (PL (Fn n)) +type PullF (n :: Nat) = PullRet (Fn n) + +-- | Recursively unwrap indexed or in-order wrapper tags into underlying modes. +type family UnwrapMode (op :: Type) :: Type where + UnwrapMode (_ # mode) = UnwrapMode mode + UnwrapMode (InOrder mode) = UnwrapMode mode + UnwrapMode stackOp = stackOp + +-- | Map 'UnwrapMode' across a list of operation tags. +type family OpModes (ops :: [Type]) :: [Type] where + OpModes '[] = '[] + OpModes (op ': ops) = UnwrapMode op ': OpModes ops + +-- | Detect whether any operation in the list specifies an explicit numerical index. +type family HasExplicitIndex (ops :: [Type]) :: Bool where + HasExplicitIndex '[] = 'False + HasExplicitIndex ((_ # _) ': _) = 'True + HasExplicitIndex (_ ': ops) = HasExplicitIndex ops + +-- | Extract the list of indices from an operation list if explicitly indexed. +type family OpIndices (ops :: [Type]) :: [Peano] where + OpIndices ops = OpIndicesIf (HasExplicitIndex ops) ops + +-- | Helper family generating the index list depending on explicit tagging. +type family OpIndicesIf (indexed :: Bool) (ops :: [Type]) :: [Peano] where + OpIndicesIf 'False _ = '[] + OpIndicesIf 'True '[] = '[] + OpIndicesIf 'True ((i # _) ': ops) = ToPeano i ': OpIndicesIf 'True ops + OpIndicesIf 'True (InOrder _ ': ops) = 'Z ': OpIndicesIf 'True ops + OpIndicesIf 'True (_ ': ops) = OpIndicesIf 'True ops + +-- | Take @d@ elements from a type-level list. +type family TakePeano (d :: Peano) (xs :: [k]) :: [k] where + TakePeano 'Z _ = '[] + TakePeano ('S d) (x ': xs) = x ': TakePeano d xs + +-- | Index into a type-level list at Peano position @d@. +type family AtPeano (d :: Peano) (xs :: [k]) :: k where + AtPeano 'Z (x ': _) = x + AtPeano ('S d) (_ ': xs) = AtPeano d xs + +-- | Swap adjacent elements in a type-level list at depth @d@. +type family SwapAtPeano (d :: Peano) (xs :: [k]) :: [k] where + SwapAtPeano 'Z (x ': y ': xs) = y ': x ': xs + SwapAtPeano ('S d) (x ': xs) = x ': SwapAtPeano d xs + +-- Core StepRole Instances: + +instance (ExpectArrow "StepRole PP" acc a rTail, StepPathMask base '[] ms m t3 rTail out') + => StepRole PP base '[] ms m t3 acc (a -> out') where + stepRole f acc a = stepPathMask @base @'[] @ms f (acc a) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' a rTail. + ( MapPath (l ': ls) (a -> rTail) rTail acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PP base (l ': ls) ms m t3 acc (a -> out') where + stepRole f acc a = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' + f + (mapPath @(l ': ls) @(a -> rTail) @rTail @acc @acc' ($ a) acc) + {-# INLINE stepRole #-} + +instance (ExpectArrow "StepRole PZ" acc a rTail, MapPath base a rTail fa acc', StepPathMask base base ms m t3 acc' out') + => StepRole PZ base '[] ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @base @ms @m @t3 @acc' @out' f (mapPath @base acc fa) + {-# INLINE stepRole #-} + +instance (ApPath (l ': ls) acc fa acc', StepPathMask base (l ': ls) ms m t3 acc' out') + => StepRole PZ base (l ': ls) ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f (apPath @(l ': ls) acc fa) + {-# INLINE stepRole #-} + +instance forall base active sub ms m t3 acc acc' out' a rTail fa inner. + ( MapPath sub a rTail fa inner + , MapPath active (a -> rTail) inner acc acc' + , StepPathMask base (Append active sub) ms m t3 acc' out' + ) => StepRole (PL sub) base active ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @(Append active sub) @ms @m @t3 @acc' @out' f + (mapPath @active @(a -> rTail) @inner @acc @acc' (\k -> mapPath @sub @a @rTail @fa @inner k fa) acc) + {-# INLINE stepRole #-} + +instance (Monad φ, ExpectArrow "StepRole PM" acc a rTail, fa ~ φ a, StepPathMask base '[ F ] ms m t3 (φ rTail) out') + => StepRole PM base '[] ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @'[ F ] @ms f (fmap acc fa) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' φ a rTail fa. + ( Monad φ, fa ~ φ a + , MapPath (Init (l ': ls)) (φ (a -> rTail)) (φ rTail) acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PM base (l ': ls) ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f + (mapPath @(Init (l ': ls)) @(φ (a -> rTail)) @(φ rTail) (\mf -> mf >>= (<$> fa)) acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out φ inner. + ( Monad φ + , MapPath (Init active) (φ (φ inner)) (φ inner) acc acc' + , StepPathMask base active ms m t3 acc' out + ) => StepRole J base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @active @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(φ (φ inner)) @(φ inner) join acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out φ inner. + ( Monad φ + , MapPath (Init (Init active)) (φ (φ inner)) (φ inner) acc acc' + , StepPathMask base (Init active) ms m t3 acc' out + ) => StepRole CS base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out f + (mapPath @(Init (Init active)) @(φ (φ inner)) @(φ inner) join acc) + {-# INLINE stepRole #-} + +instance forall (d :: Nat) base active ms m t3 acc acc' out sMid tMid dp. + ( dp ~ ToPeano d + , CommutePair (AtPeano dp active) (AtPeano ('S dp) active) sMid tMid + , MapPath (TakePeano dp active) sMid tMid acc acc' + , StepPathMask base (SwapAtPeano dp active) ms m t3 acc' out + ) => StepRole (SwapAt d) base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(SwapAtPeano dp active) @ms @m @t3 @acc' @out f + (mapPath @(TakePeano dp active) @sMid @tMid + (commutePair @(AtPeano dp active) @(AtPeano ('S dp) active) @sMid @tMid) acc) + {-# INLINE stepRole #-} + +instance forall (retPath :: [Type]) base active ms m t3 acc acc' out. + ( PullPath active retPath acc acc' + , StepPathMask base (Append retPath active) ms m t3 acc' out + ) => StepRole (PullRet retPath) base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Append retPath active) @ms @m @t3 @acc' @out f + (pullPath @active @retPath @acc @acc' acc) + {-# INLINE stepRole #-} + +-- --------------------------------------------------------------------------- +-- 6. Visible-Forall & Infix Entry Points +-- --------------------------------------------------------------------------- + +-- | Fully general visible-forall composition engine parameterized by lifting path, base, and op tape. +composeUnifiedV :: + forall (lpath :: [Type]) -> + forall (base :: [Type]) -> + forall (ops :: [Type]) -> + forall a t3 m m' g gPerm out. + ( Permute (OpIndices ops) g gPerm + , MapPath lpath a t3 m m' + , StepPathMask base '[] (OpModes ops) m m' gPerm out + ) => + (a -> t3) -> g -> out +composeUnifiedV (type lpath) (type base) (type ops) @a @t3 @m @m' @g @gPerm @out f g = + stepPathMask @base @'[] @(OpModes ops) @m @m' @gPerm @out + (mapPath @lpath @a @t3 @m @m' f) + (permute' @(OpIndices ops) @g @gPerm g) +{-# INLINE composeUnifiedV #-} + +-- | Execute an outer function over an inner function with an open operation tape. +withOps :: + forall (ops :: [Type]) -> + forall m t3 g gPerm out. + ( Permute (OpIndices ops) g gPerm + , StepPathMask '[] '[] (OpModes ops) m t3 gPerm out + ) => + (m -> t3) -> g -> out +withOps (type ops) @m @t3 @g @gPerm @out f g = + stepPathMask @'[] @'[] @(OpModes ops) @m @t3 @gPerm @out + f + (permute' @(OpIndices ops) @g @gPerm g) +{-# INLINE withOps #-} + +-- | Infix tape-driven composition operator. +-- +-- Example: +-- +-- >>> (show .@ [P, P]) (+) 10 20 +-- "30" +infixr 9 .@ +(.@) :: + forall m t3 g gPerm out. + (m -> t3) -> + forall (ops :: [Type]) -> + ( Permute (OpIndices ops) g gPerm + , StepPathMask '[] '[] (OpModes ops) m t3 gPerm out + ) => + g -> out +((.@) f (type ops)) g = withOps ops f g +{-# INLINE (.@) #-} + +-- --------------------------------------------------------------------------- +-- 7. Backward-Compatible Variadic Arity Composition +-- --------------------------------------------------------------------------- + +-- | Inductive arity composition class parameterized over Peano depth @n@. +-- +-- See Note [Variadic Composition Bidirectional Fundeps] [ref:note-variadic-composition-fundeps]. +class ComposeN (n :: Peano) b c g f | n b c g -> f, n f -> c, n f b -> g where + -- | Internal composition worker operating on inductive 'Peano' terms. + composeN' :: (b -> c) -> g -> f + +instance ComposeN 'Z b c b c where + composeN' f x = f x + {-# INLINE composeN' #-} + +instance ComposeN n b c r r' => ComposeN ('S n) b c (a -> r) (a -> r') where + composeN' f g a = composeN' @n f (g a) + {-# INLINE composeN' #-} + +-- | Compose a unary function @(b -> c)@ with a curried function consuming @n@ arguments. +-- +-- Examples: +-- +-- @ +-- compN @1 == (.) +-- compN @2 == (.:) +-- compN @3 == (..:) +-- @ +compN :: forall (n :: Nat) b c g f. ComposeN (ToPeano n) b c g f => (b -> c) -> g -> f +compN = composeN' @(ToPeano n) +{-# INLINE compN #-} + +-- | Inductive nested functor mapping class parameterized over nesting depth @n@. +class FmapN (n :: Peano) a b s t | n a b s -> t, n s t -> a b where + -- | Internal functor mapping worker operating on inductive 'Peano' terms. + fmapN' :: (a -> b) -> s -> t + +instance FmapN 'Z a b a b where + fmapN' f = f + {-# INLINE fmapN' #-} + +instance (Functor f, FmapN n a b s t) => FmapN ('S n) a b (f s) (f t) where + fmapN' f = fmap (fmapN' @n f) + {-# INLINE fmapN' #-} + +-- | Map a transformation @(a -> b)@ through @n@ nested 'Functor' layers. +fmapN :: forall (n :: Nat) a b s t. FmapN (ToPeano n) a b s t => (a -> b) -> s -> t +fmapN = fmapN' @(ToPeano n) +{-# INLINE fmapN #-} diff --git a/src/Gongju/Contravariant.hs b/src/Gongju/Contravariant.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Contravariant.hs @@ -0,0 +1,262 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE RequiredTypeArguments #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE UndecidableInstances #-} + +-- | Module: Gongju.Contravariant +-- Description: Contravariant Syntax Grids, Positional Pre-Composition, and Alternating Parity Stacks +-- +-- Replaces Template Haskell contravariant splices (such as 'composition-extra') with pure +-- type-level Peano induction, bidirectional functional dependencies, and type-safe argument pre-processing. +-- +-- Provides: +-- * Positional curried pre-composition ('PrecomposeAt', 'precomposeAt @n', '(-.)', '(-.*)', '(-.**)', '(-.***)'). +-- * 2D function splicing grid ('SpliceAt', 'spliceAt @n @m'). +-- * Alternating parity contravariant functor mapping ('ContramapN', 'contramapN @n', '(<-$>)', '(<-$$>)', '(<-$$$>)'). +-- * Canonical re-exports of 'Contravariant', 'Divisible', and 'Decidable' from @base@. +module Gongju.Contravariant + ( -- * Positional Pre-Composition + PrecomposeAt (..) + , precomposeAt + , (-.) + , (-.*) + , (-.**) + , (-.***) + -- * 2D Function Splicing Grid + , SpliceAt (..) + , spliceAt + -- * Nested Contravariant Mapping (Alternating Parity) + , ContramapN (..) + , ContravariantN + , contramapN + , (<-$>) + , (<-$$>) + , (<-$$$>) + , (<-$$$$>) + -- * Re-exported Canonical Classes & Types + , Contravariant (..) + , (>$<) + , Predicate (..) + , Comparison (..) + , Equivalence (..) + , Op (..) + , Divisible (..) + , Decidable (..) + ) where + +import Data.Functor.Contravariant + ( Comparison (..) + , Contravariant (..) + , Equivalence (..) + , Op (..) + , Predicate (..) + , (>$<) + ) +import Data.Functor.Contravariant.Divisible + ( Decidable (..) + , Divisible (..) + ) +import GHC.TypeLits (Nat) +import Gongju.Composition (ComposeN (..)) +import Gongju.Peano (Peano (..), ToPeano) + +{- Note [Contravariant Positional Pre-Composition] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-contravariant-precomposition] +Because the function arrow @(->)@ is contravariant in its argument position, +"contravariant function composition" corresponds to pre-composing a transformation +function onto an argument consumed by another function. + +In libraries relying on Template Haskell splices (such as 'composition-extra'), +operators proliferate along two distinct axes: + 1. The target argument slot index @n@ of @f@ being pre-composed: + @(-.)@ at slot 0, @(-.*)@ at slot 1, @(-.**)@ at slot 2, etc. + 2. The arity @m@ of arguments consumed by the pre-composed function @h@: + @(-.)@ for unary, @(-.:)@ for binary, @(-..:)@ for ternary, etc. + +Gongju collapses both axes into two inductively resolved typeclasses: + * 'PrecomposeAt': Unary pre-composition at positional depth @n@. + * 'SpliceAt': Full 2D generalization splicing an @m@-ary function into slot @n@. + +Full bidirectional functional dependencies are maintained across the grid: + - @n f -> b@: Determines the target argument type @b@ from slot @n@ and @f@. + - @n g -> a@: Determines the new argument type @a@ from slot @n@ and @g@. + - @n a f -> g@: Infers the transformed signature @g@ from input @a@ and @f@. + - @n b g -> f@: Recovers the original signature @f@ from target @b@ and @g@. +-} + +-- --------------------------------------------------------------------------- +-- 1. Positional Pre-Composition (PrecomposeAt) +-- --------------------------------------------------------------------------- + +-- | Pre-compose a unary function @(a -> b)@ onto the @n@-th argument (0-indexed) of @f@. +-- +-- See Note [Contravariant Positional Pre-Composition] [ref:note-contravariant-precomposition]. +class PrecomposeAt (n :: Peano) a b f g | n f -> b, n g -> a, n a f -> g, n b g -> f where + -- | Internal inductive worker operating on 'Peano' terms. + precomposeAt' :: (a -> b) -> f -> g + +instance PrecomposeAt 'Z a b (b -> r) (a -> r) where + precomposeAt' h f a = f (h a) + {-# INLINE precomposeAt' #-} + +instance PrecomposeAt n a b r r' => PrecomposeAt ('S n) a b (x -> r) (x -> r') where + precomposeAt' h f x = precomposeAt' @n h (f x) + {-# INLINE precomposeAt' #-} + +-- | User-facing positional pre-composition parameterized by visible 'Nat' literal @n@. +-- +-- Example: +-- +-- >>> let add3 x y z = (x + y + z :: Int) +-- >>> precomposeAt @1 (* 10) add3 1 2 3 +-- 24 +precomposeAt :: forall (n :: Nat) a b f g. PrecomposeAt (ToPeano n) a b f g => (a -> b) -> f -> g +precomposeAt = precomposeAt' @(ToPeano n) +{-# INLINE precomposeAt #-} + +-- | Infix pre-composition at argument slot 0: @(h -. f) a = f (h a)@. +infixr 9 -. +(-.) :: PrecomposeAt 'Z a b f g => (a -> b) -> f -> g +(-.) = precomposeAt' @'Z +{-# INLINE (-.) #-} + +-- | Infix pre-composition at argument slot 1: @(h -.* f) x a = f x (h a)@. +infixr 9 -.* +(-.*) :: PrecomposeAt ('S 'Z) a b f g => (a -> b) -> f -> g +(-.*) = precomposeAt' @('S 'Z) +{-# INLINE (-.*) #-} + +-- | Infix pre-composition at argument slot 2: @(h -.** f) x y a = f x y (h a)@. +infixr 9 -.** +(-.**) :: PrecomposeAt ('S ('S 'Z)) a b f g => (a -> b) -> f -> g +(-.