dhall-1.13.0: src/Dhall/Core.hs
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE UnicodeSyntax #-}
{-# OPTIONS_GHC -Wall #-}
{-| This module contains the core calculus for the Dhall language.
Dhall is essentially a fork of the @morte@ compiler but with more built-in
functionality, better error messages, and Haskell integration
-}
module Dhall.Core (
-- * Syntax
Const(..)
, HasHome(..)
, PathType(..)
, PathHashed(..)
, PathMode(..)
, Path(..)
, Var(..)
, Chunks(..)
, Expr(..)
-- * Normalization
, alphaNormalize
, normalize
, normalizeWith
, Normalizer
, judgmentallyEqual
, subst
, shift
, isNormalized
, isNormalizedWith
, denote
-- * Pretty-printing
, pretty
-- * Miscellaneous
, internalError
, reservedIdentifiers
, escapeText
) where
#if MIN_VERSION_base(4,8,0)
#else
import Control.Applicative (Applicative(..), (<$>))
#endif
import Control.Applicative (empty)
import Crypto.Hash (SHA256)
import Data.Bifunctor (Bifunctor(..))
import Data.Foldable
import Data.HashMap.Strict.InsOrd (InsOrdHashMap)
import Data.HashSet (HashSet)
import Data.String (IsString(..))
import Data.Scientific (Scientific)
import Data.Semigroup (Semigroup(..))
import Data.Sequence (Seq, ViewL(..), ViewR(..))
import Data.Set (Set)
import Data.Text.Lazy (Text)
import Data.Text.Lazy.Builder (Builder)
import Data.Text.Prettyprint.Doc (Pretty)
import Data.Traversable
import {-# SOURCE #-} Dhall.Pretty.Internal
import Formatting.Buildable (Buildable(..))
import Numeric.Natural (Natural)
import Prelude hiding (succ)
import qualified Control.Monad
import qualified Crypto.Hash
import qualified Data.HashMap.Strict.InsOrd
import qualified Data.HashSet
import qualified Data.Sequence
import qualified Data.Set
import qualified Data.Text
import qualified Data.Text.Lazy as Text
import qualified Data.Text.Lazy.Builder as Builder
import qualified Data.Text.Prettyprint.Doc as Pretty
{-| Constants for a pure type system
The only axiom is:
> ⊦ Type : Kind
... and the valid rule pairs are:
> ⊦ Type ↝ Type : Type -- Functions from terms to terms (ordinary functions)
> ⊦ Kind ↝ Type : Type -- Functions from types to terms (polymorphic functions)
> ⊦ Kind ↝ Kind : Kind -- Functions from types to types (type constructors)
These are the same rule pairs as System Fω
Note that Dhall does not support functions from terms to types and therefore
Dhall is not a dependently typed language
-}
data Const = Type | Kind deriving (Show, Eq, Bounded, Enum)
instance Buildable Const where
build = buildConst
-- | Whether or not a path is relative to the user's home directory
data HasHome = Home | Homeless deriving (Eq, Ord, Show)
-- | The type of path to import (i.e. local vs. remote vs. environment)
data PathType
= File HasHome FilePath
-- ^ Local path
| URL Text (Maybe PathHashed)
-- ^ URL of remote resource and optional headers stored in a path
| Env Text
-- ^ Environment variable
deriving (Eq, Ord, Show)
instance Buildable PathType where
build (File Home file)
= "~/" <> build (Text.pack file)
build (File Homeless file)
| Text.isPrefixOf "./" txt
|| Text.isPrefixOf "/" txt
|| Text.isPrefixOf "../" txt
= build txt <> " "
| otherwise
= "./" <> build txt <> " "
where
txt = Text.pack file
build (URL str Nothing ) = build str <> " "
build (URL str (Just headers)) = build str <> " using " <> build headers <> " "
build (Env env) = "env:" <> build env
-- | How to interpret the path's contents (i.e. as Dhall code or raw text)
data PathMode = Code | RawText deriving (Eq, Ord, Show)
-- | A `PathType` extended with an optional hash for semantic integrity checks
data PathHashed = PathHashed
{ hash :: Maybe (Crypto.Hash.Digest SHA256)
, pathType :: PathType
} deriving (Eq, Ord, Show)
instance Buildable PathHashed where
build (PathHashed Nothing p) = build p
build (PathHashed (Just h) p) = build p <> "sha256:" <> build (show h) <> " "
-- | Path to an external resource
data Path = Path
{ pathHashed :: PathHashed
, pathMode :: PathMode
} deriving (Eq, Ord, Show)
instance Buildable Path where
build (Path {..}) = build pathHashed <> suffix
where
suffix = case pathMode of
RawText -> "as Text"
Code -> ""
instance Pretty Path where
pretty path = Pretty.pretty (Builder.toLazyText (build path))
{-| Label for a bound variable
The `Text` field is the variable's name (i.e. \"@x@\").
The `Int` field disambiguates variables with the same name if there are
multiple bound variables of the same name in scope. Zero refers to the
nearest bound variable and the index increases by one for each bound
variable of the same name going outward. The following diagram may help:
> ┌──refers to──┐
> │ │
> v │
> λ(x : Type) → λ(y : Type) → λ(x : Type) → x@0
>
> ┌─────────────────refers to─────────────────┐
> │ │
> v │
> λ(x : Type) → λ(y : Type) → λ(x : Type) → x@1
This `Int` behaves like a De Bruijn index in the special case where all
variables have the same name.
You can optionally omit the index if it is @0@:
> ┌─refers to─┐
> │ │
> v │
> λ(x : Type) → λ(y : Type) → λ(x : Type) → x
Zero indices are omitted when pretty-printing `Var`s and non-zero indices
appear as a numeric suffix.
