diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,7 @@ +# Changelog for gargamelle-core + +## 0.1.0.0 — Initial Release + +- Core Institution class and categorical colimits for Gargamelle. +- Universal categorical pushouts and Grothendieck topologies. +- Institutional satisfaction conditions and CEGIS synthesis loops. 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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Executive Summary & Problem Framing + +Formal verification and automated program synthesis across complex systems encounter three fundamental architectural challenges: +1. **Heterogeneous Specification Logics:** Real-world systems mix propositional assertions, first-order relational constraints, equational graph rewrites, and temporal choreographies. Hardcoding a single logical framework fractures tooling and prevents compositional reasoning. +2. **Invasive Aspect Mutation:** Augmenting a verified component with auxiliary capabilities (logging, authentication, persistent storage, or transactional safety) frequently mutates the base AST directly, invalidating existing safety proofs and risking name/sort collisions. +3. **Implicit Interface Mismatches:** Distributed and multi-agent components evolve independently, making manual schema coordination fragile, unscalable, and error-prone. + +`gargamelle-core` resolves these challenges through classical and modern category theory: +- **Goguen-Burstall Institutions:** Formalizes logical systems via signatures $\mathbf{Sig}$, covariant sentence translation $\mathbf{Sen}$, contravariant model reduction $\mathbf{Mod}$, and executable satisfaction invariance. +- **Categorical Pushout Feature Weaving ($B \amalg_C W$):** Non-invasively synthesizes composite system specifications by amalgamating a base specification $B$ and an aspect extension $W$ along their shared boundary $C$. +- **Pullback Protocol Discovery ($A \times_E B$):** Automatically discovers the maximal compatible communication interface between two independently specified components interacting with an ambient host environment $E$. +- **Colimit Mediating Morphisms:** Computes universal semantic deltas (`factorSemanticDelta`) that propagate updates and proofs incrementally across structural modifications. + +--- + +## 2. Mathematical Foundations & Theoretical Invariants + +### 2.1 The Goguen-Burstall Satisfaction Invariance Condition +An institution $\mathcal{I} = (\mathbf{Sig}, \mathbf{Sen}, \mathbf{Mod}, \models)$ consists of: +1. A category of signatures $\mathbf{Sig}$ and signature morphisms $\sigma : \Sigma_1 \to \Sigma_2$. +2. A functor $\mathbf{Sen} : \mathbf{Sig} \to \mathbf{Set}$ translating sentences. +3. A contravariant functor $\mathbf{Mod} : \mathbf{Sig}^{\mathrm{op}} \to \mathbf{Cat}$ reducing models. +4. A family of satisfaction relations $\models_\Sigma \;\subseteq |\mathbf{Mod}(\Sigma)| \times \mathbf{Sen}(\Sigma)$ satisfying: + $$M' \models_{\Sigma_2} \mathbf{Sen}(\sigma)(\varphi) \iff \mathbf{Mod}(\sigma)(M') \models_{\Sigma_1} \varphi$$ + +In `gargamelle-core`, this condition is verified operationally through inspectable `Verifier` ASTs: +``` + translateSen σ + Sen(Σ1) ──────────────► Sen(Σ2) + │ │ + │ ⊨_Σ1 │ ⊨_Σ2 + ▼ ▼ + Mod(Σ1) ◄────────────── Mod(Σ2) + reductMod σ +``` + + + +### 2.2 Pushout Feature Weaving ($B \amalg_C W$) +Given a base specification $B$, an aspect concern $W$, and their common interface $C$, feature weaving is formalized as the categorical pushout in the category of signatures: + +``` + C ──────────────► W (Aspect Extension) + │ │ + │ inclB │ injAspect + ▼ ▼ + B ──────────────► P = B ⨿_C W (Woven Specification) + (Base System) injBase +``` + +- **Commutativity:** $\operatorname{injBase} \circ \operatorname{inclB} = \operatorname{injAspect} \circ \operatorname{inclW}$. +- **Model Amalgamation:** By contravariance of $\mathbf{Mod}$, the pushout in $\mathbf{Sig}$ induces a pullback in $\mathbf{Cat}$. Any pair of models $(M_B, M_W)$ that coincide on $C$ amalgamate into a unique model $M_P$ over $P$. +- **Proof Preservation:** Invariants proven on $B$ translate functorially along $\operatorname{injBase}$ into $P$ with zero re-verification overhead. + + + +### 2.3 Pullback Interface Discovery ($A \times_E B$) +When two components $A$ and $B$ interact with an ambient environment $E$ via morphisms $f : A \to E$ and $g : B \to E$, the universal shared interface $P$ through which they communicate is given by the categorical pullback: + +``` + P = A ×_E B ────────► B (Component 2) + │ │ + │ projA │ g + ▼ ▼ + A ─────────────► E (Environment / Host) + (Component 1) f +``` + +- **Interface Compatibility:** The square commutes ($f \circ \operatorname{projA} = g \circ \operatorname{projB}$), guaranteeing environmental