**) = precomposeAt' @('S ('S 'Z)) +{-# INLINE (-.**) #-} + +-- | Infix pre-composition at argument slot 3: @(h -.*** f) x y z a = f x y z (h a)@. +infixr 9 -.*** +(-.***) :: PrecomposeAt ('S ('S ('S 'Z))) a b f g => (a -> b) -> f -> g +(-.***) = precomposeAt' @('S ('S ('S 'Z))) +{-# INLINE (-.***) #-} + +-- --------------------------------------------------------------------------- +-- 2. 2D Function Splicing Grid (SpliceAt) +-- --------------------------------------------------------------------------- + +-- | Splice an @m@-ary function @h@ directly into the @n@-th argument slot of @f@. +-- +-- The resulting function @g@ consumes @n@ arguments, then the @m@ arguments required by @h@, +-- followed by the remaining arguments of @f@. +-- +-- See Note [Contravariant Positional Pre-Composition] [ref:note-contravariant-precomposition]. +class SpliceAt (n :: Peano) (m :: Peano) h f g | n m h f -> g where + -- | Internal inductive worker operating on 'Peano' depths. + spliceAt' :: h -> f -> g + +instance ComposeN m d r h g => SpliceAt 'Z m h (d -> r) g where + spliceAt' h f = composeN' @m f h + {-# INLINE spliceAt' #-} + +instance SpliceAt n m h r r' => SpliceAt ('S n) m h (a -> r) (a -> r') where + spliceAt' h f a = spliceAt' @n @m h (f a) + {-# INLINE spliceAt' #-} + +-- | User-facing 2D function splicing parameterized by visible 'Nat' literals @n@ (target slot) +-- and @m@ (spliced function arity). +-- +-- Example: +-- +-- >>> let add3 x y z = (x + y + z :: Int) +-- >>> let mult2 u v = (u * v :: Int) +-- >>> spliceAt @1 @2 mult2 add3 10 3 4 5 +-- 27 +spliceAt :: forall (n :: Nat) (m :: Nat) h f g. SpliceAt (ToPeano n) (ToPeano m) h f g => h -> f -> g +spliceAt = spliceAt' @(ToPeano n) @(ToPeano m) +{-# INLINE spliceAt #-} + +{- Note [Contravariant Functor Alternating Parity] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-contravariant-alternating-parity] +In 'Data.Functor.Contravariant.Syntax' (operators @<-$@, @<-$$@, @<-$$$@, ...), +mapping a transformation function @(a -> b)@ through nested 'Contravariant' functor layers +introduces an alternating parity flip: + - 1 layer (@1): @(a -> b) -> f b -> f a@ (contravariant: reverses arrow) + - 2 layers (@2): @(a -> b) -> f (g a) -> f (g b)@ (covariant: two reversals cancel!) + - 3 layers (@3): @(a -> b) -> f (g (h b)) -> f (g (h a))@ (contravariant again) + +With Peano induction, swapping @s@ and @t@ in the recursive constraint: + @instance (Contravariant f, ContramapN n a b t s) => ContramapN ('S n) a b (f s) (f t)@ +tracks this variance reversal automatically. + +Furthermore, the pair of bidirectional functional dependencies: + @n a b s -> t, n a b t -> s@ +mutually inductive-check each other across the parity swap, preserving full type inference. +-} + +-- --------------------------------------------------------------------------- +-- 3. Nested Contravariant Functor Mapping (Alternating Parity) +-- --------------------------------------------------------------------------- + +-- | Map a transformation through @n@ nested 'Contravariant' functor layers with alternating parity. +-- +-- See Note [Contravariant Functor Alternating Parity] [ref:note-contravariant-alternating-parity]. +class ContramapN (n :: Peano) a b s t | n s t -> a b, n a b s -> t, n a b t -> s where + -- | Internal inductive worker operating on 'Peano' depth. + contramapN' :: (a -> b) -> s -> t + +instance ContramapN 'Z a b a b where + contramapN' f = f + {-# INLINE contramapN' #-} + +instance (Contravariant f, ContramapN n a b t s) => ContramapN ('S n) a b (f s) (f t) where + contramapN' f = contramap (contramapN' @n f) + {-# INLINE contramapN' #-} + +-- | User-facing constraint synonym parameterized by visible 'Nat' depth @n@. +type ContravariantN (n :: Nat) a b s t = ContramapN (ToPeano n) a b s t + +-- | Map a transformation through @n@ nested 'Contravariant' functor layers. +-- +-- Examples: +-- +-- >>> let p = Predicate (> 0) :: Predicate Int +-- >>> let p' = contramapN @1 (* 2) p +-- >>> getPredicate p' 5 +-- True +contramapN :: forall (n :: Nat) a b s t. ContramapN (ToPeano n) a b s t => (a -> b) -> s -> t +contramapN = contramapN' @(ToPeano n) +{-# INLINE contramapN #-} + +-- | Infix contravariant mapping at depth 1 (equivalent to 'contramap' / '(>$<)'). +infixr 4 <-$> +(<-$>) :: ContramapN ('S 'Z) a b s t => (a -> b) -> s -> t +(<-$>) = contramapN' @('S 'Z) +{-# INLINE (<-$>) #-} + +-- | Infix contravariant mapping at depth 2 (covariant due to parity cancellation). +infixr 4 <-$$> +(<-$$>) :: ContramapN ('S ('S 'Z)) a b s t => (a -> b) -> s -> t +(<-$$>) = contramapN' @('S ('S 'Z)) +{-# INLINE (<-$$>) #-} + +-- | Infix contravariant mapping at depth 3 (contravariant). +infixr 4 <-$$$> +(<-$$$>) :: ContramapN ('S ('S ('S 'Z))) a b s t => (a -> b) -> s -> t +(<-$$$>) = contramapN' @('S ('S ('S 'Z))) +{-# INLINE (<-$$$>) #-} + +-- | Infix contravariant mapping at depth 4 (covariant). +infixr 4 <-$$$$> +(<-$$$$>) :: ContramapN ('S ('S ('S ('S 'Z)))) a b s t => (a -> b) -> s -> t +(<-$$$$>) = contramapN' @('S ('S ('S ('S 'Z)))) +{-# INLINE (<-$$$$>) #-} diff --git a/src/Gongju/Core.hs b/src/Gongju/Core.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Core.hs @@ -0,0 +1,112 @@ +-- | Module: Gongju.Core +-- Description: Core re-exports and introductory guide for Gongju +-- +-- @Gongju@ (공구 / 工具, tools/implement) is a pure type-level Haskell utility suite +-- replacing Template Haskell splices (like 'composition-extra') and finite tuple +-- generics (like 'tuple-sop') with an open-world tag-driven tape engine, Peano +-- induction, bidirectional functional dependencies, and arbitrary curried argument +-- manipulation. +-- +-- = When to Use This Library +-- +-- * **Grand Unified Composition:** Infix tape-driven composition with visible type arguments +-- (@(f .@ [P, P, M]) g@ or @withOps [P, Z, J] f g@). +-- * **Variadic Arity Composition:** Composing unary functions with functions of arbitrary arities +-- (@compN @3@ instead of Template Haskell @(...:)@). +-- * **Positional Argument Manipulation:** Pulling arguments to the front (@slipr @2@), shoving them +-- deeper (@slipl @2@), or transposing adjacent arguments (@twist @1@). +-- * **Arbitrary Argument Permutations:** Specifying a desired argument order as a type-level +-- index list (@permute @'[2, 0, 1]@). +-- * **Indexed Monads & Comonads:** Composing transition-carrying indexed arrows with zero orphans. +-- * **Distributive & Representable Functors:** Commuting infinite streams and comonads outside +-- representable layers without requiring Traversable instances. +-- +-- = Worked Example +-- +-- >>> import Gongju.Core +-- >>> :set -XTypeApplications -XDataKinds -XRequiredTypeArguments +-- >>> -- 1. Tape-driven composition: mapping and zipping arguments +-- >>> let add3 x y z = (x + y + z :: Int) +-- >>> ((+ 100) .@ [P, P, P]) add3 10 20 30 +-- 160 +-- >>> -- 2. Reordering curried arguments via indexed mode tags: +-- >>> let tuple3 x y z = (x, y, z) +-- >>> (id .@ [2 # P, 0 # P, 1 # P]) tuple3 True (42 :: Int) "hello" +-- (42,"hello",True) +-- >>> -- 3. Positional argument manipulation: +-- >>> slipr @1 (-) 5 20 +-- 15 +-- +-- = Zero-Cost Compiler Invariants +-- +-- All inductive typeclasses in Gongju ('ComposeN', 'Permute', 'Yank', 'Shove', 'Twist', +-- 'PrecomposeAt', 'SpliceAt', 'BindPos', 'BindAfter', 'LiftMask', 'PermuteTuple', 'CurriedCat') +-- are aggressively annotated with '{-# INLINE #-}'. Under GHC's Simplifier (@-O2@), +-- all typeclass dictionary passing, Peano induction, and intermediate tuples/records +-- evaporate completely into direct inlined lambda applications with zero runtime overhead. +-- +-- See Note [Zero-Cost Inlining and Core Simplification] [ref:note-zero-cost-core-simplification]. + +{- Note [Zero-Cost Inlining and Core Simplification] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-zero-cost-core-simplification] +Gongju replaces Template Haskell arity generators and runtime tuple coercions with +pure typeclass induction over structural Peano numbers. A critical architectural +invariant is that this high-level inductive machinery must incur zero runtime overhead: +when compiled under '-O2', every Gongju combinator pipeline must simplify in GHC Core +into the exact same lambda terms as hand-written, specialized functions. + +This zero-cost guarantee is achieved through three cooperating invariants: + 1. Aggressive Inlining: Every inductive method ('composeN'', 'yank'', 'shove'', + 'twist'', 'permute'', 'precomposeAt'', 'spliceAt'', 'bindPos'', 'bindAfter'', + 'liftMask', 'yankTuple'', 'permuteTuple'', 'yankCat'', 'permuteCat'') is annotated + with '{-# INLINE #-}'. + 2. Static Resolution of Peano Depths: Because TypeLits literals (@2, @3, @'[2, 0, 1]) + are resolved to concrete Peano terms ('Z, 'S 'Z, ...) at compile time, the instance + search is completely known and terminated during typechecking. + 3. Beta-Reduction and Dictionary Elimination: Under GHC's Simplifier (-O2), the + inlined dictionary methods unroll statically into direct lambda applications. + Intermediate records and typeclass dictionaries ($fComposeN, $fPermute, $fYank, + $fPrecomposeAt, $fBindPos, $fYankTuple) are completely eliminated via beta-reduction, + yielding pure nested function applications and tuple projections with zero allocations + and zero indirect calls. + +This invariant is mechanically verified on every build by the automated Core inspection +gate ('bin/gongju-inspect-core' and 'packages/gongju/test/CoreInspection.hs'). +-} +module Gongju.Core + ( -- * Peano Naturals & Type-Level List Utilities + module Gongju.Peano + -- * Guarded Positional Combinators + , module Gongju.Positional + -- * Arbitrary Argument Permutations + , module Gongju.Permute + -- * Grand Unified Tape Composition Engine + , module Gongju.Composition + -- * Indexed Functors, Monads, and Comonads + , module Gongju.Indexed + -- * Comonads, Distributive, and Representable Functors + , module Gongju.Comonad + -- * Adjunction Transitions and Dual Annihilation + , module Gongju.Adjunction + -- * Kan Extensions, Yoneda, and Codensity Fusion + , module Gongju.Kan + -- * Profunctors and Indexed Profunctors + , module Gongju.Profunctor + -- * Contravariant Syntax Grids & Variance-Flipping Stacks + , module Gongju.Contravariant + -- * Positional Monadic Binding & Lifting Masks + , module Gongju.Monad + ) where + +import Gongju.Peano +import Gongju.Positional +import Gongju.Permute +import Gongju.Composition +import Gongju.Indexed +import Gongju.Comonad +import Gongju.Adjunction +import Gongju.Kan +import Gongju.Profunctor +import Gongju.Contravariant +import Gongju.Monad diff --git a/src/Gongju/Indexed.hs b/src/Gongju/Indexed.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Indexed.hs @@ -0,0 +1,196 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Indexed +-- Description: Indexed Monads and Indexed Comonads for Gongju +-- +-- Plugs indexed functorial structures ('IxFunctor', 'IxApplicative', 'IxMonad', +-- 'IxComonad') into Gongju's open tape composition engine without modifying Core. +module Gongju.Indexed + ( -- * Re-exported Canonical Indexed Classes + IxFunctor(..) + , IxPointed(..) + , IxCopointed(..) + , IxApplicative(..) + , ipure + , iliftA2 + , IxMonad(..) + , (>>>=) + , (=<<<) + , ijoin + , IxComonad(..) + , iduplicate + -- * Open Indexed Tags + , IxF + , PIM + , IJ + , PIxW + , IxDup + , IxEx + -- * Ergonomic Aliases + , IxM + , IxW + ) where + +import Control.Comonad.Indexed + ( IxComonad (..) + , iduplicate + ) +import Control.Monad.Indexed + ( IxApplicative (..) + , IxMonad (..) + , ijoin + , (=<<<) + , (>>>=) + ) +import Data.Functor.Indexed + ( IxCopointed (..) + , IxFunctor (..) + , IxPointed (..) + ) +import Data.Kind (Type) +import Gongju.Composition + ( ApPath (..) + , ApStep (..) + , InOrder + , MapPath (..) + , MapStep (..) + , StepPathMask (..) + , StepRole (..) + ) +import Gongju.Peano (Append, Init) +import Gongju.Positional (ExpectArrow) + +-- | Ergonomic alias for 'ireturn'. +ipure :: IxPointed m => a -> m i i a +ipure = ireturn +{-# INLINE ipure #-} + +-- | Lift a binary function across two indexed applicatives. +iliftA2 :: IxApplicative m => (a -> b -> c) -> m i j a -> m j l b -> m i l c +iliftA2 f ma mb = iap (imap f ma) mb +{-# INLINE iliftA2 #-} + +-- --------------------------------------------------------------------------- +-- 2. Open Indexed Tags +-- --------------------------------------------------------------------------- + +-- | Tag for an indexed functor layer @m i j a@. +data IxF + +-- | Tag for indexed monadic bind ('ibind'). +data PIM + +-- | Tag for indexed monadic join ('ijoin'). +data IJ + +-- | Tag for indexed comonadic extend ('iextend'). +data PIxW + +-- | Tag for indexed comonadic duplication ('iduplicate'). +data IxDup + +-- | Tag for indexed comonadic extraction ('iextract'). +data IxEx + +-- | In-order unindexed indexed monad bind alias. +type IxM = InOrder PIM + +-- | In-order unindexed indexed comonad extend alias. +type IxW = InOrder PIxW + +-- --------------------------------------------------------------------------- +-- 3. Mapping & Zipping Instances +-- --------------------------------------------------------------------------- + +instance (IxFunctor m, s ~ m i j s', t ~ m i j t', MapPath ls a b s' t') + => MapStep IxF ls a b s t where + mapStep f = imap (mapPath @ls f) + {-# INLINE mapStep #-} + +instance (IxApplicative m, fab ~ m i j fab', fa ~ m j l fa', fb ~ m i l fb', ApPath ls fab' fa' fb') + => ApStep IxF ls fab fa fb where + apStep = iliftA2 (apPath @ls) + {-# INLINE apStep #-} + +-- --------------------------------------------------------------------------- +-- 4. StepRole Instances (IxMonad & IxComonad Transitions) +-- --------------------------------------------------------------------------- + +instance (IxMonad φ, ExpectArrow "StepRole PIM" acc a rTail, fa ~ φ i j a, StepPathMask base '[ IxF ] ms m t3 (φ i j rTail) out') + => StepRole PIM base '[] ms m t3 acc (fa -> out') where + stepRole f acc fa = stepPathMask @base @'[ IxF ] @ms f (imap acc fa) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' idx (φ :: idx -> idx -> Type -> Type) i j rIdx a rTail fa. + ( IxMonad φ, fa ~ φ j rIdx a + , MapPath (Init (l ': ls)) (φ i j (a -> rTail)) (φ i rIdx rTail) acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PIM base (l ': ls) ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f + (mapPath @(Init (l ': ls)) @(φ i j (a -> rTail)) @(φ i rIdx rTail) + (\mf -> mf >>>= (`imap` fa)) acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out idx (φ :: idx -> idx -> Type -> Type) i j rIdx inner. + ( IxMonad φ + , MapPath (Init active) (φ i j (φ j rIdx inner)) (φ i rIdx inner) acc acc' + , StepPathMask base active ms m t3 acc' out + ) => StepRole IJ base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @active @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(φ i j (φ j rIdx inner)) @(φ i rIdx inner) ijoin acc) + {-# INLINE stepRole #-} + +instance ( IxComonad w + , ExpectArrow "StepRole PIxW" acc (w j k a) rTail + , wa ~ w i k a + , StepPathMask base '[ IxF ] ms m t3 (w i j rTail) out' + ) => StepRole PIxW base '[] ms m t3 acc (wa -> out') where + stepRole f acc wa = stepPathMask @base @'[ IxF ] @ms f (iextend acc wa) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out' knd (w :: knd -> knd -> Type -> Type) i j k a rTail wa. + ( IxComonad w + , wa ~ w i k a + , MapPath active (w j k a -> rTail) (w i j rTail) acc acc' + , StepPathMask base (Append active '[ IxF ]) ms m t3 acc' out' + ) => StepRole PIxW base active ms m t3 acc (wa -> out') where + stepRole f acc wa = + stepPathMask @base @(Append active '[ IxF ]) @ms @m @t3 @acc' @out' f + (mapPath @active @(w j k a -> rTail) @(w i j rTail) (`iextend` wa) acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out knd (w :: knd -> knd -> Type -> Type) i j k inner. + ( IxComonad w + , MapPath (Init active) (w i k inner) (w i j (w j k inner)) acc acc' + , StepPathMask base (Append active '[ IxF ]) ms m t3 acc' out + ) => StepRole IxDup base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Append active '[ IxF ]) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(w i k inner) @(w i j (w j k inner)) iduplicate acc) + {-# INLINE stepRole #-} + +instance forall base active ms m t3 acc acc' out knd (w :: knd -> knd -> Type -> Type) i inner. + ( IxComonad w + , MapPath (Init active) (w i i inner) inner acc acc' + , StepPathMask base (Init active) ms m t3 acc' out + ) => StepRole IxEx base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(w i i inner) @inner iextract acc) + {-# INLINE stepRole #-} diff --git a/src/Gongju/Kan.hs b/src/Gongju/Kan.