-}
data Var = V Text !Integer
deriving (Eq, Show)
instance IsString Var where
fromString str = V (fromString str) 0
instance Buildable Var where
build = buildVar
-- | Syntax tree for expressions
data Expr s a
-- | > Const c ~ c
= Const Const
-- | > Var (V x 0) ~ x
-- > Var (V x n) ~ x@n
| Var Var
-- | > Lam x A b ~ λ(x : A) -> b
| Lam Text (Expr s a) (Expr s a)
-- | > Pi "_" A B ~ A -> B
-- > Pi x A B ~ ∀(x : A) -> B
| Pi Text (Expr s a) (Expr s a)
-- | > App f a ~ f a
| App (Expr s a) (Expr s a)
-- | > Let x Nothing r e ~ let x = r in e
-- > Let x (Just t) r e ~ let x : t = r in e
| Let Text (Maybe (Expr s a)) (Expr s a) (Expr s a)
-- | > Annot x t ~ x : t
| Annot (Expr s a) (Expr s a)
-- | > Bool ~ Bool
| Bool
-- | > BoolLit b ~ b
| BoolLit Bool
-- | > BoolAnd x y ~ x && y
| BoolAnd (Expr s a) (Expr s a)
-- | > BoolOr x y ~ x || y
| BoolOr (Expr s a) (Expr s a)
-- | > BoolEQ x y ~ x == y
| BoolEQ (Expr s a) (Expr s a)
-- | > BoolNE x y ~ x != y
| BoolNE (Expr s a) (Expr s a)
-- | > BoolIf x y z ~ if x then y else z
| BoolIf (Expr s a) (Expr s a) (Expr s a)
-- | > Natural ~ Natural
| Natural
-- | > NaturalLit n ~ +n
| NaturalLit Natural
-- | > NaturalFold ~ Natural/fold
| NaturalFold
-- | > NaturalBuild ~ Natural/build
| NaturalBuild
-- | > NaturalIsZero ~ Natural/isZero
| NaturalIsZero
-- | > NaturalEven ~ Natural/even
| NaturalEven
-- | > NaturalOdd ~ Natural/odd
| NaturalOdd
-- | > NaturalToInteger ~ Natural/toInteger
| NaturalToInteger
-- | > NaturalShow ~ Natural/show
| NaturalShow
-- | > NaturalPlus x y ~ x + y
| NaturalPlus (Expr s a) (Expr s a)
-- | > NaturalTimes x y ~ x * y
| NaturalTimes (Expr s a) (Expr s a)
-- | > Integer ~ Integer
| Integer
-- | > IntegerLit n ~ n
| IntegerLit Integer
-- | > IntegerShow ~ Integer/show
| IntegerShow
-- | > Double ~ Double
| Double
-- | > DoubleLit n ~ n
| DoubleLit Scientific
-- | > DoubleShow ~ Double/show
| DoubleShow
-- | > Text ~ Text
| Text
-- | > TextLit (Chunks [(t1, e1), (t2, e2)] t3) ~ "t1${e1}t2${e2}t3"
| TextLit (Chunks s a)
-- | > TextAppend x y ~ x ++ y
| TextAppend (Expr s a) (Expr s a)
-- | > List ~ List
| List
-- | > ListLit (Just t ) [x, y, z] ~ [x, y, z] : List t
-- > ListLit Nothing [x, y, z] ~ [x, y, z]
| ListLit (Maybe (Expr s a)) (Seq (Expr s a))
-- | > ListAppend x y ~ x # y
| ListAppend (Expr s a) (Expr s a)
-- | > ListBuild ~ List/build
| ListBuild
-- | > ListFold ~ List/fold
| ListFold
-- | > ListLength ~ List/length
| ListLength
-- | > ListHead ~ List/head
| ListHead
-- | > ListLast ~ List/last
| ListLast
-- | > ListIndexed ~ List/indexed
| ListIndexed
-- | > ListReverse ~ List/reverse
| ListReverse
-- | > Optional ~ Optional
| Optional
-- | > OptionalLit t (Just e) ~ [e] : Optional t
-- > OptionalLit t Nothing ~ [] : Optional t
| OptionalLit (Expr s a) (Maybe (Expr s a))
-- | > OptionalFold ~ Optional/fold
| OptionalFold
-- | > OptionalBuild ~ Optional/build
| OptionalBuild
-- | > Record [(k1, t1), (k2, t2)] ~ { k1 : t1, k2 : t1 }
| Record (InsOrdHashMap Text (Expr s a))
-- | > RecordLit [(k1, v1), (k2, v2)] ~ { k1 = v1, k2 = v2 }
| RecordLit (InsOrdHashMap Text (Expr s a))
-- | > Union [(k1, t1), (k2, t2)] ~ < k1 : t1 | k2 : t2 >
| Union (InsOrdHashMap Text (Expr s a))
-- | > UnionLit k v [(k1, t1), (k2, t2)] ~ < k = v | k1 : t1 | k2 : t2 >
| UnionLit Text (Expr s a) (InsOrdHashMap Text (Expr s a))
-- | > Combine x y ~ x ∧ y
| Combine (Expr s a) (Expr s a)
-- | > CombineTypes x y ~ x ⩓ y
| CombineTypes (Expr s a) (Expr s a)
-- | > CombineRight x y ~ x ⫽ y
| Prefer (Expr s a) (Expr s a)
-- | > Merge x y (Just t ) ~ merge x y : t
-- > Merge x y Nothing ~ merge x y
| Merge (Expr s a) (Expr s a) (Maybe (Expr s a))
-- | > Constructors e ~ constructors e
| Constructors (Expr s a)
-- | > Field e x ~ e.x
| Field (Expr s a) Text
-- | > Project e xs ~ e.{ xs }
| Project (Expr s a) (Set Text)
-- | > Note s x ~ e
| Note s (Expr s a)
-- | > Embed path ~ path
| Embed a
deriving (Functor, Foldable, Traversable, Show, Eq)
instance Applicative (Expr s) where
pure = Embed
(<*>) = Control.Monad.ap
instance Monad (Expr s) where
return = pure
Const a >>= _ = Const a
Var a >>= _ = Var a
Lam a b c >>= k = Lam a (b >>= k) (c >>= k)
Pi a b c >>= k = Pi a (b >>= k) (c >>= k)
App a b >>= k = App (a >>= k) (b >>= k)
Let a b c d >>= k = Let a (fmap (>>= k) b) (c >>= k) (d >>= k)
Annot a b >>= k = Annot (a >>= k) (b >>= k)
Bool >>= _ = Bool
BoolLit a >>= _ = BoolLit a
BoolAnd a b >>= k = BoolAnd (a >>= k) (b >>= k)
BoolOr a b >>= k = BoolOr (a >>= k) (b >>= k)
BoolEQ a b >>= k = BoolEQ (a >>= k) (b >>= k)
BoolNE a b >>= k = BoolNE (a >>= k) (b >>= k)
BoolIf a b c >>= k = BoolIf (a >>= k) (b >>= k) (c >>= k)
Natural >>= _ = Natural
NaturalLit a >>= _ = NaturalLit a
NaturalFold >>= _ = NaturalFold
NaturalBuild >>= _ = NaturalBuild
NaturalIsZero >>= _ = NaturalIsZero
NaturalEven >>= _ = NaturalEven
NaturalOdd >>= _ = NaturalOdd
NaturalToInteger >>= _ = NaturalToInteger
NaturalShow >>= _ = NaturalShow
NaturalPlus a b >>= k = NaturalPlus (a >>= k) (b >>= k)
NaturalTimes a b >>= k = NaturalTimes (a >>= k) (b >>= k)
Integer >>= _ = Integer
IntegerLit a >>= _ = IntegerLit a
IntegerShow >>= _ = IntegerShow
Double >>= _ = Double
DoubleLit a >>= _ = DoubleLit a
DoubleShow >>= _ = DoubleShow
Text >>= _ = Text
TextLit (Chunks a b) >>= k = TextLit (Chunks (fmap (fmap (>>= k)) a) b)
TextAppend a b >>= k = TextAppend (a >>= k) (b >>= k)
List >>= _ = List
ListLit a b >>= k = ListLit (fmap (>>= k) a) (fmap (>>= k) b)
ListAppend a b >>= k = ListAppend (a >>= k) (b >>= k)
ListBuild >>= _ = ListBuild
ListFold >>= _ = ListFold
ListLength >>= _ = ListLength
ListHead >>= _ = ListHead
ListLast >>= _ = ListLast
ListIndexed >>= _ = ListIndexed
ListReverse >>= _ = ListReverse
Optional >>= _ = Optional
OptionalLit a b >>= k = OptionalLit (a >>= k) (fmap (>>= k) b)
OptionalFold >>= _ = OptionalFold
OptionalBuild >>= _ = OptionalBuild
Record a >>= k = Record (fmap (>>= k) a)
RecordLit a >>= k = RecordLit (fmap (>>= k) a)
Union a >>= k = Union (fmap (>>= k) a)
UnionLit a b c >>= k = UnionLit a (b >>= k) (fmap (>>= k) c)
Combine a b >>= k = Combine (a >>= k) (b >>= k)
CombineTypes a b >>= k = CombineTypes (a >>= k) (b >>= k)
Prefer a b >>= k = Prefer (a >>= k) (b >>= k)
Merge a b c >>= k = Merge (a >>= k) (b >>= k) (fmap (>>= k) c)
Constructors a >>= k = Constructors (a >>= k)
Field a b >>= k = Field (a >>= k) b
Project a b >>= k = Project (a >>= k) b