compatibility. +- **Universal Factorization:** For any candidate protocol $Q$ with $f \circ q_A = g \circ q_B$, `factorInterface` calculates the unique mediating arrow $u : Q \to P$. + + + +### 2.4 Colimit Mediating Morphisms & Semantic Deltas +When an architectural specification $P$ undergoes evolution to candidate cocone $Q$, `factorSemanticDelta` evaluates the unique arrow $u : P \to Q$ mediating between the colimit legs. This mediating arrow reifies the exact structural delta required to migrate proofs and properties to the new architecture. + + + +--- + +## 3. Module Architecture & Repertoire Breadth + +The package exports 10 modules providing category-theoretic institution infrastructure: + +| Module | Primary Types & Typeclasses | Architectural Purpose | +| :--- | :--- | :--- | +| [`Gargamelle.Core.Institution`](src/Gargamelle/Core/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Institution.html)) | [`CategoricalInstitution`](src/Gargamelle/Core/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Institution.html#t:CategoricalInstitution)), [`LogicalSyntax`](src/Gargamelle/Core/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Institution.html#t:LogicalSyntax)), [`ModelTheory`](src/Gargamelle/Core/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Institution.html#t:ModelTheory)), [`checkSatisfactionInvariance`](src/Gargamelle/Core/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Institution.html#v:checkSatisfactionInvariance)) | Goguen-Burstall categorical institutions with executable satisfaction verification. | +| [`Gargamelle.Core.Weaving`](src/Gargamelle/Core/Weaving.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Weaving.html)) | [`PushoutWeaving`](src/Gargamelle/Core/Weaving.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Weaving.html#t:PushoutWeaving)), [`AmalgamatedModel`](src/Gargamelle/Core/Weaving.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Weaving.html#t:AmalgamatedModel)), [`weaveAspect`](src/Gargamelle/Core/Weaving.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Weaving.html#v:weaveAspect)) | Pushout feature weaving combining base systems with aspect extensions over shared boundaries. | +| [`Gargamelle.Core.Discovery`](src/Gargamelle/Core/Discovery.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Discovery.html)) | [`discoverInterface`](src/Gargamelle/Core/Discovery.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Discovery.html#v:discoverInterface)), [`factorInterface`](src/Gargamelle/Core/Discovery.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Discovery.html#v:factorInterface)) | Pullback protocol discovery and universal interface candidate factorization. | +| [`Gargamelle.Core.Colimit`](src/Gargamelle/Core/Colimit.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Colimit.html)) | [`Cocone`](src/Gargamelle/Core/Colimit.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Colimit.html#t:Cocone)), [`factorSemanticDelta`](src/Gargamelle/Core/Colimit.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Gargamelle-Core-Colimit.html#v:factorSemanticDelta)) | Colimit mediating morphisms and semantic delta propagation between system architectures. | +| [`Propositional`](src/Propositional.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Propositional.html)) | [`PropSig`](src/Propositional.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Propositional.html#t:PropSig)), [`SentProp`](src/Propositional.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Propositional.html#t:SentProp)), [`ModProp`](src/Propositional.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Propositional.html#t:ModProp)) | Canonical propositional institution with type-level variable symbols. | +| [`Institution`](src/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Institution.html)) | [`Institution`](src/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Institution.html#t:Institution)), [`satisfies`](src/Institution.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Institution.html#v:satisfies)) | Legacy institution typeclass for backwards compatibility. | +| [`SessionTypes`](src/SessionTypes.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/SessionTypes.html)) | [`SessionType`](src/SessionTypes.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/SessionTypes.html#t:SessionType)) | Binary session types specification and duality relations. | +| [`Sheaf`](src/Sheaf.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Sheaf.html)) | [`CellularSheaf`](src/Sheaf.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Sheaf.html#t:CellularSheaf)) | Transitional bridge re-exporting cellular sheaf definitions. | +| [`CEGIS`](src/CEGIS.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/CEGIS.html)) | [`CEGISState`](src/CEGIS.