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Kan.hs @@ -0,0 +1,375 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Kan +-- Description: Kan Extensions, Yoneda, and Codensity Fusion for Gongju +-- +-- Integrates Right and Left Kan extensions ('t:Ran', 't:Lan'), Yoneda lemma embeddings +-- ('t:Yoneda', 't:Coyoneda'), and Codensity / Density monad-comonad generators +-- ('t:Codensity', 't:Density') from @kan-extensions@ into Gongju's open tape composition engine. +-- +-- Enables: +-- * Structural Kan rewrites without typeclass constraints on @g@ or @h@. +-- * $O(1)$ functor mapping fusion via 't:Yoneda' and 't:Coyoneda'. +-- * $O(1)$ monad bind optimization via 't:Codensity' CPS transformations. +module Gongju.Kan + ( -- * Re-exported Canonical Kan Types + Lan(..) + , Ran(..) + , toRan + , fromRan + , Yoneda(..) + , liftYoneda + , lowerYoneda + , Coyoneda(..) + , liftCoyoneda + , lowerCoyoneda + , Codensity(..) + , liftCodensity + , lowerCodensity + , Density(..) + , liftDensity + , lowerDensity + -- * Kan Structural Unit & Counit Operations + , ranCounit + , ranUnit + , lanUnit + , lanCounit + -- * Open Kan Tags + , PRanC + , PRanU + , PLanU + , PLanC + , PCoY + , PUnCoY + , PYon + , PUnYon + , PCodM + , PUnCod + , PDenW + , PUnDen + -- * Ergonomic Aliases + , RanC + , RanU + , LanU + , LanC + , CoY + , UnCoY + , Yon + , UnYon + , CodM + , UnCod + , DenW + , UnDen + ) where + +import Control.Comonad (Comonad, extend) +import Control.Comonad.Density + ( Density (..) + , liftDensity + ) +import Control.Monad.Codensity + ( Codensity (..) + , lowerCodensity + ) +import Data.Functor.Coyoneda + ( Coyoneda (..) + , liftCoyoneda + , lowerCoyoneda + ) +import Data.Functor.Kan.Lan + ( Lan (..) + ) +import Data.Functor.Kan.Ran + ( Ran (..) + , fromRan + , toRan + ) +import Data.Functor.Yoneda + ( Yoneda (..) + , liftYoneda + , lowerYoneda + ) +import Gongju.Composition + ( F + , InOrder + , MapPath (..) + , StepPathMask (..) + , StepRole (..) + ) +import Gongju.Peano (Append, Init) +import Gongju.Positional (ExpectArrow) + +-- --------------------------------------------------------------------------- +-- 1. Kan Universal Unit & Counit Operations +-- --------------------------------------------------------------------------- + +-- | Universal Counit of Ran: @Ran g h (g a) -> h a@ (zero constraints). +ranCounit :: Ran g h (g a) -> h a +ranCounit (Ran k) = k id +{-# INLINE ranCounit #-} + +-- | Identity Unit of Ran: @a -> Ran g g a@ (zero constraints). +ranUnit :: a -> Ran g g a +ranUnit a = Ran ($ a) +{-# INLINE ranUnit #-} + +-- | Universal Unit of Lan: @h a -> Lan g h (g a)@ (zero constraints). +lanUnit :: h a -> Lan g h (g a) +lanUnit ha = Lan id ha +{-# INLINE lanUnit #-} + +-- | Identity Counit of Lan: @Lan g g a -> a@ (zero constraints). +lanCounit :: Lan g g a -> a +lanCounit (Lan f ga) = f ga +{-# INLINE lanCounit #-} + +-- | Lift a monadic action into 't:Codensity' for CPS fusion. +liftCodensity :: Monad m => m a -> Codensity m a +liftCodensity m = Codensity (m >>=) +{-# INLINE liftCodensity #-} + +-- | Lower 't:Density' back into the underlying comonad. +lowerDensity :: Comonad w => Density w a -> w a +lowerDensity (Density f wb) = extend f wb +{-# INLINE lowerDensity #-} + +-- --------------------------------------------------------------------------- +-- 2. Open Mode Tags & Aliases +-- --------------------------------------------------------------------------- + +-- | Tag for Ran Counit: collapses @Ran g h (g inner) -> h inner@. +data PRanC + +-- | Tag for Ran Unit: expands @inner -> Ran g g inner@. +data PRanU + +-- | Tag for Lan Unit: expands @h inner -> Lan g h (g inner)@. +data PLanU + +-- | Tag for Lan Counit: collapses @Lan g g inner -> inner@. +data PLanC + +-- | Tag for lifting arguments into 't:Coyoneda'. +data PCoY + +-- | Tag for lowering 't:Coyoneda' via single 'fmap'. +data PUnCoY + +-- | Tag for lifting arguments into 't:Yoneda'. +data PYon + +-- | Tag for lowering 't:Yoneda' into the underlying functor. +data PUnYon + +-- | Tag for lifting monadic arguments into 't:Codensity'. +data PCodM + +-- | Tag for lowering 't:Codensity' back to the underlying monad. +data PUnCod + +-- | Tag for lifting comonadic arguments into 't:Density'. +data PDenW + +-- | Tag for lowering 't:Density' back to the underlying comonad. +data PUnDen + +-- | In-order Ran Counit alias. +type RanC = InOrder PRanC + +-- | In-order Ran Unit alias. +type RanU = InOrder PRanU + +-- | In-order Lan Unit alias. +type LanU = InOrder PLanU + +-- | In-order Lan Counit alias. +type LanC = InOrder PLanC + +-- | In-order Coyoneda lifting alias. +type CoY = InOrder PCoY + +-- | In-order Coyoneda lowering alias. +type UnCoY = InOrder PUnCoY + +-- | In-order Yoneda lifting alias. +type Yon = InOrder PYon + +-- | In-order Yoneda lowering alias. +type UnYon = InOrder PUnYon + +-- | In-order Codensity lifting alias. +type CodM = InOrder PCodM + +-- | In-order Codensity lowering alias. +type UnCod = InOrder PUnCod + +-- | In-order Density lifting alias. +type DenW = InOrder PDenW + +-- | In-order Density lowering alias. +type UnDen = InOrder PUnDen + +-- --------------------------------------------------------------------------- +-- 3. StepRole Instances (Kan Extensions & Yoneda Fusion) +-- --------------------------------------------------------------------------- + +-- | Ran Counit: collapses @Ran g h (g inner)@ to @h inner@ at the tip. +instance forall base active ms m t3 acc acc' out g h inner. + ( MapPath (Init (Init active)) (Ran g h (g inner)) (h inner) acc acc' + , StepPathMask base (Init active) ms m t3 acc' out + ) => StepRole PRanC base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out f + (mapPath @(Init (Init active)) @(Ran g h (g inner)) @(h inner) ranCounit acc) + {-# INLINE stepRole #-} + +-- | Ran Unit: inserts @Ran g g@ around @inner@. +instance forall base active ms m t3 acc acc' out g inner. + ( MapPath active inner (Ran g g inner) acc acc' + , StepPathMask base (Append active '[ F ]) ms m t3 acc' out + ) => StepRole PRanU base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Append active '[ F ]) @ms @m @t3 @acc' @out f + (mapPath @active @inner @(Ran g g inner) ranUnit acc) + {-# INLINE stepRole #-} + +-- | Lan Unit: expands @h inner@ to @Lan g h (g inner)@. +instance forall base active ms m t3 acc acc' out g h inner. + ( MapPath (Init active) (h inner) (Lan g h (g inner)) acc acc' + , StepPathMask base (Append active '[ F ]) ms m t3 acc' out + ) => StepRole PLanU base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Append active '[ F ]) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(h inner) @(Lan g h (g inner)) lanUnit acc) + {-# INLINE stepRole #-} + +-- | Lan Counit: collapses @Lan g g inner@ to @inner@. +instance forall base active ms m t3 acc acc' out g inner. + ( MapPath (Init active) (Lan g g inner) inner acc acc' + , StepPathMask base (Init active) ms m t3 acc' out + ) => StepRole PLanC base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @(Init active) @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(Lan g g inner) @inner lanCounit acc) + {-# INLINE stepRole #-} + +-- | Coyoneda lifting: wraps argument in 't:Coyoneda' with zero constraints. +instance (ExpectArrow "StepRole PCoY" acc (Coyoneda φ a) rTail, fa ~ φ a, StepPathMask base '[] ms m t3 rTail out') + => StepRole PCoY base '[] ms m t3 acc (fa -> out') where + stepRole f acc fa = stepPathMask @base @'[] @ms f (acc (liftCoyoneda fa)) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' φ a rTail fa. + ( fa ~ φ a + , MapPath (l ': ls) (Coyoneda φ a -> rTail) rTail acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PCoY base (l ': ls) ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f + (mapPath @(l ': ls) @(Coyoneda φ a -> rTail) @rTail (\g -> g (liftCoyoneda fa)) acc) + {-# INLINE stepRole #-} + +-- | Coyoneda lowering: unrolls 't:Coyoneda' to underlying functor via single 'fmap'. +instance forall base active ms m t3 acc acc' out φ inner. + ( Functor φ + , MapPath (Init active) (Coyoneda φ inner) (φ inner) acc acc' + , StepPathMask base active ms m t3 acc' out + ) => StepRole PUnCoY base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @active @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(Coyoneda φ inner) @(φ inner) lowerCoyoneda acc) + {-# INLINE stepRole #-} + +-- | Yoneda lifting: wraps argument in 't:Yoneda' for $O(1)$ composition. +instance (Functor φ, ExpectArrow "StepRole PYon" acc (Yoneda φ a) rTail, fa ~ φ a, StepPathMask base '[] ms m t3 rTail out') + => StepRole PYon base '[] ms m t3 acc (fa -> out') where + stepRole f acc fa = stepPathMask @base @'[] @ms f (acc (liftYoneda fa)) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' φ a rTail fa. + ( Functor φ, fa ~ φ a + , MapPath (l ': ls) (Yoneda φ a -> rTail) rTail acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PYon base (l ': ls) ms m t3 acc (fa -> out') where + stepRole f acc fa = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f + (mapPath @(l ': ls) @(Yoneda φ a -> rTail) @rTail (\g -> g (liftYoneda fa)) acc) + {-# INLINE stepRole #-} + +-- | Yoneda lowering: extracts underlying functor from 't:Yoneda' (zero constraints). +instance forall base active ms m t3 acc acc' out φ inner. + ( MapPath (Init active) (Yoneda φ inner) (φ inner) acc acc' + , StepPathMask base active ms m t3 acc' out + ) => StepRole PUnYon base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @active @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(Yoneda φ inner) @(φ inner) lowerYoneda acc) + {-# INLINE stepRole #-} + +-- | Codensity lifting: lifts monadic argument into 't:Codensity' for CPS fusion. +instance (Monad m', ExpectArrow "StepRole PCodM" acc (Codensity m' a) rTail, ma ~ m' a, StepPathMask base '[] ms m t3 rTail out') + => StepRole PCodM base '[] ms m t3 acc (ma -> out') where + stepRole f acc ma = stepPathMask @base @'[] @ms f (acc (liftCodensity ma)) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' m' a rTail ma. + ( Monad m', ma ~ m' a + , MapPath (l ': ls) (Codensity m' a -> rTail) rTail acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PCodM base (l ': ls) ms m t3 acc (ma -> out') where + stepRole f acc ma = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f + (mapPath @(l ': ls) @(Codensity m' a -> rTail) @rTail (\g -> g (liftCodensity ma)) acc) + {-# INLINE stepRole #-} + +-- | Codensity lowering: runs 't:Codensity' back to underlying monad. +instance forall base active ms m t3 acc acc' out m' inner. + ( Applicative m' + , MapPath (Init active) (Codensity m' inner) (m' inner) acc acc' + , StepPathMask base active ms m t3 acc' out + ) => StepRole PUnCod base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @active @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(Codensity m' inner) @(m' inner) lowerCodensity acc) + {-# INLINE stepRole #-} + +-- | Density lifting: lifts comonadic argument into 't:Density'. +instance (Comonad w, ExpectArrow "StepRole PDenW" acc (Density w a) rTail, wa ~ w a, StepPathMask base '[] ms m t3 rTail out') + => StepRole PDenW base '[] ms m t3 acc (wa -> out') where + stepRole f acc wa = stepPathMask @base @'[] @ms f (acc (liftDensity wa)) + {-# INLINE stepRole #-} + +instance forall base l ls ms m t3 acc acc' out' w a rTail wa. + ( Comonad w, wa ~ w a + , MapPath (l ': ls) (Density w a -> rTail) rTail acc acc' + , StepPathMask base (l ': ls) ms m t3 acc' out' + ) => StepRole PDenW base (l ': ls) ms m t3 acc (wa -> out') where + stepRole f acc wa = + stepPathMask @base @(l ': ls) @ms @m @t3 @acc' @out' f + (mapPath @(l ': ls) @(Density w a -> rTail) @rTail (\g -> g (liftDensity wa)) acc) + {-# INLINE stepRole #-} + +-- | Density lowering: runs 't:Density' back to underlying comonad. +instance forall base active ms m t3 acc acc' out w inner. + ( Comonad w + , MapPath (Init active) (Density w inner) (w inner) acc acc' + , StepPathMask base active ms m t3 acc' out + ) => StepRole PUnDen base active ms m t3 acc out where + stepRole f acc = + stepPathMask @base @active @ms @m @t3 @acc' @out f + (mapPath @(Init active) @(Density w inner) @(w inner) lowerDensity acc) + {-# INLINE stepRole #-} diff --git a/src/Gongju/Monad.hs b/src/Gongju/Monad.