Note a b >>= k = Note a (b >>= k)
Embed a >>= k = k a
instance Bifunctor Expr where
first _ (Const a ) = Const a
first _ (Var a ) = Var a
first k (Lam a b c ) = Lam a (first k b) (first k c)
first k (Pi a b c ) = Pi a (first k b) (first k c)
first k (App a b ) = App (first k a) (first k b)
first k (Let a b c d ) = Let a (fmap (first k) b) (first k c) (first k d)
first k (Annot a b ) = Annot (first k a) (first k b)
first _ Bool = Bool
first _ (BoolLit a ) = BoolLit a
first k (BoolAnd a b ) = BoolAnd (first k a) (first k b)
first k (BoolOr a b ) = BoolOr (first k a) (first k b)
first k (BoolEQ a b ) = BoolEQ (first k a) (first k b)
first k (BoolNE a b ) = BoolNE (first k a) (first k b)
first k (BoolIf a b c ) = BoolIf (first k a) (first k b) (first k c)
first _ Natural = Natural
first _ (NaturalLit a ) = NaturalLit a
first _ NaturalFold = NaturalFold
first _ NaturalBuild = NaturalBuild
first _ NaturalIsZero = NaturalIsZero
first _ NaturalEven = NaturalEven
first _ NaturalOdd = NaturalOdd
first _ NaturalToInteger = NaturalToInteger
first _ NaturalShow = NaturalShow
first k (NaturalPlus a b ) = NaturalPlus (first k a) (first k b)
first k (NaturalTimes a b ) = NaturalTimes (first k a) (first k b)
first _ Integer = Integer
first _ (IntegerLit a ) = IntegerLit a
first _ IntegerShow = IntegerShow
first _ Double = Double
first _ (DoubleLit a ) = DoubleLit a
first _ DoubleShow = DoubleShow
first _ Text = Text
first k (TextLit (Chunks a b)) = TextLit (Chunks (fmap (fmap (first k)) a) b)
first k (TextAppend a b ) = TextAppend (first k a) (first k b)
first _ List = List
first k (ListLit a b ) = ListLit (fmap (first k) a) (fmap (first k) b)
first k (ListAppend a b ) = ListAppend (first k a) (first k b)
first _ ListBuild = ListBuild
first _ ListFold = ListFold
first _ ListLength = ListLength
first _ ListHead = ListHead
first _ ListLast = ListLast
first _ ListIndexed = ListIndexed
first _ ListReverse = ListReverse
first _ Optional = Optional
first k (OptionalLit a b ) = OptionalLit (first k a) (fmap (first k) b)
first _ OptionalFold = OptionalFold
first _ OptionalBuild = OptionalBuild
first k (Record a ) = Record (fmap (first k) a)
first k (RecordLit a ) = RecordLit (fmap (first k) a)
first k (Union a ) = Union (fmap (first k) a)
first k (UnionLit a b c ) = UnionLit a (first k b) (fmap (first k) c)
first k (Combine a b ) = Combine (first k a) (first k b)
first k (CombineTypes a b ) = CombineTypes (first k a) (first k b)
first k (Prefer a b ) = Prefer (first k a) (first k b)
first k (Merge a b c ) = Merge (first k a) (first k b) (fmap (first k) c)
first k (Constructors a ) = Constructors (first k a)
first k (Field a b ) = Field (first k a) b
first k (Project a b ) = Project (first k a) b
first k (Note a b ) = Note (k a) (first k b)
first _ (Embed a ) = Embed a
second = fmap
instance IsString (Expr s a) where
fromString str = Var (fromString str)
-- | The body of an interpolated @Text@ literal
data Chunks s a = Chunks [(Builder, Expr s a)] Builder
deriving (Functor, Foldable, Traversable, Show, Eq)
instance Data.Semigroup.Semigroup (Chunks s a) where
Chunks xysL zL <> Chunks [] zR =
Chunks xysL (zL <> zR)
Chunks xysL zL <> Chunks ((x, y):xysR) zR =
Chunks (xysL ++ (zL <> x, y):xysR) zR
instance Monoid (Chunks s a) where
mempty = Chunks [] mempty
#if !(MIN_VERSION_base(4,11,0))
mappend = (<>)
#endif
instance IsString (Chunks s a) where
fromString str = Chunks [] (fromString str)
{- There is a one-to-one correspondence between the builders in this section
and the sub-parsers in "Dhall.Parser". Each builder is named after the
corresponding parser and the relationship between builders exactly matches
the relationship between parsers. This leads to the nice emergent property
of automatically getting all the parentheses and precedences right.
This approach has one major disadvantage: you can get an infinite loop if
you add a new constructor to the syntax tree without adding a matching
case the corresponding builder.
-}
-- | Generates a syntactically valid Dhall program
instance Buildable a => Buildable (Expr s a) where
build = buildExpr
instance Pretty a => Pretty (Expr s a) where
pretty = Pretty.unAnnotate . prettyExpr
{-| `shift` is used by both normalization and type-checking to avoid variable
capture by shifting variable indices
For example, suppose that you were to normalize the following expression:
> λ(a : Type) → λ(x : a) → (λ(y : a) → λ(x : a) → y) x
If you were to substitute @y@ with @x@ without shifting any variable
indices, then you would get the following incorrect result:
> λ(a : Type) → λ(x : a) → λ(x : a) → x -- Incorrect normalized form
In order to substitute @x@ in place of @y@ we need to `shift` @x@ by @1@ in
order to avoid being misinterpreted as the @x@ bound by the innermost
lambda. If we perform that `shift` then we get the correct result:
> λ(a : Type) → λ(x : a) → λ(x : a) → x@1
As a more worked example, suppose that you were to normalize the following
expression:
> λ(a : Type)
> → λ(f : a → a → a)
> → λ(x : a)
> → λ(x : a)
> → (λ(x : a) → f x x@1) x@1
The correct normalized result would be:
> λ(a : Type)
> → λ(f : a → a → a)
> → λ(x : a)
> → λ(x : a)
> → f x@1 x
The above example illustrates how we need to both increase and decrease
variable indices as part of substitution:
* We need to increase the index of the outer @x\@1@ to @x\@2@ before we
substitute it into the body of the innermost lambda expression in order
to avoid variable capture. This substitution changes the body of the
lambda expression to @(f x\@2 x\@1)@
* We then remove the innermost lambda and therefore decrease the indices of
both @x@s in @(f x\@2 x\@1)@ to @(f x\@1 x)@ in order to reflect that one
less @x@ variable is now bound within that scope
Formally, @(shift d (V x n) e)@ modifies the expression @e@ by adding @d@ to
the indices of all variables named @x@ whose indices are greater than
@(n + m)@, where @m@ is the number of bound variables of the same name
within that scope
In practice, @d@ is always @1@ or @-1@ because we either:
* increment variables by @1@ to avoid variable capture during substitution
* decrement variables by @1@ when deleting lambdas after substitution
@n@ starts off at @0@ when substitution begins and increments every time we
descend into a lambda or let expression that binds a variable of the same
name in order to avoid shifting the bound variables by mistake.