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Monad.hs @@ -0,0 +1,367 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE RequiredTypeArguments #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} + +-- | Module: Gongju.Monad +-- Description: Positional Monadic Curried Binding, Multi-Slot Lifting Masks, and Kleisli Arity Chains +-- +-- Replaces Template Haskell monadic splices (such as 'Control.Monad.Syntax' in 'composition-extra') +-- with pure type-level Peano induction, bidirectional functional dependencies, and multi-slot +-- monadic lifting masks. +-- +-- Provides: +-- * Two-phase positional monadic binding ('BindAfter', 'BindPos', 'bindPos', 'bindAt'). +-- * Classic monadic binding operators for curried functions: +-- * Tail binds: '(==<<)', '(===<<)', '(====<<)' and flips '(>>==)', '(>>===)', '(>>====)'. +-- * Interior binds: '(=.=<<)', '(==.<<)', '(=..<<)' and flips '(>>=.=)', '(>>.==)', '(>>..=)'. +-- * Multi-slot monadic lifting masks ('LiftMask', 'liftMask', 'ArgMode(Pure, Monadic)'). +-- * Arity-indexed Kleisli composition and pure lifting ('liftPureN', 'bindKleisliN', '(<=<.)', '(<=<..)', '(.>=>)', '(..>=>)'). +module Gongju.Monad + ( -- * Two-Phase Positional Monadic Binding + BindAfter (..) + , BindPos (..) + , bindPos + , bindAt + -- * Tail Monadic Binding Operators (after = 0) + , (==<<) + , (===<<) + , (====<<) + , (>>==) + , (>>===) + , (>>====) + -- * Interior Monadic Binding Operators (after > 0) + , (=.=<<) + , (==.<<) + , (=..<<) + , (>>=.=) + , (>>.==) + , (>>..=) + -- * Multi-Slot Monadic Lifting Masks + , ArgMode (..) + , PureArg + , MonadicArg + , PArg + , MArg + , LiftMask (..) + -- * Arity-Indexed Kleisli Composition & Pure Lifting + , liftPureN + , bindKleisliN + , (<=<.) + , (<=<..) + , (.>=>) + , (..>=>) + ) where + +import Data.Kind (Type) +import GHC.TypeLits (Nat) +import Gongju.Composition (ComposeN (..), compN) +import Gongju.Peano (Length, Peano (..), ToPeano) + +{- Note [Positional Monadic Curried Binding] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-positional-monadic-binding] +In multi-argument Haskell functions returning a monadic result: + @f :: a -> b -> c -> m d@ +one often wishes to bind a monadic value @m b@ into an interior or trailing argument +slot while leaving all other pure arguments curried outside. + +In libraries relying on Template Haskell splices (such as 'composition-extra'), +separate modules ('Control.Monad.Syntax.Two', '.Three', ..., '.Six') generate fixed +splices for every permutation of argument count and binding position. + +Gongju replaces this combinatorial explosion with two-phase structural Peano induction: + 1. 'BindAfter (after :: Peano) (m :: Type -> Type) b f g': + Floats @after@ trailing pure arguments outside of '(>>=)'. + When @after = 0@ (@'Z@), the binding reduces to standard monadic bind @mb >>= f@. + When @after > 0@ (@'S after@), applying @f b@ yields a function @c -> r@, not a + monadic computation. 'BindAfter' suspends argument @c@, threading it inside the + continuation @\b -> f b c@ before executing @mb >>= ...@. + 2. 'BindPos (before :: Peano) (after :: Peano) (m :: Type -> Type) b f g': + Skips @before@ leading pure arguments by peeling them off with lambda abstraction, + then delegates to 'BindAfter' to float the remaining @after@ trailing arguments. + +Bidirectional functional dependencies: + - @before after f -> b m g@: Determines the target argument @b@, monad @m@, and result @g@ + uniquely from the input function @f@ and position coordinates. + - @before after m b g -> f@: Reconstructs the original curried function type @f@ when the + bound type and result type are specified. +-} + +-- --------------------------------------------------------------------------- +-- 1. Two-Phase Positional Monadic Binding (BindAfter & BindPos) +-- --------------------------------------------------------------------------- + +-- | Phase 1: Float @after@ trailing pure arguments outside '(>>=)'. +-- +-- See Note [Positional Monadic Curried Binding] [ref:note-positional-monadic-binding]. +class Monad m => BindAfter (after :: Peano) (m :: Type -> Type) b f g | after f -> m g, after m b g -> f where + -- | Internal inductive worker floating trailing pure arguments outside '(>>=)'. + bindAfter' :: (b -> f) -> m b -> g + +instance Monad m => BindAfter 'Z m b (m r) (m r) where + bindAfter' f mb = mb >>= f + {-# INLINE bindAfter' #-} + +instance BindAfter after m b r r' => BindAfter ('S after) m b (c -> r) (c -> r') where + bindAfter' f mb c = bindAfter' @after (`f` c) mb + {-# INLINE bindAfter' #-} + +-- | Phase 2: Skip @before@ leading pure arguments, then hand off to 'BindAfter'. +-- +-- See Note [Positional Monadic Curried Binding] [ref:note-positional-monadic-binding]. +class Monad m => BindPos (before :: Peano) (after :: Peano) (m :: Type -> Type) b f g | before after f -> b m g, before after m b g -> f where + -- | Internal inductive worker skipping leading pure arguments. + bindPos' :: f -> m b -> g + +instance BindAfter after m b rest g => BindPos 'Z after m b (b -> rest) g where + bindPos' f mb = bindAfter' @after f mb + {-# INLINE bindPos' #-} + +instance BindPos before after m b r r' => BindPos ('S before) after m b (a -> r) (a -> r') where + bindPos' f mb a = bindPos' @before @after (f a) mb + {-# INLINE bindPos' #-} + +-- | User-facing positional monadic bind parameterized by visible 'Nat' literals: +-- @before@ (leading pure arguments to skip) and @after@ (trailing pure arguments to float). +-- +-- Examples: +-- +-- >>> let add3 x y z = pure (x + y + z) :: Maybe Int +-- >>> bindPos @1 @1 add3 (Just 20) 1 3 +-- Just 24 +-- >>> bindPos @0 @2 add3 (Just 10) 2 3 +-- Just 15 +bindPos :: forall (before :: Nat) (after :: Nat) m b f g. + BindPos (ToPeano before) (ToPeano after) m b f g => f -> m b -> g +bindPos = bindPos' @(ToPeano before) @(ToPeano after) +{-# INLINE bindPos #-} + +-- | Top-level positional monadic bind for argument index @n@ (0-indexed) where all +-- subsequent arguments have already been applied or are pure (@after = 0@). +-- +-- @bindAt \@0@ corresponds to '(=<<)'. +-- @bindAt \@1@ corresponds to '(==<<)'. +-- @bindAt \@2@ corresponds to '(===<<)'. +-- +-- Example: +-- +-- >>> let f x y = pure (x * y) :: Maybe Int +-- >>> bindAt @1 f (Just 7) 6 +-- Just 42 +bindAt :: forall (n :: Nat) m b f g. + BindPos (ToPeano n) 'Z m b f g => f -> m b -> g +bindAt = bindPos' @(ToPeano n) @'Z +{-# INLINE bindAt #-} + +-- --------------------------------------------------------------------------- +-- 2. Tail Monadic Binding Operators (after = 0) +-- --------------------------------------------------------------------------- + +-- | Infix positional monadic bind at argument slot 1 (@after = 0@). +-- Binds 'm b' into '(a -> b -> m c)', returning 'a -> m c'. +infixr 1 ==<< +(==<<) :: BindPos ('S 'Z) 'Z m b f g => f -> m b -> g +(==<<) = bindPos' @('S 'Z) @'Z +{-# INLINE (==<<) #-} + +-- | Infix positional monadic bind at argument slot 2 (@after = 0@). +-- Binds 'm c' into '(a -> b -> c -> m d)', returning 'a -> b -> m d'. +infixr 1 ===<< +(===<<) :: BindPos ('S ('S 'Z)) 'Z m b f g => f -> m b -> g +(===<<) = bindPos' @('S ('S 'Z)) @'Z +{-# INLINE (===<<) #-} + +-- | Infix positional monadic bind at argument slot 3 (@after = 0@). +-- Binds 'm d' into '(a -> b -> c -> d -> m e)', returning 'a -> b -> c -> m e'. +infixr 1 ====<< +(====<<) :: BindPos ('S ('S ('S 'Z))) 'Z m b f g => f -> m b -> g +(====<<) = bindPos' @('S ('S ('S 'Z))) @'Z +{-# INLINE (====<<) #-} + +-- | Forward positional monadic bind at argument slot 1: @mb >>== f = f ==<< mb@. +infixl 1 >>== +(>>==) :: BindPos ('S 'Z) 'Z m b f g => m b -> f -> g +(>>==) = flip (==<<) +{-# INLINE (>>==) #-} + +-- | Forward positional monadic bind at argument slot 2: @mc >>=== f = f ===<< mc@. +infixl 1 >>=== +(>>===) :: BindPos ('S ('S 'Z)) 'Z m b f g => m b -> f -> g +(>>===) = flip (===<<) +{-# INLINE (>>===) #-} + +-- | Forward positional monadic bind at argument slot 3: @md >>==== f = f ====<< md@. +infixl 1 >>==== +(>>====) :: BindPos ('S ('S ('S 'Z))) 'Z m b f g => m b -> f -> g +(>>====) = flip (====<<) +{-# INLINE (>>====) #-} + +-- --------------------------------------------------------------------------- +-- 3. Interior Monadic Binding Operators (after > 0) +-- --------------------------------------------------------------------------- + +-- | Infix positional monadic bind for 3-argument function at slot 1 (@before = 1, after = 1@). +-- Binds 'm b' into '(a -> b -> c -> m d)', returning 'a -> c -> m d'. +infixr 1 =.=<< +(=.=<<) :: BindPos ('S 'Z) ('S 'Z) m b f g => f -> m b -> g +(=.=<<) = bindPos' @('S 'Z) @('S 'Z) +{-# INLINE (=.=<<) #-} + +-- | Infix positional monadic bind for 3-argument function at slot 0 (@before = 0, after = 2@). +-- Binds 'm a' into '(a -> b -> c -> m d)', returning 'b -> c -> m d'. +infixr 1 ==.<<, =..<< +(==.<<), (=..<<) :: BindPos 'Z ('S ('S 'Z)) m b f g => f -> m b -> g +(==.<<) = bindPos' @'Z @('S ('S 'Z)) +(=..<<) = bindPos' @'Z @('S ('S 'Z)) +{-# INLINE (==.<<) #-} +{-# INLINE (=..<<) #-} + +-- | Forward positional monadic bind for 3-argument function at slot 1: @mb >>=.= f = f =.=<< mb@. +infixl 1 >>=.= +(>>=.=) :: BindPos ('S 'Z) ('S 'Z) m b f g => m b -> f -> g +(>>=.=) = flip (=.=<<) +{-# INLINE (>>=.=) #-} + +-- | Forward positional monadic bind for 3-argument function at slot 0: @ma >>.== f = f ==.<< ma@. +infixl 1 >>.==, >>..= +(>>.==), (>>..=) :: BindPos 'Z ('S ('S 'Z)) m b f g => m b -> f -> g +(>>.==) = flip (==.<<) +(>>..=) = flip (=..<<) +{-# INLINE (>>.==) #-} +{-# INLINE (>>..=) #-} + +{- Note [Multi-Slot Monadic Lifting Masks] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-multislot-monadic-masks] +In 'Control.Monad.Syntax', operators allow binding only a single monadic argument at a time. +With a promoted two-element kind 'ArgMode = Pure | Monadic', callers can lift any arbitrary +subset of a curried function's arguments into 'Monad m' simultaneously in a single pass. + +Given @f :: a -> b -> c -> m d@: + @liftMask @'[MArg, PArg, MArg] f :: m a -> b -> m c -> m d@ + +The transformation proceeds inductively on the type-level list @mask :: [ArgMode]@: + 1. Base case @'[]@: The return type must already be of the form @m r@. + 2. Pure step @'Pure ': ms@: Leaves the current argument pure @(a -> ...)@ and recurses on @ms@. + 3. Monadic step @'Monadic ': ms@: Transforms @a@ into @m a@, recurses on @ms@ producing + transformed tail @r'@, and uses 'BindAfter (Length ms)' to float all trailing arguments + outside the bind. Monadic effects are sequenced strictly from left to right. +-} + +-- --------------------------------------------------------------------------- +-- 4. Multi-Slot Monadic Lifting Masks (LiftMask) +-- --------------------------------------------------------------------------- + +-- | Argument lifting mode for multi-slot monadic masks. +-- 'Pure keeps the curried argument as pure @a@. +-- 'Monadic lifts the argument from @a@ to @m a@ and sequences its monadic effect. +data ArgMode + = Pure -- ^ Keep the curried argument pure. + | Monadic -- ^ Lift the curried argument into the monad @m@. + deriving (Eq, Ord, Show, Enum, Bounded) + +-- | Convenient type synonyms for mask annotations. +type PureArg = 'Pure +type MonadicArg = 'Monadic +type PArg = 'Pure +type MArg = 'Monadic + +-- | Multi-slot monadic lifting mask. +-- +-- Transforms a curried function @f@ into @g@ by lifting arguments marked 'Monadic +-- into the monad @m@ while preserving pure arguments marked 'Pure'. +-- +-- See Note [Multi-Slot Monadic Lifting Masks] [ref:note-multislot-monadic-masks]. +class Monad m => LiftMask (mask :: [ArgMode]) (m :: Type -> Type) f g | mask f -> m g, mask m g -> f where + -- | Lift a curried function according to the type-level mode mask. + liftMask :: f -> g + +instance Monad m => LiftMask '[] m (m r) (m r) where + liftMask = id + {-# INLINE liftMask #-} + +instance LiftMask ms m r r' => LiftMask ('Pure ': ms) m (a -> r) (a -> r') where + liftMask f a = liftMask @ms (f a) + {-# INLINE liftMask #-} + +instance (Monad m, BindAfter (Length ms) m a r' g, LiftMask ms m r r') + => LiftMask ('Monadic ': ms) m (a -> r) (m a -> g) where + liftMask f ma = bindAfter' @(Length ms) (liftMask @ms . f) ma + {-# INLINE liftMask #-} + +-- --------------------------------------------------------------------------- +-- 5. Arity-Indexed Kleisli Composition & Pure Lifting +-- --------------------------------------------------------------------------- + +-- | Lift a pure @n@-ary curried function to produce results inside an 'Applicative' functor. +-- +-- Equivalent to @compN \@n pure@. +-- +-- Examples: +-- +-- >>> liftPureN @1 (+ 1) 5 :: Maybe Int +-- Just 6 +-- >>> liftPureN @2 (+) 3 4 :: Maybe Int +-- Just 7 +liftPureN :: forall (n :: Nat) m a f g. + (Applicative m, ComposeN (ToPeano n) a (m a) f g) => f -> g +liftPureN = compN @n pure +{-# INLINE liftPureN #-} + +-- | Post-compose a monadic Kleisli arrow @(b -> m c)@ after an @n@-ary curried monadic function +-- @(a1 -> ... -> an -> m b)@. +-- +-- Equivalent to @compN \@n (>>= k)@. +-- +-- Examples: +-- +-- >>> let f x y = Just (x + y) +-- >>> let checkEven z = if even z then Just z else Nothing +-- >>> bindKleisliN @2 checkEven f 2 4 +-- Just 6 +-- >>> bindKleisliN @2 checkEven f 2 3 +-- Nothing +bindKleisliN :: forall (n :: Nat) m b c f g. + (Monad m, ComposeN (ToPeano n) (m b) (m c) f g) => (b -> m c) -> f -> g +bindKleisliN k = compN @n (>>= k) +{-# INLINE bindKleisliN #-} + +-- | Binary Kleisli composition: post-composes @k :: b -> m c@ onto a binary monadic function. +-- +-- @(k <=<. f) x y = f x y >>= k@ +infixr 1 <=<. +(<=<.) :: (Monad m, ComposeN ('S ('S 'Z)) (m b) (m c) f g) => (b -> m c) -> f -> g +(<=<.) = bindKleisliN @2 +{-# INLINE (<=<.) #-} + +-- | Ternary Kleisli composition: post-composes @k :: b -> m c@ onto a ternary monadic function. +-- +-- @(k <=<.. f) x y z = f x y z >>= k@ +infixr 1 <=<.. +(<=<..) :: (Monad m, ComposeN ('S ('S ('S 'Z))) (m b) (m c) f g) => (b -> m c) -> f -> g +(<=<..) = bindKleisliN @3 +{-# INLINE (<=<..) #-} + +-- | Forward binary Kleisli composition: @(f .>=> k) x y = f x y >>= k@. +infixr 1 .>=> +(.>=>) :: (Monad m, ComposeN ('S ('S 'Z)) (m b) (m c) f g) => f -> (b -> m c) -> g +(.>=>) f k = (<=<.) k f +{-# INLINE (.>=>) #-} + +-- | Forward ternary Kleisli composition: @(f ..>=> k) x y z = f x y z >>= k@. +infixr 1 ..>=> +(..>=>) :: (Monad m, ComposeN ('S ('S ('S 'Z))) (m b) (m c) f g) => f -> (b -> m c) -> g +(..>=>) f k = (<=<..) k f +{-# INLINE (..>=>) #-} diff --git a/src/Gongju/Peano.hs b/src/Gongju/Peano.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Peano.hs @@ -0,0 +1,80 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} + +-- | Module: Gongju.Peano +-- Description: Bridge between GHC.TypeLits.Nat, inductive Peano data kinds, and type-level list utilities +-- +-- Provides inductive Peano naturals for driving typeclass induction while exposing +-- ergonomic 'GHC.TypeLits.Nat' type application interfaces, as well as fundamental +-- inductive type-level list operations ('Append', 'Init', 'Replicate'). +module Gongju.Peano + ( Peano(..) + , ToPeano + , FromPeano + , Append + , Init + , Replicate + , Length + ) where + +import GHC.TypeLits (Nat, type (-), type (+)) + +{- Note [Peano TypeLits Bridge] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-peano-typelits-bridge] +GHC's built-in 'GHC.TypeLits.Nat' represents numeric type literals (0, 1, 2, ...) as +known runtime symbols, which provides clean ergonomics for call sites (e.g. @compN @3@). +However, GHC's constraint solver cannot inductively pattern-match on '0' versus 'n + 1' +during standard typeclass instance resolution without generating overlapping or undecidable +instance loops. + +Conversely, a custom inductive Peano data kind ('Z | 'S Peano) drives typeclass resolution +and bidirectional functional dependencies effortlessly by structurally peeling one successor +layer at a time. + +By defining closed type families 'ToPeano' and 'FromPeano', Gongju bridges these two representations: + - Callers use familiar numeric literals (@0, @1, @2, ...). + - Typeclasses induct upon structural 'Peano' terms ('Z, 'S 'Z, 'S ('S 'Z), ...). +-} + +-- | Inductive Peano natural numbers at the type level. +data Peano = Z | S Peano + deriving (Eq, Show) + +-- | Convert a 'GHC.TypeLits.Nat' into an inductive 'Peano' representation. +-- +-- See Note [Peano TypeLits Bridge] [ref:note-peano-typelits-bridge]. +type family ToPeano (n :: Nat) :: Peano where + ToPeano 0 = 'Z + ToPeano n = 'S (ToPeano (n - 1)) + +-- | Convert an inductive 'Peano' representation back to a 'GHC.TypeLits.Nat'. +type family FromPeano (p :: Peano) :: Nat where + FromPeano 'Z = 0 + FromPeano ('S p) = 1 + FromPeano p + +-- | Concatenate two type-level lists. +type family Append (xs :: [k]) (ys :: [k]) :: [k] where + Append '[] ys = ys + Append (x ': xs) ys = x ': Append xs ys + +-- | Return all elements of a type-level list except the last element. +type family Init (xs :: [k]) :: [k] where + Init '[] = '[] + Init '[_] = '[] + Init (x ': xs) = x ': Init xs + +-- | Generate a type-level list containing @n@ copies of element @x@. +type family Replicate (n :: Nat) (x :: k) :: [k] where + Replicate 0 _ = '[] + Replicate n x = x ': Replicate (n - 1) x + +-- | Compute the length of a type-level list as an inductive 'Peano' natural. +type family Length (xs :: [k]) :: Peano where + Length '[] = 'Z + Length (_ ': xs) = 'S (Length xs) diff --git a/src/Gongju/Permute.hs b/src/Gongju/Permute.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Permute.hs @@ -0,0 +1,92 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} + +-- | Module: Gongju.Permute +-- Description: Arbitrary curried function argument permutations via iterated Yank +-- +-- Enables reordering curried function arguments arbitrarily according to a type-level +-- permutation list, without tuple-size limits or type-directed ambiguity. +module Gongju.Permute + ( -- * Type Families + Adjust + , MapAdjust + , MapToPeano + -- * Arbitrary Permutation + , Permute(..) + , permute + ) where + +import GHC.TypeLits (Nat) +import Gongju.Peano (Peano(..), ToPeano) +import Gongju.Positional (Yank(..)) + +{- Note [Iterated Yank Index Adjustment] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-iterated-yank-adjustment] +Arbitrary argument permutation (e.g. taking f :: a -> b -> c -> d -> r and producing +c -> a -> d -> b -> r via @'[2, 0, 3, 1]) is achieved by decomposing the permutation +into sequential 'Yank' operations. + +When an argument at index `p` is pulled to position 0: + 1. Any remaining original target index `i > p` shifts down by 1 in the residual function. + 2. Any remaining original target index `i < p` retains its relative position. + +The closed type family 'Adjust' recalculates remaining indices at each inductive step, +and 'Permute' recurses over the updated index list. This provides: + - Zero tuple size limits (functions of arity 10, 20, 50 can be reordered). + - Immunity to duplicate types (e.g. Int -> Int -> Int -> r). + - Support for partial permutations (arguments not mentioned in the permutation list + remain in their original relative positions at the tail). +-} + +-- | Recalculate index @i@ after an element at position @picked@ has been removed. +-- +-- See Note [Iterated Yank Index Adjustment] [ref:note-iterated-yank-adjustment]. +type family Adjust (picked :: Peano) (i :: Peano) :: Peano where + Adjust 'Z ('S i) = i + Adjust ('S p) ('S i) = 'S (Adjust p i) + Adjust _ i = i + +-- | Map 'Adjust' over a type-level list of Peano indices. +type family MapAdjust (p :: Peano) (ps :: [Peano]) :: [Peano] where + MapAdjust _ '[] = '[] + MapAdjust p (i ': is) = Adjust p i ': MapAdjust p is + +-- | Convert a type-level list of 'Nat' indices to inductive 'Peano' numbers. +type family MapToPeano (ns :: [Nat]) :: [Peano] where + MapToPeano '[] = '[] + MapToPeano (n ': ns) = ToPeano n ': MapToPeano ns + +-- | Inductive class computing the permutation of curried function arguments. +class Permute (ps :: [Peano]) f g | ps f -> g where + -- | Internal worker for executing iterated permutation. + permute' :: f -> g + +instance Permute '[] f f where + permute' = id + {-# INLINE permute' #-} + +instance (Yank p f arg rest, Permute (MapAdjust p ps) rest rest') + => Permute (p ': ps) f (arg -> rest') where + permute' f arg = permute' @(MapAdjust p ps) (yank' @p f arg) + {-# INLINE permute' #-} + +-- | Reorder the arguments of a curried function according to a 0-indexed list of 'Nat' positions. +-- +-- Example: +-- +-- >>> let f x y z = (x, y, z) +-- >>> permute @'[2, 0, 1] f 3 1 2 +-- (1, 2, 3) +permute :: forall (ns :: [Nat]) f g. Permute (MapToPeano ns) f g => f -> g +permute = permute' @(MapToPeano ns) +{-# INLINE permute #-} diff --git a/src/Gongju/Positional.hs b/src/Gongju/Positional.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Positional.hs @@ -0,0 +1,150 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Positional +-- Description: Guarded arrow unification and positional combinators (Yank, Shove, Twist) +-- +-- Provides inductive combinators for manipulating curried function arguments by position: +-- pulling arguments to the front (Yank), pushing arguments deeper (Shove), and swapping +-- adjacent arguments (Twist), accompanied by guarded error messages for arity mismatches. +module Gongju.Positional + ( -- * Guarded Arrow Unification + CheckArrow + , ExpectArrow + -- * Yank (Pull to Front) + , Yank(..) + , slipr + , yank + -- * Shove (Push Deeper) + , Shove(..) + , slipl + , shove + -- * Twist (Adjacent Swap) + , Twist(..) + , twist + ) where + +import Data.Kind (Constraint, Type) +import GHC.TypeLits + ( ErrorMessage (ShowType, Text, (:$$:), (:<>:)) + , Nat + , Symbol + , TypeError + ) +import Gongju.Peano (Peano(..), ToPeano) + +{- Note [Positional Curried Arrow Manipulation] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-positional-arrow-manipulation] +Manipulating the positional arguments of curried functions (a0 -> a1 -> ... -> r) is +conventionally approached by either: + 1. Converting to an n-tuple via 'Generics.SOP' / 'tuple-sop', which requires finite + tuple instances and loses bidirectional type inference. + 2. Generating dozens of ad-hoc permutations via Template Haskell. + +Gongju manipulates curried function arrows directly in place using three fundamental +primitives: + 1. 'Yank' ('slipr'): Pulls the n-th argument (0-indexed) to position 0, shifting + intervening arguments [0 .. n-1] one slot to the right. + 2. 'Shove' ('slipl'): Pushes argument 0 into depth n, shifting intervening arguments + [1 .. n] one slot to the left. + 3. 'Twist' ('twist'): Transposes adjacent arguments at depth n and n+1. + +Furthermore, 'CheckArrow' and 'ExpectArrow' provide compile-time guard rails that report +clear, descriptive custom type errors when arity boundaries are exceeded. +-} + +-- | Guard family asserting that type @f@ is a function arrow @(a -> b)@. +type family CheckArrow (ctx :: Symbol) (f :: Type) :: Constraint where + CheckArrow _ (_ -> _) = () + CheckArrow ctx nonFn = + TypeError + ( 'Text "• [" :<>: 'Text ctx :<>: 'Text "] Arity / Index Mismatch:" + ':$$: 'Text " Expected a function (a -> r), but reached: " :<>: 'ShowType nonFn + ) + +-- | Constraint requiring @f@ to unify with @(a -> r)@ with diagnostic context @ctx@. +class (CheckArrow ctx f, f ~ (a -> r)) => ExpectArrow (ctx :: Symbol) f a r +instance (CheckArrow ctx f, f ~ (a -> r)) => ExpectArrow ctx f a r + +-- | Pull the @n@-th curried argument (0-indexed) to the front position. +-- +-- See Note [Positional Curried Arrow Manipulation] [ref:note-positional-arrow-manipulation]. +class Yank (n :: Peano) f target rest | n f -> target rest where + -- | Internal worker for pulling the @n@-th argument forward. + yank' :: f -> target -> rest + +instance ExpectArrow "Yank" (a -> r) a r => Yank 'Z (a -> r) a r where + yank' f target = f target + {-# INLINE yank' #-} + +instance (ExpectArrow "Yank" (a -> r) a r, Yank n r target rest') + => Yank ('S n) (a -> r) target (a -> rest') where + yank' f target a = yank' @n (f a) target + {-# INLINE yank' #-} + +-- | Pull the @n@-th argument (0-indexed) to position 0. +-- +-- Equivalent to @slipr@ in 'composition-extra'. +slipr :: forall (n :: Nat) f target rest. Yank (ToPeano n) f target rest => f -> target -> rest +slipr = yank' @(ToPeano n) +{-# INLINE slipr #-} + +-- | User-facing synonym for 'slipr': pulls the @n@-th argument (0-indexed) to position 0. +yank :: forall (n :: Nat) f target rest. Yank (ToPeano n) f target rest => f -> target -> rest +yank = yank' @(ToPeano n) +{-# INLINE yank #-} + +-- | Push the 0-th argument into position @n@, shifting arguments 1 through @n@ to the left. +class Shove (n :: Peano) a rest f | n a rest -> f, n f -> a rest where + -- | Internal worker for pushing the head argument deeper. + shove' :: (a -> rest) -> f + +instance Shove 'Z a r (a -> r) where + shove' = id + {-# INLINE shove' #-} + +instance Shove n a rest r => Shove ('S n) a (b -> rest) (b -> r) where + shove' f b = shove' @n (`f` b) + {-# INLINE shove' #-} + +-- | Push the 0-th argument into position @n@. +-- +-- Equivalent to @slipl@ in 'composition-extra'. +slipl :: forall (n :: Nat) a rest f. Shove (ToPeano n) a rest f => (a -> rest) -> f +slipl = shove' @(ToPeano n) +{-# INLINE slipl #-} + +-- | User-facing synonym for 'slipl': pushes the 0-th argument into position @n@. +shove :: forall (n :: Nat) a rest f. Shove (ToPeano n) a rest f => (a -> rest) -> f +shove = shove' @(ToPeano n) +{-# INLINE shove #-} + +-- | Swap adjacent arguments at depth @n@ and @n + 1@. +class Twist (n :: Peano) f g | n f -> g, n g -> f where + -- | Internal worker for transposing adjacent arguments. + twist' :: f -> g + +instance Twist 'Z (a -> b -> r) (b -> a -> r) where + twist' = flip + {-# INLINE twist' #-} + +instance Twist n r r' => Twist ('S n) (a -> r) (a -> r') where + twist' f a = twist' @n (f a) + {-# INLINE twist' #-} + +-- | Swap adjacent arguments at depth @n@ and @n + 1@. +twist :: forall (n :: Nat) f g. Twist (ToPeano n) f g => f -> g +twist = twist' @(ToPeano n) +{-# INLINE twist #-} diff --git a/src/Gongju/Profunctor.hs b/src/Gongju/Profunctor.hs new file mode 100644 --- /dev/null +++ b/src/Gongju/Profunctor.hs @@ -0,0 +1,412 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ConstraintKinds #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE RequiredTypeArguments #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE UndecidableSuperClasses #-} + +-- | Module: Gongju.Profunctor +-- Description: Profunctors, Indexed Profunctors, and Effect Handler Permutations for Gongju +-- +-- Plugs canonical 'Profunctor' from 'Data.Profunctor' and 'IxProfunctor' from +-- 'Data.Profunctor.Indexed' into Gongju's open tape composition engine, and provides +-- zero-cost argument permutations for binary profunctor strands and curried effect handlers +-- (such as in @kernmantle-polytropos@). +-- +-- Supports: +-- * Contravariant input pre-processing via 'P1' / 'lmap'. +-- * Covariant output post-processing via 'P2' / 'rmap'. +-- * Simultaneous bidirectional mapping via 'dimap'. +-- * Curried category spine generalization and point-free permutations ('CurriedCat', 'ComposeCatN', 'YankCat', 'PermuteCat'). +-- * Tuple-spine arrow input/output permutations ('YankTuple', 'PermuteTuple', 'permuteInputs', 'permuteOutputs', 'dimapPermute'). +-- * Curried effect handler environment reordering ('permuteHandler', 'compHandlerN'). +module Gongju.Profunctor + ( -- * Re-exported Canonical Profunctor Classes + Profunctor(..) + , dimap' + , lmap' + , rmap' + -- * Re-exported Indexed Profunctors + , IxProfunctor + , ixcontramap + -- * Open Profunctor Tags + , P1 + , P2 + -- * Ergonomic Aliases + , PP1 + , PP2 + -- * Curried Category Permutations + , CurriedCat (..) + , ComposeCatN (..) + , compCatN + , YankCat (..) + , yankCat + , PermuteCat (..) + , permuteCat + -- * Tuple-Spine Arrow Permutations + , YankTuple (..) + , yankTuple + , PermuteTuple (..) + , permuteTuple + -- * Profunctor Strand Permutations + , permuteInputs + , permuteOutputs + , dimapPermute + , swapStrand + -- * Curried Effect Handler Permutations + , permuteHandler + , compHandlerN + ) where + +import Control.Arrow (Arrow (arr, second)) +import Control.Category (Category) +import qualified Control.Category as Cat +import Data.Kind (Type) +import qualified Data.Profunctor as P +import Data.Profunctor + ( Profunctor (..) + ) +import qualified Data.Profunctor.Indexed as IxP +import GHC.TypeLits (Nat) +import Gongju.Composition + ( ComposeN (..) + , InOrder + , MapPath (..) + , MapStep (..) + , PL + , compN + ) +import Gongju.Peano (Peano (..), ToPeano) +import Gongju.Permute + ( MapAdjust + , MapToPeano + , Permute (..) + , permute + ) +import Prelude hiding (id) + +{- Note [Profunctor Effect Handler Permutations] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-profunctor-handler-permutations] +In arrow-based architectures and profunctor effect frameworks (such as 'kernmantle' +and 'kernmantle-polytropos'), effect strands are modeled as binary profunctors: + @strand :: Type -> Type -> Type@ +while effect handlers are curried functions taking environment configuration parameters +before producing or interpreting a strand: + @handler :: env1 -> env2 -> ... -> p a b@ + +Permuting profunctor handlers requires addressing two distinct structural axes: + 1. Curried environment parameter permutations: + Reordering @env1 -> env2 -> ... -> envk@ via 'permuteHandler @ns' (which delegates + to Gongju's Peano-indexed 'Permute' engine). + 2. Curried category spine generalization: + Generalizing from @(->)@ to an arbitrary Cartesian Closed Category ('CurriedCat cat') + via 'YankCat' and 'PermuteCat'. Here, arguments are permuted point-free using only + 'catFlip' and category composition '(.)', never inspecting or allocating Haskell values. +-} + +{- Note [Tuple-Spine Arrow Permutations] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-tuple-spine-permutations] +When binary profunctors or arrows consume multiple arguments simultaneously, they package +their input domain as right-nested tuples: + @(a0, (a1, (a2, ())))@ + +Permuting slots in an arrow input spine requires structural induction dual to curried 'Yank': + 1. 