-}
shift :: Integer -> Var -> Expr s a -> Expr s a
shift _ _ (Const a) = Const a
shift d (V x n) (Var (V x' n')) = Var (V x' n'')
where
n'' = if x == x' && n <= n' then n' + d else n'
shift d (V x n) (Lam x' _A b) = Lam x' _A' b'
where
_A' = shift d (V x n ) _A
b' = shift d (V x n') b
where
n' = if x == x' then n + 1 else n
shift d (V x n) (Pi x' _A _B) = Pi x' _A' _B'
where
_A' = shift d (V x n ) _A
_B' = shift d (V x n') _B
where
n' = if x == x' then n + 1 else n
shift d v (App f a) = App f' a'
where
f' = shift d v f
a' = shift d v a
shift d (V x n) (Let f mt r e) = Let f mt' r' e'
where
e' = shift d (V x n') e
where
n' = if x == f then n + 1 else n
mt' = fmap (shift d (V x n)) mt
r' = shift d (V x n) r
shift d v (Annot a b) = Annot a' b'
where
a' = shift d v a
b' = shift d v b
shift _ _ Bool = Bool
shift _ _ (BoolLit a) = BoolLit a
shift d v (BoolAnd a b) = BoolAnd a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (BoolOr a b) = BoolOr a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (BoolEQ a b) = BoolEQ a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (BoolNE a b) = BoolNE a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (BoolIf a b c) = BoolIf a' b' c'
where
a' = shift d v a
b' = shift d v b
c' = shift d v c
shift _ _ Natural = Natural
shift _ _ (NaturalLit a) = NaturalLit a
shift _ _ NaturalFold = NaturalFold
shift _ _ NaturalBuild = NaturalBuild
shift _ _ NaturalIsZero = NaturalIsZero
shift _ _ NaturalEven = NaturalEven
shift _ _ NaturalOdd = NaturalOdd
shift _ _ NaturalToInteger = NaturalToInteger
shift _ _ NaturalShow = NaturalShow
shift d v (NaturalPlus a b) = NaturalPlus a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (NaturalTimes a b) = NaturalTimes a' b'
where
a' = shift d v a
b' = shift d v b
shift _ _ Integer = Integer
shift _ _ (IntegerLit a) = IntegerLit a
shift _ _ IntegerShow = IntegerShow
shift _ _ Double = Double
shift _ _ (DoubleLit a) = DoubleLit a
shift _ _ DoubleShow = DoubleShow
shift _ _ Text = Text
shift d v (TextLit (Chunks a b)) = TextLit (Chunks a' b)
where
a' = fmap (fmap (shift d v)) a
shift d v (TextAppend a b) = TextAppend a' b'
where
a' = shift d v a
b' = shift d v b
shift _ _ List = List
shift d v (ListLit a b) = ListLit a' b'
where
a' = fmap (shift d v) a
b' = fmap (shift d v) b
shift _ _ ListBuild = ListBuild
shift d v (ListAppend a b) = ListAppend a' b'
where
a' = shift d v a
b' = shift d v b
shift _ _ ListFold = ListFold
shift _ _ ListLength = ListLength
shift _ _ ListHead = ListHead
shift _ _ ListLast = ListLast
shift _ _ ListIndexed = ListIndexed
shift _ _ ListReverse = ListReverse
shift _ _ Optional = Optional
shift d v (OptionalLit a b) = OptionalLit a' b'
where
a' = shift d v a
b' = fmap (shift d v) b
shift _ _ OptionalFold = OptionalFold
shift _ _ OptionalBuild = OptionalBuild
shift d v (Record a) = Record a'
where
a' = fmap (shift d v) a
shift d v (RecordLit a) = RecordLit a'
where
a' = fmap (shift d v) a
shift d v (Union a) = Union a'
where
a' = fmap (shift d v) a
shift d v (UnionLit a b c) = UnionLit a b' c'
where
b' = shift d v b
c' = fmap (shift d v) c
shift d v (Combine a b) = Combine a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (CombineTypes a b) = CombineTypes a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (Prefer a b) = Prefer a' b'
where
a' = shift d v a
b' = shift d v b
shift d v (Merge a b c) = Merge a' b' c'
where
a' = shift d v a
b' = shift d v b
c' = fmap (shift d v) c
shift d v (Constructors a) = Constructors a'
where
a' = shift d v a
shift d v (Field a b) = Field a' b
where
a' = shift d v a
shift d v (Project a b) = Project a' b
where
a' = shift d v a
shift d v (Note a b) = Note a b'
where
b' = shift d v b
-- The Dhall compiler enforces that all embedded values are closed expressions
-- and `shift` does nothing to a closed expression
shift _ _ (Embed p) = Embed p
{-| Substitute all occurrences of a variable with an expression
> subst x C B ~ B[x := C]
-}
subst :: Var -> Expr s a -> Expr s a -> Expr s a
subst _ _ (Const a) = Const a
subst (V x n) e (Lam y _A b) = Lam y _A' b'
where
_A' = subst (V x n ) e _A
b' = subst (V x n') (shift 1 (V y 0) e) b
n' = if x == y then n + 1 else n
subst (V x n) e (Pi y _A _B) = Pi y _A' _B'
where
_A' = subst (V x n ) e _A
_B' = subst (V x n') (shift 1 (V y 0) e) _B
n' = if x == y then n + 1 else n
subst v e (App f a) = App f' a'
where
f' = subst v e f
a' = subst v e a
subst v e (Var v') = if v == v' then e else Var v'
subst (V x n) e (Let f mt r b) = Let f mt' r' b'
where
b' = subst (V x n') (shift 1 (V f 0) e) b
where
n' = if x == f then n + 1 else n
mt' = fmap (subst (V x n) e) mt
r' = subst (V x n) e r
subst x e (Annot a b) = Annot a' b'
where
a' = subst x e a
b' = subst x e b
subst _ _ Bool = Bool
subst _ _ (BoolLit a) = BoolLit a
subst x e (BoolAnd a b) = BoolAnd a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (BoolOr a b) = BoolOr a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (BoolEQ a b) = BoolEQ a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (BoolNE a b) = BoolNE a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (BoolIf a b c) = BoolIf a' b' c'
where
a' = subst x e a
b' = subst x e b
c' = subst x e c
subst _ _ Natural = Natural
subst _ _ (NaturalLit a) = NaturalLit a
subst _ _ NaturalFold = NaturalFold
subst _ _ NaturalBuild = NaturalBuild
subst _ _ NaturalIsZero = NaturalIsZero
subst _ _ NaturalEven = NaturalEven
subst _ _ NaturalOdd = NaturalOdd
subst _ _ NaturalToInteger = NaturalToInteger
subst _ _ NaturalShow = NaturalShow
subst x e (NaturalPlus a b) = NaturalPlus a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (NaturalTimes a b) = NaturalTimes a' b'
where
a' = subst x e a
b' = subst x e b
subst _ _ Integer = Integer
subst _ _ (IntegerLit a) = IntegerLit a
subst _ _ IntegerShow = IntegerShow
subst _ _ Double = Double
subst _ _ (DoubleLit a) = DoubleLit a
subst _ _ DoubleShow = DoubleShow
subst _ _ Text = Text
subst x e (TextLit (Chunks a b)) = TextLit (Chunks a' b)
where
a' = fmap (fmap (subst x e)) a
subst x e (TextAppend a b) = TextAppend a' b'
where
a' = subst x e a
b' = subst x e b
subst _ _ List = List
subst x e (ListLit a b) = ListLit a' b'
where
a' = fmap (subst x e) a
b' = fmap (subst x e) b
subst x e (ListAppend a b) = ListAppend a' b'
where
a' = subst x e a
b' = subst x e b
subst _ _ ListBuild = ListBuild
subst _ _ ListFold = ListFold
subst _ _ ListLength = ListLength
subst _ _ ListHead = ListHead
subst _ _ ListLast = ListLast