'YankTuple (n :: Peano) arr s t': + Pulls the @n@-th slot of the nested tuple to position 0. + - Base case (@'Z@): The 0-th element is already at the head; returns 'Cat.id'. + - Step case (@'S n@): Recursively pulls the @n@-th slot in the tail @r@ via + 'second (yankTuple @n)', then swaps the head and extracted slot using + 'arr (\(a, (target, rest)) -> (target, (a, rest)))'. + 2. 'PermuteTuple (ps :: [Peano]) arr s t': + Iterates 'YankTuple' across a permutation index list, updating residual indices + at each step with 'MapAdjust'. + 3. 'permuteInputs @ns' and 'permuteOutputs @ns': + For any 'Profunctor p', pre-composing 'lmap (permuteTuple @ns)' or post-composing + 'rmap (permuteTuple @ns)' reorders the strand's input or output domain directly + with zero runtime tuple packaging overhead. +-} + +-- --------------------------------------------------------------------------- +-- 1. Open Profunctor Tags & Re-exports +-- --------------------------------------------------------------------------- + +-- | Profunctor first slot tag (contravariant). +data P1 + +-- | Profunctor second slot tag (covariant). +data P2 + +-- | In-order profunctor first-slot (contravariant) mapping alias. +type PP1 = InOrder (PL '[P1]) + +-- | In-order profunctor second-slot (covariant) mapping alias. +type PP2 = InOrder (PL '[P2]) + +-- | Type alias specializing 'Data.Profunctor.Indexed.Profunctor' as 'IxProfunctor'. +type IxProfunctor = IxP.Profunctor + +-- | Re-export indexed profunctor index contramap. +ixcontramap :: IxProfunctor p => (j -> i) -> p i a b -> p j a b +ixcontramap = IxP.ixcontramap +{-# INLINE ixcontramap #-} + +-- | Strict variant of 'dimap'. +dimap' :: Profunctor p => (a -> b) -> (c -> d) -> p b c -> p a d +dimap' = P.dimap +{-# INLINE dimap' #-} + +-- | Strict variant of 'lmap'. +lmap' :: Profunctor p => (a -> b) -> p b c -> p a c +lmap' = P.lmap +{-# INLINE lmap' #-} + +-- | Strict variant of 'rmap'. +rmap' :: Profunctor p => (b -> c) -> p a b -> p a c +rmap' = P.rmap +{-# INLINE rmap' #-} + +-- --------------------------------------------------------------------------- +-- 2. MapStep Instances for Profunctor Layers +-- --------------------------------------------------------------------------- + +-- | Pre-compose argument 1 of a Profunctor contravariantly via 'lmap'. +instance (Profunctor p, s ~ p b c, t ~ p a c, MapPath ls a b a b) + => MapStep P1 ls a b s t where + mapStep f = P.lmap (mapPath @ls f) + {-# INLINE mapStep #-} + +-- | Post-compose argument 2 of a Profunctor covariantly via 'rmap'. +instance (Profunctor p, s ~ p a b, t ~ p a c, MapPath ls b c b c) + => MapStep P2 ls b c s t where + mapStep f = P.rmap (mapPath @ls f) + {-# INLINE mapStep #-} + +-- --------------------------------------------------------------------------- +-- 3. Curried Category Permutations (CurriedCat) +-- --------------------------------------------------------------------------- + +-- | Cartesian Closed Category / Curried Category with morphism flipping and application. +-- +-- See Note [Profunctor Effect Handler Permutations] [ref:note-profunctor-handler-permutations]. +class Category cat => CurriedCat (cat :: Type -> Type -> Type) where + -- | Post-compose a transformation onto the return slot of a morphism in @cat@. + catMap :: (b -> c) -> cat a b -> cat a c + -- | Swap the first two curried inputs of a morphism in @cat@. + catFlip :: cat a (cat b c) -> cat b (cat a c) + -- | Bridge morphism execution from Haskell values. + catApply :: cat a b -> a -> b + +instance CurriedCat (->) where + catMap f g = f . g + catFlip f b a = f a b + catApply f x = f x + {-# INLINE catMap #-} + {-# INLINE catFlip #-} + {-# INLINE catApply #-} + +-- | Generalized arity composition over a 'Category' @cat@ at the leaf. +class Category cat => ComposeCatN (n :: Peano) (cat :: Type -> Type -> Type) x y z g out | n g -> cat x y, n cat y z g -> out where + -- | Internal inductive worker for category composition. + composeCatN' :: cat y z -> g -> out + +instance (Category cat, g ~ cat x y, out ~ cat x z) => ComposeCatN 'Z cat x y z g out where + composeCatN' f g = f Cat.. g + {-# INLINE composeCatN' #-} + +instance ( Category cat + , ComposeCatN n cat x y z r r' + , g ~ (a -> r) + , out ~ (a -> r') + ) => ComposeCatN ('S n) cat x y z g out where + composeCatN' f g a = composeCatN' @n @cat @x @y @z f (g a) + {-# INLINE composeCatN' #-} + +-- | User-facing arity composition over any 'Category' @cat@. +compCatN :: forall (n :: Nat) cat x y z g out. + ComposeCatN (ToPeano n) cat x y z g out => cat y z -> g -> out +compCatN = composeCatN' @(ToPeano n) @cat @x @y @z +{-# INLINE compCatN #-} + +-- | Point-free bubbling of the @n@-th curried category input using 'catFlip' and 'catMap'. +-- +-- See Note [Profunctor Effect Handler Permutations] [ref:note-profunctor-handler-permutations]. +class CurriedCat cat => YankCat (n :: Peano) (cat :: Type -> Type -> Type) f g | n f -> g where + -- | Internal inductive worker pulling the @n@-th input to position 0. + yankCat' :: f -> g + +instance (CurriedCat cat, f ~ cat a r, g ~ cat a r) => YankCat 'Z cat f g where + yankCat' = Cat.id + {-# INLINE yankCat' #-} + +instance ( CurriedCat cat + , f ~ cat a r + , r' ~ cat target rest + , g ~ cat target (cat a rest) + , YankCat n cat r r' + ) => YankCat ('S n) cat f g where + yankCat' f = catFlip (catMap (yankCat' @n @cat) f) + {-# INLINE yankCat' #-} + +-- | User-facing positional yank over any 'CurriedCat'. +yankCat :: forall (n :: Nat) cat f g. + YankCat (ToPeano n) cat f g => f -> g +yankCat = yankCat' @(ToPeano n) @cat +{-# INLINE yankCat #-} + +-- | Arbitrary permutation of curried category inputs over any 'CurriedCat'. +-- +-- See Note [Profunctor Effect Handler Permutations] [ref:note-profunctor-handler-permutations]. +class CurriedCat cat => PermuteCat (ps :: [Peano]) (cat :: Type -> Type -> Type) f g | ps f -> g where + -- | Internal inductive worker executing iterated point-free permutation. + permuteCat' :: f -> g + +instance (CurriedCat cat, f ~ g) => PermuteCat '[] cat f g where + permuteCat' = Cat.id + {-# INLINE permuteCat' #-} + +instance ( CurriedCat cat + , mid ~ cat arg rest + , g ~ cat arg rest' + , YankCat p cat f mid + , PermuteCat (MapAdjust p ps) cat rest rest' + ) => PermuteCat (p ': ps) cat f g where + permuteCat' f = catMap (permuteCat' @(MapAdjust p ps) @cat) (yankCat' @p @cat f) + {-# INLINE permuteCat' #-} + +-- | User-facing permutation of curried category inputs. +permuteCat :: forall (ns :: [Nat]) cat f g. + PermuteCat (MapToPeano ns) cat f g => f -> g +permuteCat = permuteCat' @(MapToPeano ns) @cat +{-# INLINE permuteCat #-} + +-- --------------------------------------------------------------------------- +-- 4. Tuple-Spine Arrow Permutations (YankTuple & PermuteTuple) +-- --------------------------------------------------------------------------- + +-- | Pull the @n@-th element of a right-nested tuple @s@ to the front. +-- +-- See Note [Tuple-Spine Arrow Permutations] [ref:note-tuple-spine-permutations]. +class Arrow ar => YankTuple (n :: Peano) (ar :: Type -> Type -> Type) s t | n s -> t where + -- | Internal inductive worker pulling the @n@-th tuple slot to position 0. + yankTuple' :: ar s t + +instance Arrow ar => YankTuple 'Z ar s s where + yankTuple' = Cat.id + {-# INLINE yankTuple' #-} + +instance ( Arrow ar + , YankTuple n ar r (target, rest) + ) => YankTuple ('S n) ar (a, r) (target, (a, rest)) where + yankTuple' = arr (\(a, (target, rest)) -> (target, (a, rest))) Cat.. second (yankTuple' @n @ar) + {-# INLINE yankTuple' #-} + +-- | User-facing tuple slot yank for any 'Arrow'. +yankTuple :: forall (n :: Nat) ar s t. + YankTuple (ToPeano n) ar s t => ar s t +yankTuple = yankTuple' @(ToPeano n) @ar +{-# INLINE yankTuple #-} + +-- | Arbitrary permutation of slots in a right-nested tuple spine for an 'Arrow'. +-- +-- See Note [Tuple-Spine Arrow Permutations] [ref:note-tuple-spine-permutations]. +class Arrow ar => PermuteTuple (ps :: [Peano]) (ar :: Type -> Type -> Type) s t | ps s -> t where + -- | Internal inductive worker executing iterated tuple slot permutation. + permuteTuple' :: ar s t + +instance Arrow ar => PermuteTuple '[] ar s s where + permuteTuple' = Cat.id + {-# INLINE permuteTuple' #-} + +instance ( Arrow ar + , mid ~ (arg, rest) + , t ~ (arg, rest') + , YankTuple p ar s mid + , PermuteTuple (MapAdjust p ps) ar rest rest' + ) => PermuteTuple (p ': ps) ar s t where + permuteTuple' = second (permuteTuple' @(MapAdjust p ps) @ar) Cat.. yankTuple' @p @ar + {-# INLINE permuteTuple' #-} + +-- | User-facing tuple spine permutation for any 'Arrow'. +-- +-- Examples: +-- +-- >>> let t = (10 :: Int, (20 :: Int, (30 :: Int, ()))) +-- >>> permuteTuple @'[2, 0, 1] t +-- (30,(10,(20,()))) +permuteTuple :: forall (ns :: [Nat]) ar s t. + PermuteTuple (MapToPeano ns) ar s t => ar s t +permuteTuple = permuteTuple' @(MapToPeano ns) @ar +{-# INLINE permuteTuple #-} + +-- --------------------------------------------------------------------------- +-- 5. Profunctor Strand Permutations +-- --------------------------------------------------------------------------- + +-- | Permute the right-nested tuple input spine of a 'Profunctor' according to visible 'Nat' list @ns@. +-- +-- See Note [Tuple-Spine Arrow Permutations] [ref:note-tuple-spine-permutations]. +permuteInputs :: forall (ns :: [Nat]) p s t b. + (Profunctor p, PermuteTuple (MapToPeano ns) (->) s t) => p t b -> p s b +permuteInputs = P.lmap (permuteTuple @ns) +{-# INLINE permuteInputs #-} + +-- | Permute the right-nested tuple output spine of a 'Profunctor' according to visible 'Nat' list @ns@. +-- +-- See Note [Tuple-Spine Arrow Permutations] [ref:note-tuple-spine-permutations]. +permuteOutputs :: forall (ns :: [Nat]) p a s t. + (Profunctor p, PermuteTuple (MapToPeano ns) (->) s t) => p a s -> p a t +permuteOutputs = P.rmap (permuteTuple @ns) +{-# INLINE permuteOutputs #-} + +-- | Simultaneously permute both the input and output tuple spines of a 'Profunctor'. +dimapPermute :: forall (nsIn :: [Nat]) (nsOut :: [Nat]) p sIn tIn sOut tOut. + ( Profunctor p + , PermuteTuple (MapToPeano nsIn) (->) sIn tIn + , PermuteTuple (MapToPeano nsOut) (->) sOut tOut + ) => p tIn sOut -> p sIn tOut +dimapPermute = P.dimap (permuteTuple @nsIn) (permuteTuple @nsOut) +{-# INLINE dimapPermute #-} + +-- | Swap the binary pair inputs of a 'Profunctor' strand: @p (b, a) c -> p (a, b) c@. +swapStrand :: Profunctor p => p (b, a) c -> p (a, b) c +swapStrand = P.lmap (\(a, b) -> (b, a)) +{-# INLINE swapStrand #-} + +-- --------------------------------------------------------------------------- +-- 6. Curried Effect Handler Permutations +-- --------------------------------------------------------------------------- + +-- | Permute the leading curried environment/configuration arguments of an effect handler. +-- +-- See Note [Profunctor Effect Handler Permutations] [ref:note-profunctor-handler-permutations]. +-- +-- For example, given @handler :: Env1 -> Env2 -> Env3 -> p a b@: +-- +-- @ +-- let handler' = permuteHandler @'[2, 0, 1] handler +-- -- handler' now expects: Env3 -> Env1 -> Env2 -> p a b +-- @ +permuteHandler :: forall (ns :: [Nat]) f g. + Permute (MapToPeano ns) f g => f -> g +permuteHandler = permute @ns +{-# INLINE permuteHandler #-} + +-- | Post-compose an arrow/profunctor transformation onto an @n@-ary curried effect handler. +-- +-- For example, applying a strand adapter @(p b c -> q a d)@ to @handler :: env1 -> ... -> envn -> p b c@. +compHandlerN :: forall (n :: Nat) p q a b c d f g. + ComposeN (ToPeano n) (p b c) (q a d) f g => (p b c -> q a d) -> f -> g +compHandlerN = compN @n +{-# INLINE compHandlerN #-} diff --git a/test/CoreInspection.hs b/test/CoreInspection.hs new file mode 100644 --- /dev/null +++ b/test/CoreInspection.hs @@ -0,0 +1,189 @@ +{-# LANGUAGE BlockArguments #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE TypeApplications #-} + +-- | Module: CoreInspection +-- Description: Representative pipelines for mechanical GHC Core zero-cost verification +-- +-- This module defines concrete, representative combinator pipelines over curried functions, +-- tuples, monadic bindings, contravariant syntax grids, and profunctor effect handlers. +-- +-- When compiled under @-O2@, GHC's Simplifier must beta-reduce and inline every single one of +-- these definitions down to direct lambda expressions with ZERO dictionary allocations and +-- ZERO indirect typeclass calls ($fComposeN, $fPermute, $fYank, $fPrecomposeAt, $fBindPos, etc.). +-- +-- Tested and mechanically verified against: +-- Note [Zero-Cost Inlining and Core Simplification] [ref:note-zero-cost-core-simplification]. +module CoreInspection + ( -- * Variadic Composition Fixtures + testComp2 + , testComp3 + -- * Positional Arrow Manipulation Fixtures + , testSlipr1 + , testSlipl2 + , testTwist1 + , testYank1 + , testShove2 + -- * Arbitrary Permutation Fixtures + , testPermute3 + -- * Contravariant Grid & Splicing Fixtures + , testPrecompose1 + , testSplice12 + -- * Positional Monadic Binding Fixtures + , testBind1 + , testBindPos11 + , testLiftPure2 + -- * Tuple-Spine Arrow Permutations + , testPermuteTuple3 + , testPermuteInputs + , testSwapStrand + -- * Curried Category & Handler Permutations + , testCatFlip + , testCatApply + , testCompCat2 + , testYankCat1 + , testPermuteCat3 + , testPermuteHandler3 + ) where + +import Gongju.Core + +-- --------------------------------------------------------------------------- +-- 1. Variadic Arity Composition +-- --------------------------------------------------------------------------- + +-- | Variadic composition over a binary function: simplifies to @\f g x y -> f (g x y)@. +testComp2 :: (Int -> Int) -> (Int -> Int -> Int) -> Int -> Int -> Int +testComp2 f g x y = compN @2 f g x y +{-# NOINLINE testComp2 #-} + +-- | Variadic composition over a ternary function: simplifies to @\f g x y z -> f (g x y z)@. +testComp3 :: (Int -> Int) -> (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testComp3 f g x y z = compN @3 f g x y z +{-# NOINLINE testComp3 #-} + +-- --------------------------------------------------------------------------- +-- 2. Positional Curried Arrow Manipulation +-- --------------------------------------------------------------------------- + +-- | Pull argument 1 to position 0 via 'slipr': simplifies to @\f y x -> f x y@. +testSlipr1 :: (Int -> Int -> Int) -> Int -> Int -> Int +testSlipr1 f y x = slipr @1 f y x +{-# NOINLINE testSlipr1 #-} + +-- | Push argument 0 to position 2 via 'slipl': simplifies to @\f x y z -> f z x y@. +testSlipl2 :: (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testSlipl2 f x y z = slipl @2 f x y z +{-# NOINLINE testSlipl2 #-} + +-- | Transpose adjacent arguments 1 and 2 via 'twist': simplifies to @\f x z y -> f x y z@. +testTwist1 :: (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testTwist1 f x z y = twist @1 f x z y +{-# NOINLINE testTwist1 #-} + +-- | Synonym 'yank' pulling argument 1 to position 0: simplifies to @\f y x -> f x y@. +testYank1 :: (Int -> Int -> Int) -> Int -> Int -> Int +testYank1 f y x = yank @1 f y x +{-# NOINLINE testYank1 #-} + +-- | Synonym 'shove' pushing argument 0 to position 2: simplifies to @\f x y z -> f z x y@. +testShove2 :: (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testShove2 f x y z = shove @2 f x y z +{-# NOINLINE testShove2 #-} + +-- --------------------------------------------------------------------------- +-- 3. Arbitrary Permutations +-- --------------------------------------------------------------------------- + +-- | Permute ternary arguments @'[2, 0, 1]@: simplifies to @\f z x y -> f x y z@. +testPermute3 :: (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testPermute3 f z x y = permute @'[2, 0, 1] f z x y +{-# NOINLINE testPermute3 #-} + +-- --------------------------------------------------------------------------- +-- 4. Contravariant Syntax Grids & 2D Splicing +-- --------------------------------------------------------------------------- + +-- | Precompose at argument slot 1: simplifies to @\h f x y -> f x (h y)@. +testPrecompose1 :: (Int -> Int) -> (Int -> Int -> Int) -> Int -> Int -> Int +testPrecompose1 h f x y = precomposeAt @1 h f x y +{-# NOINLINE testPrecompose1 #-} + +-- | Splice a binary function into slot 1 of a ternary function: +-- simplifies to @\h f x u v z -> f x (h u v) z@. +testSplice12 :: (Int -> Int -> Int) -> (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int -> Int +testSplice12 h f x u v z = spliceAt @1 @2 h f x u v z +{-# NOINLINE testSplice12 #-} + +-- --------------------------------------------------------------------------- +-- 5. Positional Monadic Binding +-- --------------------------------------------------------------------------- + +-- | Monadic bind at slot 1: simplifies to direct pattern matching on 'mb'. +testBind1 :: (Int -> Int -> Maybe Int) -> Maybe Int -> Int -> Maybe Int +testBind1 f mb x = bindAt @1 f mb x +{-# NOINLINE testBind1 #-} + +-- | Interior monadic bind at slot 1 with 1 trailing argument: +-- simplifies to direct pattern matching on 'mb' and application to 'z'. +testBindPos11 :: (Int -> Int -> Int -> Maybe Int) -> Maybe Int -> Int -> Int -> Maybe Int +testBindPos11 f mb x z = bindPos @1 @1 f mb x z +{-# NOINLINE testBindPos11 #-} + +-- | Pure lifting of binary function into 'Monad': simplifies to @\f x y -> Just (f x y)@. +testLiftPure2 :: (Int -> Int -> Int) -> Int -> Int -> Maybe Int +testLiftPure2 f x y = liftPureN @2 f x y +{-# NOINLINE testLiftPure2 #-} + +-- --------------------------------------------------------------------------- +-- 6. Right-Nested Tuple-Spine Arrow Permutations +-- --------------------------------------------------------------------------- + +-- | Reorder right-nested 3-tuple spine: simplifies to direct nested unboxing and tuple construction. +testPermuteTuple3 :: (Int, (Int, (Int, ()))) -> (Int, (Int, (Int, ()))) +testPermuteTuple3 t = permuteTuple @'[2, 0, 1] t +{-# NOINLINE testPermuteTuple3 #-} + +-- | Reorder input tuple spine of a profunctor strand: simplifies to direct projection into @p@. +testPermuteInputs :: ((Int, (Int, (Int, ()))) -> Int) -> (Int, (Int, (Int, ()))) -> Int +testPermuteInputs p inp = permuteInputs @'[2, 0, 1] p inp +{-# NOINLINE testPermuteInputs #-} + +-- | Swap inputs of binary pair profunctor strand: simplifies to @\p inp -> p (case inp of (a, b) -> (b, a))@. +testSwapStrand :: ((Int, Int) -> Int) -> (Int, Int) -> Int +testSwapStrand p inp = swapStrand p inp +{-# NOINLINE testSwapStrand #-} + +-- --------------------------------------------------------------------------- +-- 7. Curried Category & Effect Handler Permutations +-- --------------------------------------------------------------------------- + +-- | Curried category morphism argument swap: simplifies to @\f y x -> f x y@. +testCatFlip :: (Int -> Int -> Int) -> Int -> Int -> Int +testCatFlip f y x = catFlip f y x +{-# NOINLINE testCatFlip #-} + +-- | Bridge category morphism application: simplifies to @\f x y -> f x y@. +testCatApply :: (Int -> Int -> Int) -> Int -> Int -> Int +testCatApply f x y = catApply f x y +{-# NOINLINE testCatApply #-} + +-- | Curried category arity composition: simplifies to @\g f x y z -> g (f x y z)@. +testCompCat2 :: (Int -> Int) -> (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testCompCat2 g f x y z = compCatN @2 g f x y z +{-# NOINLINE testCompCat2 #-} + +-- | Pull category input at position 1 forward: simplifies to @\f y x -> f x y@. +testYankCat1 :: (Int -> Int -> Int) -> Int -> Int -> Int +testYankCat1 f y x = yankCat @1 f y x +{-# NOINLINE testYankCat1 #-} + +-- | Arbitrary category input permutation: simplifies to @\f z x y -> f x y z@. +testPermuteCat3 :: (Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int +testPermuteCat3 f z x y = permuteCat @'[2, 0, 1] f z x y +{-# NOINLINE testPermuteCat3 #-} + +-- | Effect handler environment parameter permutation: simplifies to @\h z x y env -> h x y z env@. +testPermuteHandler3 :: (Int -> Int -> Int -> Int -> Int) -> Int -> Int -> Int -> Int -> Int +testPermuteHandler3 h z x y env = permuteHandler @'[2, 0, 1] h z x y env +{-# NOINLINE testPermuteHandler3 #-} diff --git a/test/Main.hs b/test/Main.hs new file mode 100644 --- /dev/null +++ b/test/Main.hs @@ -0,0 +1,521 @@ +{-# LANGUAGE BlockArguments #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RequiredTypeArguments #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TupleSections #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} + +-- | Test Suite for Gongju: Grand Unified Open-World Tape Engine and Permutation Library +-- +-- Validates: +-- * Peano natural transformations and bidirectional fundep inference. +-- * Variadic composition and open-world tape execution via visible-forall (.@). +-- * Positional combinators (slipr, slipl, twist) and arbitrary permutation (permute). +-- * Indexed monad and comonad transitions (IxFunctor, IxPointed, IxApplicative, IxMonad). +-- * Canonical comonads, distributive functors, and representable commute laws. +-- * Canonical adjunctions with dual annihilation (zapLR, zapRL, unit, counit). +-- * Canonical Kan extensions (Ran, Lan), Yoneda fusion, and Codensity CPS optimizations. +-- * Canonical profunctors with contravariant/covariant slot mappings. +module Main (main) where + +import Test.Hspec +import Data.Functor.Identity (Identity (..)) +import Gongju.Core +import CoreInspection + +-- | Minimal Comonad fixture for verifying cokleisli extension via 'W'. +-- Implements canonical 'Control.Comonad.Comonad'. +newtype IdW a = IdW a + deriving (Eq, Show) + +instance Functor IdW where + fmap f (IdW a) = IdW (f a) + +instance Comonad IdW where + extract (IdW a) = a + duplicate (IdW a) = IdW (IdW a) + +-- | Minimal Distributive and Representable Functor fixture (Reader functor). +-- Validates effect commutation outside a comonad via 'Dist'. +newtype ReaderR r a = ReaderR { runReaderR :: r -> a } + +instance Functor (ReaderR r) where + fmap f (ReaderR g) = ReaderR (f . g) + +instance Distributive (ReaderR r) where + distribute f = ReaderR \r -> fmap (\(ReaderR g) -> g r) f + +instance Representable (ReaderR r) where + type Rep (ReaderR r) = r + tabulate = ReaderR + index (ReaderR f) = f + +-- | Minimal Indexed State Monad fixture. +-- Implements canonical 'Data.Functor.Indexed' and 'Control.Monad.Indexed'. +newtype IxState i j a = IxState { runIxState :: i -> (a, j) } + +instance IxFunctor IxState where + imap f (IxState g) = IxState \i -> + let (a, j) = g i in (f a, j) + +instance IxPointed IxState where + ireturn a = IxState (a,) + +instance IxApplicative IxState where + iap (IxState gf) (IxState ga) = IxState \i -> + let (f, j) = gf i + (a, l) = ga j + in (f a, l) + +instance IxMonad IxState where + ibind k (IxState g) = IxState \i -> + let (a, j) = g i + in runIxState (k a) j + +main :: IO () +main = hspec do + -- Tested against Note [Peano TypeLits Bridge] [ref:note-peano-typelits-bridge] + describe "Gongju.Peano Naturals & List Type Families" do + it "converts numeric TypeLits to Peano and verifies term equality" do + show (Z :: Peano) `shouldBe` "Z" + show (S Z :: Peano) `shouldBe` "S Z" + + -- Tested against Note [Variadic Composition Bidirectional Fundeps] [ref:note-variadic-composition-fundeps] + describe "Gongju.Composition Variadic Composition & Tape Engine" do + it "compN @1 behaves identically to standard function composition (.)" do + let f = (+ 1) :: Int -> Int + g = (* 2) :: Int -> Int + compN @1 f g 5 `shouldBe` f (g 5) + + it "compN @2 composes over a 2-argument curried function" do + let f = show :: Int -> String + add2 x y = (x + y :: Int) + compN @2 f add2 10 20 `shouldBe` "30" + + it "compN @3 composes over a 3-argument curried function" do + let f = (* 2) :: Int -> Int + add3 x y z = (x + y + z :: Int) + compN @3 f add3 1 2 3 `shouldBe` 12 + + it "fmapN @2 maps through a nested functor layer" do + let nested = Just [1, 2, 3 :: Int] + fmapN @2 (+ 10) nested `shouldBe` Just [11, 12, 13] + + it "executes tape-driven composition via infix (.@) on pure arguments" do + let add3 x y z = (x + y + z :: Int) + h = ((+ 100) .@ [P, P, P]) add3 + h 10 20 30 `shouldBe` 160 + + it "executes tape-driven composition with explicit argument indices" do + let tuple3 x y z = (x, y, z) :: (Int, String, Bool) + p = (id .@ [2 # P, 0 # P, 1 # P]) tuple3 + p True (42 :: Int) "gongju" `shouldBe` (42, "gongju", True) + + it "executes tape-driven monadic binding" do + let mAction :: Int -> Int -> [Int] + mAction x y = [x + y, x * y] + mComp = (fmap show .@ [P, M]) mAction + mComp 3 [10, 20 :: Int] `shouldBe` ["[13,30]", "[23,60]"] + + -- Tested against Note [Positional Curried Arrow Manipulation] [ref:note-positional-arrow-manipulation] + describe "Gongju.Positional Combinators" do + it "slipr @1 pulls the 1st argument (0-indexed) to position 0" do + let sub x y = (x - y :: Int) + slipr @1 sub 5 20 `shouldBe` 15 + + it "slipr @2 pulls the 2nd argument (0-indexed) to position 0" do + let f x y z = (x, y, z) :: (Int, String, Bool) + slipr @2 f True 42 "hello" `shouldBe` (42, "hello", True) + + it "slipl @1 pushes the 0th argument to position 1" do + let f x y = (x - y :: Int) + slipl @1 f 5 20 `shouldBe` 15 + + it "twist @0 swaps adjacent arguments at position 0 and 1" do + let sub x y = (x - y :: Int) + twist @0 sub 5 20 `shouldBe` 15 + + -- Tested against Note [Iterated Yank Index Adjustment] [ref:note-iterated-yank-adjustment] + describe "Gongju.Permute Arbitrary Argument Permutation" do + it "permute @'[2, 0, 1] permutes a 3-argument function" do + let f x y z = (x, y, z) :: (Int, String, Bool) + permute @'[2, 0, 1] f True 10 "gongju" `shouldBe` (10, "gongju", True) + + it "permutes functions with identical argument types without ambiguity" do + let f x y z = (x - y + z :: Int) + permute @'[1, 2, 0] f 20 30 10 `shouldBe` (10 - 20 + 30) + + describe "Gongju.Indexed Transitions" do + it "composes transitions over indexed state monad" do + let step1 :: Int -> Int -> String + step1 x y = show (x + y) + comp = (imap (++ "!") .@ [P, IxM]) step1 + res = comp 10 (IxState \s -> (5 :: Int, s + 1)) + runIxState res (0 :: Int) `shouldBe` ("15!", 1 :: Int) + + describe "Gongju.Comonad & Distributive Functors" do + it "extends cokleisli functions using W tag" do + let wAction :: IdW Int -> Int -> String + wAction (IdW x) y = show (x + y) + wComp = (fmap (++ "!") .