subst _ _ ListIndexed = ListIndexed
subst _ _ ListReverse = ListReverse
subst _ _ Optional = Optional
subst x e (OptionalLit a b) = OptionalLit a' b'
where
a' = subst x e a
b' = fmap (subst x e) b
subst _ _ OptionalFold = OptionalFold
subst _ _ OptionalBuild = OptionalBuild
subst x e (Record kts) = Record (fmap (subst x e) kts)
subst x e (RecordLit kvs) = RecordLit (fmap (subst x e) kvs)
subst x e (Union kts) = Union (fmap (subst x e) kts)
subst x e (UnionLit a b kts) = UnionLit a (subst x e b) (fmap (subst x e) kts)
subst x e (Combine a b) = Combine a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (CombineTypes a b) = CombineTypes a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (Prefer a b) = Prefer a' b'
where
a' = subst x e a
b' = subst x e b
subst x e (Merge a b c) = Merge a' b' c'
where
a' = subst x e a
b' = subst x e b
c' = fmap (subst x e) c
subst x e (Constructors a) = Constructors a'
where
a' = subst x e a
subst x e (Field a b) = Field a' b
where
a' = subst x e a
subst x e (Project a b) = Project a' b
where
a' = subst x e a
subst x e (Note a b) = Note a b'
where
b' = subst x e b
-- The Dhall compiler enforces that all embedded values are closed expressions
-- and `subst` does nothing to a closed expression
subst _ _ (Embed p) = Embed p
{-| α-normalize an expression by renaming all variables to @\"_\"@ and using
De Bruijn indices to distinguish them
-}
alphaNormalize :: Expr s a -> Expr s a
alphaNormalize (Const c) =
Const c
alphaNormalize (Var v) =
Var v
alphaNormalize (Lam x _A₀ b₀) =
Lam "_" _A₁ b₃
where
_A₁ = alphaNormalize _A₀
v₀ = Var (V "_" 0)
v₁ = shift 1 (V x 0) v₀
b₁ = subst (V x 0) v₁ b₀
b₂ = shift (-1) (V x 0) b₁
b₃ = alphaNormalize b₂
alphaNormalize (Pi x _A₀ _B₀) =
Pi "_" _A₁ _B₃
where
_A₁ = alphaNormalize _A₀
v₀ = Var (V "_" 0)
v₁ = shift 1 (V x 0) v₀
_B₁ = subst (V x 0) v₁ _B₀
_B₂ = shift (-1) (V x 0) _B₁
_B₃ = alphaNormalize _B₂
alphaNormalize (App f₀ a₀) =
App f₁ a₁
where
f₁ = alphaNormalize f₀
a₁ = alphaNormalize a₀
alphaNormalize (Let x (Just _A₀) a₀ b₀) =
Let "_" (Just _A₁) a₁ b₃
where
_A₁ = alphaNormalize _A₀
a₁ = alphaNormalize a₀
v₀ = Var (V "_" 0)
v₁ = shift 1 (V x 0) v₀
b₁ = subst (V x 0) v₁ b₀
b₂ = shift (-1) (V x 0) b₁
b₃ = alphaNormalize b₂
alphaNormalize (Let x Nothing a₀ b₀) =
Let "_" Nothing a₁ b₃
where
a₁ = alphaNormalize a₀
v₀ = Var (V "_" 0)
v₁ = shift 1 (V x 0) v₀
b₁ = subst (V x 0) v₁ b₀
b₂ = shift (-1) (V x 0) b₁
b₃ = alphaNormalize b₂
alphaNormalize (Annot t₀ _T₀) =
Annot t₁ _T₁
where
t₁ = alphaNormalize t₀
_T₁ = alphaNormalize _T₀
alphaNormalize Bool =
Bool
alphaNormalize (BoolLit b) =
BoolLit b
alphaNormalize (BoolAnd l₀ r₀) =
BoolAnd l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (BoolOr l₀ r₀) =
BoolOr l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (BoolEQ l₀ r₀) =
BoolEQ l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (BoolNE l₀ r₀) =
BoolNE l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (BoolIf t₀ l₀ r₀) =
BoolIf t₁ l₁ r₁
where
t₁ = alphaNormalize t₀
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize Natural =
Natural
alphaNormalize (NaturalLit n) =
NaturalLit n
alphaNormalize NaturalFold =
NaturalFold
alphaNormalize NaturalBuild =
NaturalBuild
alphaNormalize NaturalIsZero =
NaturalIsZero
alphaNormalize NaturalEven =
NaturalEven
alphaNormalize NaturalOdd =
NaturalOdd
alphaNormalize NaturalToInteger =
NaturalToInteger
alphaNormalize NaturalShow =
NaturalShow
alphaNormalize (NaturalPlus l₀ r₀) =
NaturalPlus l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (NaturalTimes l₀ r₀) =
NaturalTimes l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize Integer =
Integer
alphaNormalize (IntegerLit n) =
IntegerLit n
alphaNormalize IntegerShow =
IntegerShow
alphaNormalize Double =
Double
alphaNormalize (DoubleLit n) =
DoubleLit n
alphaNormalize DoubleShow =
DoubleShow
alphaNormalize Text =
Text
alphaNormalize (TextLit (Chunks xys₀ z)) =
TextLit (Chunks xys₁ z)
where
xys₁ = do
(x, y₀) <- xys₀
let y₁ = alphaNormalize y₀
return (x, y₁)
alphaNormalize (TextAppend l₀ r₀) =
TextAppend l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize List =
List
alphaNormalize (ListLit (Just _T₀) ts₀) =
ListLit (Just _T₁) ts₁
where
_T₁ = alphaNormalize _T₀
ts₁ = fmap alphaNormalize ts₀
alphaNormalize (ListLit Nothing ts₀) =
ListLit Nothing ts₁
where
ts₁ = fmap alphaNormalize ts₀
alphaNormalize (ListAppend l₀ r₀) =
ListAppend l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize ListBuild =
ListBuild
alphaNormalize ListFold =
ListFold
alphaNormalize ListLength =
ListLength
alphaNormalize ListHead =
ListHead
alphaNormalize ListLast =
ListLast
alphaNormalize ListIndexed =
ListIndexed
alphaNormalize ListReverse =
ListReverse
alphaNormalize Optional =
Optional
alphaNormalize (OptionalLit _T₀ ts₀) =
OptionalLit _T₁ ts₁
where
_T₁ = alphaNormalize _T₀
ts₁ = fmap alphaNormalize ts₀
alphaNormalize OptionalFold =
OptionalFold
alphaNormalize OptionalBuild =
OptionalBuild
alphaNormalize (Record kts₀) =
Record kts₁
where
kts₁ = fmap alphaNormalize kts₀
alphaNormalize (RecordLit kvs₀) =
RecordLit kvs₁
where
kvs₁ = fmap alphaNormalize kvs₀
alphaNormalize (Union kts₀) =
Union kts₁
where
kts₁ = fmap alphaNormalize kts₀
alphaNormalize (UnionLit k v₀ kts₀) =
UnionLit k v₁ kts₁
where
v₁ = alphaNormalize v₀
kts₁ = fmap alphaNormalize kts₀
alphaNormalize (Combine l₀ r₀) =
Combine l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (CombineTypes l₀ r₀) =
CombineTypes l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (Prefer l₀ r₀) =
Prefer l₁ r₁
where
l₁ = alphaNormalize l₀
r₁ = alphaNormalize r₀
alphaNormalize (Merge t₀ u₀ _T₀) =
Merge t₁ u₁ _T₁
where
t₁ = alphaNormalize t₀
u₁ = alphaNormalize u₀
_T₁ = fmap alphaNormalize _T₀
alphaNormalize (Constructors u₀) =
Constructors u₁
where
u₁ = alphaNormalize u₀
alphaNormalize (Field e₀ a) =
Field e₁ a
where
e₁ = alphaNormalize e₀
alphaNormalize (Project e₀ a) =
Project e₁ a
where
e₁ = alphaNormalize e₀
alphaNormalize (Note s e₀) =
Note s e₁
where
e₁ = alphaNormalize e₀
alphaNormalize (Embed a) =
Embed a
{-| Reduce an expression to its normal form, performing beta reduction
`normalize` does not type-check the expression. You may want to type-check
expressions before normalizing them since normalization can convert an
ill-typed expression into a well-typed expression.
However, `normalize` will not fail if the expression is ill-typed and will
leave ill-typed sub-expressions unevaluated.
-}
normalize :: Eq a => Expr s a -> Expr t a
normalize = normalizeWith (const Nothing)
{-| This function is used to determine whether folds like @Natural/fold@ or
@List/fold@ should be lazy or strict in their accumulator based on the type
of the accumulator
If this function returns `True`, then they will be strict in their
accumulator since we can guarantee an upper bound on the amount of work to
normalize the accumulator on each step of the loop. If this function
returns `False` then they will be lazy in their accumulator and only
normalize the final result at the end of the fold
-}
boundedType :: Expr s a -> Bool
boundedType Bool = True
boundedType Natural = True
boundedType Integer = True
boundedType Double = True
boundedType Text = True
boundedType (App List _) = False
boundedType (App Optional t) = boundedType t
boundedType (Record kvs) = all boundedType kvs
boundedType (Union kvs) = all boundedType kvs
boundedType _ = False
-- | Remove all `Note` constructors from an `Expr` (i.e. de-`Note`)
denote :: Expr s a -> Expr t a
denote (Note _ b ) = denote b
denote (Const a ) = Const a
denote (Var a ) = Var a
denote (Lam a b c ) = Lam a (denote b) (denote c)
denote (Pi a b c ) = Pi a (denote b) (denote c)
denote (App a b ) = App (denote a) (denote b)
denote (Let a b c d ) = Let a (fmap denote b) (denote c) (denote d)
denote (Annot a b ) = Annot (denote a) (denote b)
denote Bool = Bool
denote (BoolLit a ) = BoolLit a
denote (BoolAnd a b ) = BoolAnd (denote a) (denote b)
denote (BoolOr a b ) = BoolOr (denote a) (denote b)
denote (BoolEQ a b ) = BoolEQ (denote a) (denote b)
denote (BoolNE a b ) = BoolNE (denote a) (denote b)
denote (BoolIf a b c ) = BoolIf (denote a) (denote b) (denote c)
denote Natural = Natural
denote (NaturalLit a ) = NaturalLit a
denote NaturalFold = NaturalFold
denote NaturalBuild = NaturalBuild
denote NaturalIsZero = NaturalIsZero
denote NaturalEven = NaturalEven
denote NaturalOdd = NaturalOdd
denote NaturalToInteger = NaturalToInteger
denote NaturalShow = NaturalShow
denote (NaturalPlus a b ) = NaturalPlus (denote a) (denote b)
denote (NaturalTimes a b ) = NaturalTimes (denote a) (denote b)
denote Integer = Integer
denote (IntegerLit a ) = IntegerLit a
denote IntegerShow = IntegerShow
denote Double = Double
denote (DoubleLit a ) = DoubleLit a
denote DoubleShow = DoubleShow
denote Text = Text
denote (TextLit (Chunks a b)) = TextLit (Chunks (fmap (fmap denote) a) b)
denote (TextAppend a b ) = TextAppend (denote a) (denote b)
denote List = List
denote (ListLit a b ) = ListLit (fmap denote a) (fmap denote b)
denote (ListAppend a b ) = ListAppend (denote a) (denote b)
denote ListBuild = ListBuild
denote ListFold = ListFold
denote ListLength = ListLength
denote ListHead = ListHead
denote ListLast = ListLast
denote ListIndexed = ListIndexed
denote ListReverse = ListReverse
denote Optional = Optional
denote (OptionalLit a b ) = OptionalLit (denote a) (fmap denote b)
denote OptionalFold = OptionalFold
denote OptionalBuild = OptionalBuild
denote (Record a ) = Record (fmap denote a)
denote (RecordLit a ) = RecordLit (fmap denote a)
denote (Union a ) = Union (fmap denote a)
denote (UnionLit a b c ) = UnionLit a (denote b) (fmap denote c)
denote (Combine a b ) = Combine (denote a) (denote b)
denote (CombineTypes a b ) = CombineTypes (denote a) (denote b)
denote (Prefer a b ) = Prefer (denote a) (denote b)
denote (Merge a b c ) = Merge (denote a) (denote b) (fmap denote c)
denote (Constructors a ) = Constructors (denote a)
denote (Field a b ) = Field (denote a) b
denote (Project a b ) = Project (denote a) b
denote (Embed a ) = Embed a
{-| Reduce an expression to its normal form, performing beta reduction and applying
any custom definitions.
`normalizeWith` is designed to be used with function `typeWith`. The `typeWith`
function allows typing of Dhall functions in a custom typing context whereas
`normalizeWith` allows evaluating Dhall expressions in a custom context.
To be more precise `normalizeWith` applies the given normalizer when it finds an
application term that it cannot reduce by other means.
Note that the context used in normalization will determine the properties of normalization.
That is, if the functions in custom context are not total then the Dhall language, evaluated
with those functions is not total either.
-}
normalizeWith :: Eq a => Normalizer a -> Expr s a -> Expr t a
normalizeWith ctx e0 = loop (denote e0)
where
loop e = case e of
Const k -> Const k
Var v -> Var v
Lam x _A b -> Lam x _A' b'
where
_A' = loop _A
b' = loop b
Pi x _A _B -> Pi x _A' _B'
where
_A' = loop _A
_B' = loop _B
App f a -> case loop f of
Lam x _A b -> loop b'' -- Beta reduce
where
a' = shift 1 (V x 0) a
b' = subst (V x 0) a' b
b'' = shift (-1) (V x 0) b'
f' -> case App f' a' of
-- build/fold fusion for `List`
App (App ListBuild _) (App (App ListFold _) e') -> loop e'
-- build/fold fusion for `Natural`
App NaturalBuild (App NaturalFold e') -> loop e'
-- build/fold fusion for `Optional`
App (App OptionalBuild _) (App (App OptionalFold _) e') -> loop e'
App (App (App (App NaturalFold (NaturalLit n0)) t) succ') zero ->
if boundedType (loop t) then strict else lazy
where
strict = strictLoop n0
lazy = loop ( lazyLoop n0)
strictLoop !0 = loop zero
strictLoop !n = loop (App succ' (strictLoop (n - 1)))
lazyLoop !0 = zero
lazyLoop !n = App succ' (lazyLoop (n - 1))
App NaturalBuild g -> loop (App (App (App g Natural) succ) zero)
where
succ = Lam "x" Natural (NaturalPlus "x" (NaturalLit 1))
zero = NaturalLit 0
App NaturalIsZero (NaturalLit n) -> BoolLit (n == 0)
App NaturalEven (NaturalLit n) -> BoolLit (even n)
App NaturalOdd (NaturalLit n) -> BoolLit (odd n)
App NaturalToInteger (NaturalLit n) -> IntegerLit (toInteger n)
App NaturalShow (NaturalLit n) ->
TextLit (Chunks [] ("+" <> buildNatural n))
App IntegerShow (IntegerLit n) ->
TextLit (Chunks [] (buildNumber n))
App DoubleShow (DoubleLit n) ->
TextLit (Chunks [] (buildScientific n))
App (App OptionalBuild _A₀) g ->
loop (App (App (App g optional) just) nothing)
where
_A₁ = shift 1 "a" _A₀
optional = App Optional _A₀
just = Lam "a" _A₀ (OptionalLit _A₁ (pure "a"))
nothing = OptionalLit _A₀ empty
App (App ListBuild _A₀) g -> loop (App (App (App g list) cons) nil)
where
_A₁ = shift 1 "a" _A₀
list = App List _A₀
cons =
Lam "a" _A₀
(Lam "as"
(App List _A₁)
(ListAppend (ListLit Nothing (pure "a")) "as")
)
nil = ListLit (Just _A₀) empty
App (App (App (App (App ListFold _) (ListLit _ xs)) t) cons) nil ->
if boundedType (loop t) then strict else lazy
where
strict = foldr strictCons strictNil xs
lazy = loop (foldr lazyCons lazyNil xs)
strictNil = loop nil
lazyNil = nil
strictCons y ys = loop (App (App cons y) ys)
lazyCons y ys = App (App cons y) ys
App (App ListLength _) (ListLit _ ys) ->
NaturalLit (fromIntegral (Data.Sequence.length ys))
App (App ListHead t) (ListLit _ ys) -> loop (OptionalLit t m)
where
m = case Data.Sequence.viewl ys of
y :< _ -> Just y