@ [W, P]) wAction + wComp (IdW 5) (10 :: Int) `shouldBe` IdW "15!" + + it "commutes a Representable effect outside a Comonad via PullRet '[Dist]" do + let g :: IdW Int -> Int -> ReaderR String Int + g (IdW baseVal) multiplier = ReaderR \env -> (baseVal + multiplier) * length env + comp = withOps [W, P, PullDist] id g + readerRes = comp (IdW 10) (5 :: Int) + runReaderR readerRes "abc" `shouldBe` IdW 45 + + -- Tested against Data.Functor.Adjunction canonical instances + describe "Gongju.Adjunction Dual Annihilation & Adjoints" do + -- Dual pairing annihilation: zapLR pairs left adjoint (,) with right adjoint (->) + it "performs dual annihilation via zapLR on ((,) e) and ((->) e)" do + let pair = (10 :: Int, length :: String -> Int) + f e = replicate e 'x' + zapLR pair f `shouldBe` 10 + + -- Dual pairing annihilation: zapRL pairs right adjoint (->) with left adjoint (,) + it "performs dual annihilation via zapRL on ((->) e) and ((,) e)" do + let pair = (10 :: Int, "hello") + f :: Int -> String -> Int + f e str = length str + e + zapRL f pair `shouldBe` 15 + + -- Adjunction counit: collapses pair of environment and accessor (e, e -> a) to a + it "applies adjunction counit via withOps [AdjC]" do + let counitTarget = (5 :: Int, (+ 10) :: Int -> Int) + comp = withOps [AdjC] id counitTarget + comp `shouldBe` 15 + + -- Tested against kan-extensions canonical Ran, Lan, Yoneda, Coyoneda, Codensity + describe "Gongju.Kan Right/Left Kan Extensions, Yoneda & Codensity" do + -- Universal counit of Right Kan extension collapses Ran g h (g a) to h a + it "counit collapses Ran to underlying functor via ranCounit" do + let ranVal = ranUnit (Identity (42 :: Int)) + runIdentity (ranCounit ranVal) `shouldBe` 42 + + -- Universal unit of Left Kan extension embeds h a into Lan g h (g a) + it "unit embeds functor into Lan via lanUnit" do + let lanVal = lanUnit (Identity (99 :: Int)) :: Lan Identity Identity (Identity Int) + runIdentity (lanCounit lanVal) `shouldBe` 99 + + -- Coyoneda allows fmap fusion without requiring Functor constraints until lowering + it "fuses mapping via Coyoneda lifting and lowering" do + let co = liftCoyoneda [1, 2, 3 :: Int] + coMapped = fmap (+ 10) co + lowerCoyoneda coMapped `shouldBe` [11, 12, 13] + + -- Yoneda provides O(1) CPS composition for arbitrary covariant functors + it "fuses mapping via Yoneda lifting and lowering" do + let yon = liftYoneda [1, 2, 3 :: Int] + yonMapped = fmap (* 2) yon + lowerYoneda yonMapped `shouldBe` [2, 4, 6] + + -- Codensity optimizes right-associated monadic bind chains into O(1) continuations + it "optimizes monad bind CPS via Codensity" do + let cod = liftCodensity (Just (100 :: Int)) + codBound = cod >>= \x -> pure (x + 23) + lowerCodensity codBound `shouldBe` Just 123 + + -- Tested against profunctors canonical Profunctor and dimap + describe "Gongju.Profunctor Contravariant/Covariant Mapping" do + -- Contravariant pre-processing of input arguments via P1 (lmap) + it "maps profunctor first slot contravariantly via mapPath @'[P1]" do + let f = (+ 10) :: Int -> Int + g = mapPath @'[P1] (* 2) f + g 5 `shouldBe` 20 + + -- Covariant post-processing of return values via P2 (rmap) + it "maps profunctor second slot covariantly via mapPath @'[P2]" do + let f = (+ 10) :: Int -> Int + g = mapPath @'[P2] (* 2) f + g 5 `shouldBe` 30 + + -- Simultaneous bidirectional transformation via dimap + it "dimaps both profunctor slots simultaneously via dimap" do + let f = (+ 10) :: Int -> Int + g = dimap (* 2) show f + g 5 `shouldBe` "20" + + -- Tested against Note [Contravariant Positional Pre-Composition] [ref:note-contravariant-precomposition] + describe "Gongju.Contravariant Positional Pre-Composition & 2D Splicing" do + it "precomposeAt @0 and (-.) pre-compose argument 0" do + let f x y = (x - y :: Int) + g = precomposeAt @0 (* 2) f + h = (* 2) -. f + g 10 3 `shouldBe` 17 + h 10 3 `shouldBe` 17 + + it "precomposeAt @1 and (-.*) pre-compose argument 1" do + let f x y z = (x + y * z :: Int) + g = precomposeAt @1 (+ 10) f + h = (+ 10) -.* f + g 5 2 3 `shouldBe` 41 + h 5 2 3 `shouldBe` 41 + + it "precomposeAt @2 and (-.**) pre-compose argument 2" do + let tuple3 x y z = (x, y, z) :: (Int, String, Bool) + g = precomposeAt @2 not tuple3 + h = not -.** tuple3 + g 10 "abc" False `shouldBe` (10, "abc", True) + h 10 "abc" False `shouldBe` (10, "abc", True) + + it "precomposeAt @3 and (-.***) pre-compose argument 3" do + let tuple4 w x y z = (w, x, y, z) :: (Int, Int, Int, Int) + g = precomposeAt @3 (* 100) tuple4 + h = (* 100) -.*** tuple4 + g 1 2 3 4 `shouldBe` (1, 2, 3, 400) + h 1 2 3 4 `shouldBe` (1, 2, 3, 400) + + it "spliceAt @1 @2 splices a binary function into slot 1 of a ternary function" do + let add3 x y z = (x + y + z :: Int) + mult2 u v = (u * v :: Int) + spliced = spliceAt @1 @2 mult2 add3 + spliced 10 3 4 5 `shouldBe` 27 + + it "spliceAt @0 @3 splices a ternary function into slot 0" do + let add2 a b = (a + b :: Int) + prod3 x y z = (x * y * z :: Int) + spliced = spliceAt @0 @3 prod3 add2 + spliced 2 3 4 10 `shouldBe` 34 + + -- Tested against Note [Contravariant Functor Alternating Parity] [ref:note-contravariant-alternating-parity] + describe "Gongju.Contravariant Alternating Parity Stacks" do + it "contramapN @1 and (<-$>) invert variance on 1-layer Predicate" do + let isPositive = Predicate (> (0 :: Int)) + p1 = contramapN @1 (* 2) isPositive + p2 = (* 2) <-$> isPositive + getPredicate p1 5 `shouldBe` True + getPredicate p1 (-1) `shouldBe` False + getPredicate p2 5 `shouldBe` True + getPredicate p2 (-1) `shouldBe` False + + it "contramapN @2 and (<-$$>) cancel variance inversion on 2-layer Predicate (covariant)" do + let pp = Predicate (\(Predicate p) -> p (10 :: Int)) :: Predicate (Predicate Int) + pp1 = contramapN @2 (* 2) pp + pp2 = (* 2) <-$$> pp + getPredicate pp1 (Predicate (> 15)) `shouldBe` True + getPredicate pp1 (Predicate (> 25)) `shouldBe` False + getPredicate pp2 (Predicate (> 15)) `shouldBe` True + getPredicate pp2 (Predicate (> 25)) `shouldBe` False + + it "contramapN @3 and (<-$$$>) invert variance on 3-layer Predicate (contravariant)" do + let ppp = Predicate (\(Predicate pp) -> pp (Predicate (> (15 :: Int)))) :: Predicate (Predicate (Predicate Int)) + ppp1 = contramapN @3 (* 2) ppp + ppp2 = (* 2) <-$$$> ppp + evalTest val = Predicate (\(Predicate p) -> p (val :: Int)) + getPredicate ppp1 (evalTest 10) `shouldBe` True + getPredicate ppp1 (evalTest 5) `shouldBe` False + getPredicate ppp2 (evalTest 10) `shouldBe` True + getPredicate ppp2 (evalTest 5) `shouldBe` False + + it "supports Divisible divide combining two predicates" do + let pEven = Predicate even :: Predicate Int + pPositive = Predicate (> 0) :: Predicate Int + pCombined = divide (\x -> (x, x)) pEven pPositive + getPredicate pCombined 4 `shouldBe` True + getPredicate pCombined 3 `shouldBe` False + getPredicate pCombined (-2) `shouldBe` False + + -- Tested against Note [Positional Monadic Curried Binding] [ref:note-positional-monadic-binding] + describe "Gongju.Monad Positional Monadic Binding" do + it "bindAt @1 and (==<<), (>>==) bind trailing argument slot 1" do + let f x y = pure (x * y) :: Maybe Int + bindAt @1 f (Just 7) 6 `shouldBe` Just 42 + (f ==<< Just 7) 6 `shouldBe` Just 42 + (Just 7 >>== f) 6 `shouldBe` Just 42 + (f ==<< Nothing) 6 `shouldBe` Nothing + + it "bindAt @2 and (===<<), (>>===) bind trailing argument slot 2" do + let add3 x y z = pure (x + y + z) :: Maybe Int + bindAt @2 add3 (Just 10) 1 2 `shouldBe` Just 13 + (add3 ===<< Just 10) 1 2 `shouldBe` Just 13 + (Just 10 >>=== add3) 1 2 `shouldBe` Just 13 + + it "bindAt @3 and (====<<), (>>====) bind trailing argument slot 3" do + let add4 w x y z = pure (w + x + y + z) :: Maybe Int + bindAt @3 add4 (Just 100) 1 2 3 `shouldBe` Just 106 + (add4 ====<< Just 100) 1 2 3 `shouldBe` Just 106 + (Just 100 >>==== add4) 1 2 3 `shouldBe` Just 106 + + it "bindPos @1 @1 and (=.=<<), (>>=.=) bind interior slot 1 of 3" do + let add3 x y z = pure (x + y + z) :: Maybe Int + bindPos @1 @1 add3 (Just 20) 1 3 `shouldBe` Just 24 + (add3 =.=<< Just 20) 1 3 `shouldBe` Just 24 + (Just 20 >>=.= add3) 1 3 `shouldBe` Just 24 + (add3 =.=<< Nothing) 1 3 `shouldBe` Nothing + + it "bindPos @0 @2 and (==.<<), (=..<<), (>>.==), (>>..=) bind interior slot 0 of 3" do + let add3 x y z = pure (x + y + z) :: Maybe Int + bindPos @0 @2 add3 (Just 10) 2 3 `shouldBe` Just 15 + (add3 ==.<< Just 10) 2 3 `shouldBe` Just 15 + (add3 =..<< Just 10) 2 3 `shouldBe` Just 15 + (Just 10 >>.== add3) 2 3 `shouldBe` Just 15 + (Just 10 >>..= add3) 2 3 `shouldBe` Just 15 + (add3 ==.<< Nothing) 2 3 `shouldBe` Nothing + + -- Tested against Note [Multi-Slot Monadic Lifting Masks] [ref:note-multislot-monadic-masks] + describe "Gongju.Monad Multi-Slot Lifting Masks" do + it "liftMask @'[MArg, PArg, MArg] sequences multiple monadic slots while preserving pure arguments" do + let f a b c = pure (a ++ ":" ++ show b ++ ":" ++ c) :: [String] + g = liftMask @'[MArg, PArg, MArg] f + g ["a", "b"] (42 :: Int) ["x", "y"] `shouldBe` ["a:42:x", "a:42:y", "b:42:x", "b:42:y"] + + it "liftMask @'[PArg, MArg] preserves pure arg 0 and binds monadic arg 1" do + let g x y = if y > 0 then Just (x * y) else Nothing :: Maybe Int + h = liftMask @'[PArg, MArg] g + h (5 :: Int) (Just 3) `shouldBe` Just 15 + h (5 :: Int) Nothing `shouldBe` Nothing + + it "liftMask @'[MArg, MArg] lifts both arguments into a monad" do + let g x y = if y > 0 then Just (x * y) else Nothing :: Maybe Int + h = liftMask @'[MArg, MArg] g + h (Just 5) (Just 3) `shouldBe` Just 15 + h Nothing (Just 3) `shouldBe` Nothing + h (Just 5) Nothing `shouldBe` Nothing + + describe "Gongju.Monad Arity-Indexed Kleisli Composition & Pure Lifting" do + it "liftPureN lifts pure functions to return monadic results" do + liftPureN @1 (+ (1 :: Int)) 5 `shouldBe` (Just 6 :: Maybe Int) + liftPureN @2 (+) (3 :: Int) 4 `shouldBe` (Just 7 :: Maybe Int) + liftPureN @3 (\x y z -> (x + y + z :: Int)) 1 2 3 `shouldBe` (Just 6 :: Maybe Int) + + it "bindKleisliN @2 and (<=<.), (.>=>) post-compose Kleisli arrows after binary functions" do + let f x y = Just (x + y :: Int) + checkEven z = if even z then Just z else Nothing + bindKleisliN @2 checkEven f 2 4 `shouldBe` Just 6 + bindKleisliN @2 checkEven f 2 3 `shouldBe` Nothing + (checkEven <=<. f) 2 4 `shouldBe` Just 6 + (checkEven <=<. f) 2 3 `shouldBe` Nothing + (f .>=> checkEven) 2 4 `shouldBe` Just 6 + (f .>=> checkEven) 2 3 `shouldBe` Nothing + + it "bindKleisliN @3 and (<=<..), (..>=>) post-compose Kleisli arrows after ternary functions" do + let add3M x y z = Just (x + y + z :: Int) + checkEven z = if even z then Just z else Nothing + bindKleisliN @3 checkEven add3M 1 2 3 `shouldBe` Just 6 + bindKleisliN @3 checkEven add3M 1 2 4 `shouldBe` Nothing + (checkEven <=<.. add3M) 1 2 3 `shouldBe` Just 6 + (checkEven <=<.. add3M) 1 2 4 `shouldBe` Nothing + (add3M ..>=> checkEven) 1 2 3 `shouldBe` Just 6 + (add3M ..>=> checkEven) 1 2 4 `shouldBe` Nothing + + -- Tested against Note [Profunctor Effect Handler Permutations] [ref:note-profunctor-handler-permutations] + describe "Gongju.Profunctor Curried Category & Handler Permutations" do + it "catFlip and catApply work over CurriedCat (->)" do + let f x y = (x - y :: Int) + catFlip f 5 20 `shouldBe` 15 + catApply f 20 5 `shouldBe` 15 + + it "compCatN composes category morphisms at the leaf" do + let f x y = \z -> (x + y + z :: Int) + g z = show (z * 2) + compCatN @2 g f 10 20 5 `shouldBe` "70" + + it "yankCat pulls curried category inputs to position 0" do + let sub3 x y z = (x - y - z :: Int) + yankCat @1 sub3 10 100 5 `shouldBe` (100 - 10 - 5) + yankCat @2 sub3 5 100 10 `shouldBe` (100 - 10 - 5) + + it "permuteCat permutes curried category inputs arbitrarily" do + let tuple3 x y z = (x, y, z) :: (Int, String, Bool) + perm = permuteCat @'[2, 0, 1] tuple3 + perm False 100 "hello" `shouldBe` (100, "hello", False) + + it "permuteHandler reorders environment parameters of an effect handler" do + let handler env1 env2 env3 = \(x :: Int) -> env1 ++ ":" ++ show env2 ++ ":" ++ env3 ++ ":" ++ show x + handler' = permuteHandler @'[2, 0, 1] handler + handler' "c" "a" (42 :: Int) 10 `shouldBe` "a:42:c:10" + + it "compHandlerN adapts profunctor strands produced by an effect handler" do + let h e1 e2 = \(x :: Int) -> show (x + e1 * e2) + adapted = compHandlerN @2 (lmap (* 2)) h + adapted 3 4 5 `shouldBe` "22" + + -- Tested against Note [Tuple-Spine Arrow Permutations] [ref:note-tuple-spine-permutations] + describe "Gongju.Profunctor Tuple-Spine Arrow & Strand Permutations" do + it "yankTuple pulls tuple slots to the head" do + let t3 = (10 :: Int, (20 :: Int, (30 :: Int, ()))) + yankTuple @0 t3 `shouldBe` t3 + yankTuple @1 t3 `shouldBe` (20, (10, (30, ()))) + yankTuple @2 t3 `shouldBe` (30, (10, (20, ()))) + + it "permuteTuple permutes right-nested tuple slots arbitrarily" do + let t3 = (10 :: Int, (20 :: Int, (30 :: Int, ()))) + permuteTuple @'[2, 0, 1] t3 `shouldBe` (30, (10, (20, ()))) + permuteTuple @'[1, 2, 0] t3 `shouldBe` (20, (30, (10, ()))) + + it "permuteInputs reorders profunctor strand input tuple spines" do + let strand = \(z, (x, (y, ()))) -> show (x * 100 + y * 10 + z :: Int) + strand' = permuteInputs @'[2, 0, 1] strand + strand' (1, (2, (3, ()))) `shouldBe` "123" + + it "permuteOutputs reorders profunctor strand output tuple spines" do + let gen = \() -> (10 :: Int, (20 :: Int, (30 :: Int, ()))) + gen' = permuteOutputs @'[2, 0, 1] gen + gen' () `shouldBe` (30, (10, (20, ()))) + + it "dimapPermute simultaneously permutes input and output tuple spines" do + let biStrand = \(y, (x, ())) -> (x ++ "!", (y + 1 :: Int, ())) + d = dimapPermute @'[1, 0] @'[1, 0] biStrand + d ("first", (100 :: Int, ())) `shouldBe` (101, ("first!", ())) + + it "swapStrand swaps binary pair inputs of a profunctor strand" do + let p = \(b, a) -> (a - b :: Int) + p (5, 20) `shouldBe` 15 + swapStrand p (5, 20) `shouldBe` (-15) + + -- Tested against Note [Zero-Cost Inlining and Core Simplification] [ref:note-zero-cost-core-simplification] + describe "Gongju.Core Zero-Cost Inspection Fixtures" do + it "testComp2 and testComp3 evaluate arity composition" do + testComp2 (* 2) (+) 10 20 `shouldBe` 60 + testComp3 (* 2) (\x y z -> x + y + z) 1 2 3 `shouldBe` 12 + + it "testSlipr1, testSlipl2, testTwist1, testYank1, testShove2 manipulate positional arguments" do + let f3 x y z = (x * 100 + y * 10 + z :: Int) + testSlipr1 (-) 5 20 `shouldBe` 15 + testYank1 (-) 5 20 `shouldBe` 15 + testSlipl2 f3 1 2 3 `shouldBe` 312 + testShove2 f3 1 2 3 `shouldBe` 312 + testTwist1 f3 1 3 2 `shouldBe` 123 + + it "testPermute3 permutes arguments [2, 0, 1]" do + let f3 x y z = (x * 100 + y * 10 + z :: Int) + testPermute3 f3 3 1 2 `shouldBe` 123 + + it "testPrecompose1 and testSplice12 perform contravariant positional pre-composition" do + testPrecompose1 (* 10) (-) 100 5 `shouldBe` 50 + testSplice12 (*) (\x y z -> x + y + z) 10 3 4 5 `shouldBe` 27 + + it "testBind1, testBindPos11, testLiftPure2 perform monadic binding and lifting" do + testBind1 (\x y -> Just (x + y)) (Just 20) 10 `shouldBe` Just 30 + testBind1 (\x y -> Just (x + y)) Nothing 10 `shouldBe` Nothing + testBindPos11 (\x y z -> Just (x + y + z)) (Just 20) 10 5 `shouldBe` Just 35 + testBindPos11 (\x y z -> Just (x + y + z)) Nothing 10 5 `shouldBe` Nothing + testLiftPure2 (+) 10 20 `shouldBe` Just 30 + + it "testPermuteTuple3, testPermuteInputs, testSwapStrand permute tuple spines and strands" do + testPermuteTuple3 (10, (20, (30, ()))) `shouldBe` (30, (10, (20, ()))) + testPermuteInputs (\(z, (x, (y, ()))) -> x * 100 + y * 10 + z) (1, (2, (3, ()))) `shouldBe` 123 + testSwapStrand (\(b, a) -> a - b) (5, 20) `shouldBe` (-15) + + it "testCatFlip, testCatApply, testCompCat2, testYankCat1, testPermuteCat3, testPermuteHandler3 manipulate category morphisms" do + let f3 x y z = (x * 100 + y * 10 + z :: Int) + f4 x y z env = (x * 1000 + y * 100 + z * 10 + env :: Int) + testCatFlip (-) 5 20 `shouldBe` 15 + testCatApply (-) 20 5 `shouldBe` 15 + testCompCat2 (* 2) (\x y z -> x + y + z) 1 2 3 `shouldBe` 12 + testYankCat1 (-) 5 20 `shouldBe` 15 + testPermuteCat3 f3 3 1 2 `shouldBe` 123 + testPermuteHandler3 f4 3 1 2 4 `shouldBe` 1234 + + + + +