_ -> Nothing
App (App ListLast t) (ListLit _ ys) -> loop (OptionalLit t m)
where
m = case Data.Sequence.viewr ys of
_ :> y -> Just y
_ -> Nothing
App (App ListIndexed _A₀) (ListLit _A₁ as₀) ->
loop (ListLit (Just _A₂) as₁)
where
as₁ = Data.Sequence.mapWithIndex adapt as₀
_A₂ = Record (Data.HashMap.Strict.InsOrd.fromList kts)
where
kts = [ ("index", Natural)
, ("value", _A₀)
]
adapt n a_ =
RecordLit (Data.HashMap.Strict.InsOrd.fromList kvs)
where
kvs = [ ("index", NaturalLit (fromIntegral n))
, ("value", a_)
]
App (App ListReverse t) (ListLit _ xs) ->
loop (ListLit m (Data.Sequence.reverse xs))
where
m = if Data.Sequence.null xs then Just t else Nothing
App (App (App (App (App OptionalFold _) (OptionalLit _ xs)) _) just) nothing ->
loop (maybe nothing just' xs)
where
just' = App just
_ -> case ctx (App f' a') of
Nothing -> App f' a'
Just app' -> loop app'
where
a' = loop a
Let f _ r b -> loop b''
where
r' = shift 1 (V f 0) r
b' = subst (V f 0) r' b
b'' = shift (-1) (V f 0) b'
Annot x _ -> loop x
Bool -> Bool
BoolLit b -> BoolLit b
BoolAnd x y -> decide (loop x) (loop y)
where
decide (BoolLit True ) r = r
decide (BoolLit False) _ = BoolLit False
decide l (BoolLit True ) = l
decide _ (BoolLit False) = BoolLit False
decide l r
| judgmentallyEqual l r = l
| otherwise = BoolAnd l r
BoolOr x y -> decide (loop x) (loop y)
where
decide (BoolLit False) r = r
decide (BoolLit True ) _ = BoolLit True
decide l (BoolLit False) = l
decide _ (BoolLit True ) = BoolLit True
decide l r
| judgmentallyEqual l r = l
| otherwise = BoolOr l r
BoolEQ x y -> decide (loop x) (loop y)
where
decide (BoolLit True ) r = r
decide l (BoolLit True ) = l
decide l r
| judgmentallyEqual l r = BoolLit True
| otherwise = BoolEQ l r
BoolNE x y -> decide (loop x) (loop y)
where
decide (BoolLit False) r = r
decide l (BoolLit False) = l
decide l r
| judgmentallyEqual l r = BoolLit False
| otherwise = BoolNE l r
BoolIf bool true false -> decide (loop bool) (loop true) (loop false)
where
decide (BoolLit True ) l _ = l
decide (BoolLit False) _ r = r
decide b (BoolLit True) (BoolLit False) = b
decide b l r
| judgmentallyEqual l r = l
| otherwise = BoolIf b l r
Natural -> Natural
NaturalLit n -> NaturalLit n
NaturalFold -> NaturalFold
NaturalBuild -> NaturalBuild
NaturalIsZero -> NaturalIsZero
NaturalEven -> NaturalEven
NaturalOdd -> NaturalOdd
NaturalToInteger -> NaturalToInteger
NaturalShow -> NaturalShow
NaturalPlus x y -> decide (loop x) (loop y)
where
decide (NaturalLit 0) r = r
decide l (NaturalLit 0) = l
decide (NaturalLit m) (NaturalLit n) = NaturalLit (m + n)
decide l r = NaturalPlus l r
NaturalTimes x y -> decide (loop x) (loop y)
where
decide (NaturalLit 1) r = r
decide l (NaturalLit 1) = l
decide (NaturalLit 0) _ = NaturalLit 0
decide _ (NaturalLit 0) = NaturalLit 0
decide (NaturalLit m) (NaturalLit n) = NaturalLit (m * n)
decide l r = NaturalTimes l r
Integer -> Integer
IntegerLit n -> IntegerLit n
IntegerShow -> IntegerShow
Double -> Double
DoubleLit n -> DoubleLit n
DoubleShow -> DoubleShow
Text -> Text
TextLit (Chunks xys z) ->
case mconcat chunks of
Chunks [("", x)] "" -> x
c -> TextLit c
where
chunks = concatMap process xys ++ [Chunks [] z]
process (x, y) = case loop y of
TextLit c -> [Chunks [] x, c]
y' -> [Chunks [(x, y')] mempty]
TextAppend x y -> decide (loop x) (loop y)
where
isEmpty (Chunks [] "") = True
isEmpty _ = False
decide (TextLit m) r | isEmpty m = r
decide l (TextLit n) | isEmpty n = l
decide (TextLit m) (TextLit n) = TextLit (m <> n)
decide l r = TextAppend l r
List -> List
ListLit t es -> ListLit t' es'
where
t' = fmap loop t
es' = fmap loop es
ListAppend x y -> decide (loop x) (loop y)
where
decide (ListLit _ m) r | Data.Sequence.null m = r
decide l (ListLit _ n) | Data.Sequence.null n = l
decide (ListLit t m) (ListLit _ n) = ListLit t (m <> n)
decide l r = ListAppend l r
ListBuild -> ListBuild
ListFold -> ListFold
ListLength -> ListLength
ListHead -> ListHead
ListLast -> ListLast
ListIndexed -> ListIndexed
ListReverse -> ListReverse
Optional -> Optional
OptionalLit t es -> OptionalLit t' es'
where
t' = loop t
es' = fmap loop es
OptionalFold -> OptionalFold
OptionalBuild -> OptionalBuild
Record kts -> Record kts'
where
kts' = fmap loop kts
RecordLit kvs -> RecordLit kvs'
where
kvs' = fmap loop kvs
Union kts -> Union kts'
where
kts' = fmap loop kts
UnionLit k v kvs -> UnionLit k v' kvs'
where
v' = loop v
kvs' = fmap loop kvs
Combine x y -> decide (loop x) (loop y)
where
decide (RecordLit m) r | Data.HashMap.Strict.InsOrd.null m =
r
decide l (RecordLit n) | Data.HashMap.Strict.InsOrd.null n =
l
decide (RecordLit m) (RecordLit n) =
RecordLit (Data.HashMap.Strict.InsOrd.unionWith decide m n)
decide l r =
Combine l r
CombineTypes x y -> decide (loop x) (loop y)
where
decide (Record m) r | Data.HashMap.Strict.InsOrd.null m =
r
decide l (Record n) | Data.HashMap.Strict.InsOrd.null n =
l
decide (Record m) (Record n) =
Record (Data.HashMap.Strict.InsOrd.unionWith decide m n)
decide l r =
CombineTypes l r
Prefer x y -> decide (loop x) (loop y)
where
decide (RecordLit m) r | Data.HashMap.Strict.InsOrd.null m =
r
decide l (RecordLit n) | Data.HashMap.Strict.InsOrd.null n =
l
decide (RecordLit m) (RecordLit n) =
RecordLit (Data.HashMap.Strict.InsOrd.union n m)
decide l r =
Prefer l r
Merge x y t ->
case x' of
RecordLit kvsX ->
case y' of
UnionLit kY vY _ ->
case Data.HashMap.Strict.InsOrd.lookup kY kvsX of
Just vX -> loop (App vX vY)
Nothing -> Merge x' y' t'
_ -> Merge x' y' t'
_ -> Merge x' y' t'
where
x' = loop x
y' = loop y
t' = fmap loop t
Constructors t ->
case t' of
Union kts -> RecordLit kvs
where
kvs = Data.HashMap.Strict.InsOrd.mapWithKey adapt kts
adapt k t_ = Lam k t_ (UnionLit k (Var (V k 0)) rest)
where
rest = Data.HashMap.Strict.InsOrd.delete k kts
_ -> Constructors t'
where
t' = loop t
Field r x ->
case loop r of
RecordLit kvs ->
case Data.HashMap.Strict.InsOrd.lookup x kvs of
Just v -> loop v
Nothing -> Field (RecordLit (fmap loop kvs)) x
r' -> Field r' x
Project r xs ->
case loop r of
RecordLit kvs ->
case traverse adapt (Data.Set.toList xs) of
Just s ->
loop (RecordLit kvs')
where
kvs' = Data.HashMap.Strict.InsOrd.fromList s
Nothing ->
Project (RecordLit (fmap loop kvs)) xs
where
adapt x = do
v <- Data.HashMap.Strict.InsOrd.lookup x kvs
return (x, v)
r' -> Project r' xs
Note _ e' -> loop e'
Embed a -> Embed a
{-| Returns `True` if two expressions are α-equivalent and β-equivalent and
`False` otherwise
-}
judgmentallyEqual :: Eq a => Expr s a -> Expr t a -> Bool
judgmentallyEqual eL0 eR0 = alphaBetaNormalize eL0 == alphaBetaNormalize eR0
where
alphaBetaNormalize :: Eq a => Expr s a -> Expr () a
alphaBetaNormalize = alphaNormalize . normalize
-- | Use this to wrap you embedded functions (see `normalizeWith`) to make them
-- polymorphic enough to be used.
type Normalizer a = forall s. Expr s a -> Maybe (Expr s a)
-- | Check if an expression is in a normal form given a context of evaluation.
-- Unlike `isNormalized`, this will fully normalize and traverse through the expression.
--
-- It is much more efficient to use `isNormalized`.
isNormalizedWith :: (Eq s, Eq a) => Normalizer a -> Expr s a -> Bool
isNormalizedWith ctx e = e == (normalizeWith ctx e)
-- | Quickly check if an expression is in normal form
isNormalized :: Expr s a -> Bool
isNormalized e = case denote e of
Const _ -> True
Var _ -> True
Lam _ a b -> isNormalized a && isNormalized b
Pi _ a b -> isNormalized a && isNormalized b
App f a -> isNormalized f && isNormalized a && case App f a of
App (Lam _ _ _) _ -> False
-- build/fold fusion for `List`
App (App ListBuild _) (App (App ListFold _) _) -> False
-- build/fold fusion for `Natural`
App NaturalBuild (App NaturalFold _) -> False
-- build/fold fusion for `Optional`
App (App OptionalBuild _) (App (App OptionalFold _) _) -> False
App (App (App (App NaturalFold (NaturalLit _)) _) _) _ -> False
App NaturalBuild _ -> False
App NaturalIsZero (NaturalLit _) -> False
App NaturalEven (NaturalLit _) -> False
App NaturalOdd (NaturalLit _) -> False
App NaturalShow (NaturalLit _) -> False
App NaturalToInteger (NaturalLit _) -> False
App IntegerShow (IntegerLit _) -> False
App DoubleShow (DoubleLit _) -> False
App (App OptionalBuild _) _ -> False
App (App ListBuild _) _ -> False
App (App (App (App (App ListFold _) (ListLit _ _)) _) _) _ ->
False
App (App ListLength _) (ListLit _ _) -> False
App (App ListHead _) (ListLit _ _) -> False
App (App ListLast _) (ListLit _ _) -> False
App (App ListIndexed _) (ListLit _ _) -> False
App (App ListReverse _) (ListLit _ _) -> False
App (App (App (App (App OptionalFold _) (OptionalLit _ _)) _) _) _ ->
False
_ -> True
Let _ _ _ _ -> False
Annot _ _ -> False
Bool -> True
BoolLit _ -> True
BoolAnd x y -> isNormalized x && isNormalized y &&
case x of
BoolLit _ ->
case y of
BoolLit _ -> False
_ -> True
_ -> True
BoolOr x y -> isNormalized x && isNormalized y &&
case x of
BoolLit _ ->
case y of
BoolLit _ -> False
_ -> True
_ -> True
BoolEQ x y -> isNormalized x && isNormalized y &&
case x of
BoolLit _ ->
case y of
BoolLit _ -> False
_ -> True
_ -> True
BoolNE x y -> isNormalized x && isNormalized y &&
case x of
BoolLit _ ->
case y of
BoolLit _ -> False
_ -> True
_ -> True
BoolIf b true false -> isNormalized b && case b of
BoolLit _ -> False
_ -> isNormalized true && isNormalized false
Natural -> True
NaturalLit _ -> True
NaturalFold -> True
NaturalBuild -> True
NaturalIsZero -> True
NaturalEven -> True
NaturalOdd -> True
NaturalShow -> True
NaturalToInteger -> True
NaturalPlus x y -> isNormalized x && isNormalized y &&
case x of
NaturalLit _ ->
case y of
NaturalLit _ -> False
_ -> True
_ -> True
NaturalTimes x y -> isNormalized x && isNormalized y &&
case x of
NaturalLit _ ->
case y of
NaturalLit _ -> False
_ -> True
_ -> True
Integer -> True
IntegerLit _ -> True
IntegerShow -> True
Double -> True
DoubleLit _ -> True
DoubleShow -> True
Text -> True
TextLit (Chunks xys _) -> all (all isNormalized) xys
TextAppend x y -> isNormalized x && isNormalized y &&
case x of
TextLit _ ->
case y of
TextLit _ -> False
_ -> True
_ -> True
List -> True
ListLit t es -> all isNormalized t && all isNormalized es
ListAppend x y -> isNormalized x && isNormalized y &&
case x of
ListLit _ _ ->
case y of
ListLit _ _ -> False
_ -> True
_ -> True
ListBuild -> True
ListFold -> True
ListLength -> True
ListHead -> True
ListLast -> True
ListIndexed -> True
ListReverse -> True
Optional -> True
OptionalLit t es -> isNormalized t && all isNormalized es
OptionalFold -> True
OptionalBuild -> True
Record kts -> all isNormalized kts
RecordLit kvs -> all isNormalized kvs
Union kts -> all isNormalized kts
UnionLit _ v kvs -> isNormalized v && all isNormalized kvs
Combine x y -> isNormalized x && isNormalized y && combine
where
combine = case x of
RecordLit _ -> case y of
RecordLit _ -> False
_ -> True
_ -> True
CombineTypes x y -> isNormalized x && isNormalized y && combine
where
combine = case x of
Record _ -> case y of
Record _ -> False
_ -> True
_ -> True
Prefer x y -> isNormalized x && isNormalized y && combine
where
combine = case x of
RecordLit _ -> case y of
RecordLit _ -> False
_ -> True
_ -> True
Merge x y t -> isNormalized x && isNormalized y && any isNormalized t &&
case x of
RecordLit kvsX ->
case y of
UnionLit kY _ _ ->
case Data.HashMap.Strict.InsOrd.lookup kY kvsX of
Just _ -> False
Nothing -> True
_ -> True
_ -> True
Constructors t -> isNormalized t &&
case t of
Union _ -> False
_ -> True
Field r x -> isNormalized r &&
case r of
RecordLit kvs ->
case Data.HashMap.Strict.InsOrd.lookup x kvs of
Just _ -> False
Nothing -> True
_ -> True
Project r xs -> isNormalized r &&
case r of
RecordLit kvs ->
if all (flip Data.HashMap.Strict.InsOrd.member kvs) xs
then False
else True
_ -> True
Note _ e' -> isNormalized e'
Embed _ -> True
_ERROR :: String
_ERROR = "\ESC[1;31mError\ESC[0m"
{-| Utility function used to throw internal errors that should never happen
(in theory) but that are not enforced by the type system
-}
internalError :: Data.Text.Text -> forall b . b
internalError text = error (unlines
[ _ERROR <> ": Compiler bug "
, " "
, "Explanation: This error message means that there is a bug in the Dhall compiler."
, "You didn't do anything wrong, but if you would like to see this problem fixed "
, "then you should report the bug at: "
, " "
, "https://github.com/dhall-lang/dhall-haskell/issues "
, " "
, "Please include the following text in your bug report: "
, " "
, "``` "
, Data.Text.unpack text <> " "
, "``` "
] )
-- | The set of reserved identifiers for the Dhall language
reservedIdentifiers :: HashSet Text
reservedIdentifiers =
Data.HashSet.fromList
[ "let"
, "in"
, "Type"
, "Kind"
, "forall"
, "Bool"
, "True"
, "False"
, "merge"
, "if"
, "then"
, "else"
, "as"
, "using"
, "constructors"
, "Natural"
, "Natural/fold"
, "Natural/build"
, "Natural/isZero"
, "Natural/even"
, "Natural/odd"
, "Natural/toInteger"
, "Natural/show"
, "Integer"
, "Integer/show"
, "Double"
, "Double/show"
, "Text"
, "List"
, "List/build"
, "List/fold"
, "List/length"
, "List/head"
, "List/last"
, "List/indexed"
, "List/reverse"
, "Optional"
, "Optional/build"
, "Optional/fold"
]