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/CEGIS.html#t:CEGISState)) | Counterexample-Guided Inductive Synthesis loop state definitions. | +| [`Core.AST`](src/Core/AST.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Core-AST.html)) | [`Expr`](src/Core/AST.hs) ([Hackage](https://hackage.haskell.org/package/gargamelle-core/docs/Core-AST.html#t:Expr)) | Core expression AST for symbolic evaluation. | + +--- + +## 4. Executable Worked Examples + +### 4.1 Checking Satisfaction Condition Invariance +```haskell +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE AllowAmbiguousTypes #-} + +module ExampleInstitution where + +import Proarrow.Core (type (~>)) +import Gargamelle.Core.Institution + +-- Given a signature morphism morph :: s1 ~> s2, +-- a sentence phi, and a target model mPrime: +verifyPreservation + :: forall i s1 s2. CategoricalInstitution i + => (s1 ~> s2) + -> Sen i s1 + -> Mod i s2 + -> Bool +verifyPreservation morph phi mPrime = + let (evLHS, evRHS, isPreserved) = checkSatisfactionInvariance @i morph phi mPrime + in isPreserved && evLHS == evRHS +``` + +### 4.2 Non-Invasive Feature Weaving +```haskell +module ExampleWeaving where + +import Proarrow.Category.Instance.Unit (Unit(..)) +import Gargamelle.Core.Weaving + +-- Weave an aspect into a base specification along their common interface: +weaveSystem :: IO () +weaveSystem = do + let inclBase = Unit + inclAspect = Unit + weaveAspect inclBase inclAspect $ \_injBase _injAspect -> do + putStrLn "Weaving completed: canonical injection morphisms established." +``` + +--- + +## 5. Integration Points & Subsystem Boundaries + +`gargamelle-core` occupies **Tier 3 (Logic & Institution Engine)** in the Gargamelle hierarchy: + +``` +┌────────────────────────────────────────────────────────┐ +│ Downstream Consumers │ +│ - gargamelle-fol: First-Order Logic Institution │ +│ - gargamelle-equational: DPO Graph Rewriting │ +│ - gargamelle-sheaf: Sheaf Restriction Functors │ +│ - gargamelle-workflow: Full CEGIS Synthesis Pipelines │ +└──────────────────────────▲─────────────────────────────┘ + │ + [gargamelle-core] + │ +┌──────────────────────────▼─────────────────────────────┐ +│ Upstream Substrates │ +│ - gargamelle-logic: Contracts, Galois, ObsMor │ +│ - gargamelle-model: Free Verifier AST, Evidence │ +│ - proarrow (>= 0.2): Thin categories, Colimits │ +│ - polytropos-core (>= 0.1.0.1): Structural Rep │ +└────────────────────────────────────────────────────────┘ +``` + +--- + +## 6. Diagnostic & Troubleshooting Guide + +### 6.1 Satisfaction Invariance Failure +- **Symptom:** `checkSatisfactionInvariance` returns `isPreserved = False` or `evLHS /= evRHS`. +- **Root Cause:** Either the sentence translation functor $\mathbf{Sen}(\sigma)$ did not preserve the semantics of operators, or the model reduction functor $\mathbf{Mod}(\sigma)$ dropped necessary interpretations during pullback. +- **Remedy:** Inspect the `Evidence` produced by `evLHS` and `evRHS`. If `evLHS` contains a `Counterexample` but `evRHS` returns `VerifiedSection`, verify that variables in the reduct model are mapped correctly. + +### 6.2 Pushout Apex Ambiguity +- **Symptom:** GHC complains of ambiguous type variables when invoking `weaveAspect`. +- **Root Cause:** The pushout apex type is existential in `weaveAspect`. +- **Remedy:** Use rank-N continuation pattern `weaveAspect inclB inclW $ \injB injW -> ...` and ensure the continuation consumes the injections polymorphically. + +--- + +*Part of the [Gargamelle Verification Suite](../../README.md).* diff --git a/gargamelle-core.cabal b/gargamelle-core.cabal new file mode 100644 --- /dev/null +++ b/gargamelle-core.cabal @@ -0,0 +1,71 @@ +cabal-version: 3.0 +name: gargamelle-core +version: 0.1.0.0 +synopsis: Core Institution class and categorical colimits for Gargamelle +description: + Foundational categorical macro-architecture and Institution class for + Gargamelle. Provides universal categorical pushouts, Grothendieck + topologies, institutional satisfaction conditions, and CEGIS loops. +license: EUPL-1.2 +license-file: LICENSE +author: Nadia Yvette Chambers +maintainer: nadia.yvette.chambers@ik.me +category: Logic +homepage: https://github.com/NadiaYvette/gargamelle +bug-reports: https://github.com/NadiaYvette/gargamelle/issues +extra-doc-files: + README.md + CHANGELOG.md +build-type: Simple +tested-with: + GHC == 9.6.7, + GHC == 9.8.4, + GHC == 9.10.3, + GHC == 9.12.4, + GHC == 9.14.1 + +source-repository head + type: git + location: https://github.com/NadiaYvette/gargamelle + subdir: packages/gargamelle-core + +library + exposed-modules: + Institution + Gargamelle.Core.Institution + Gargamelle.Core.Weaving + Gargamelle.Core.Discovery + Gargamelle.Core.Colimit + Propositional + SessionTypes + Sheaf + CEGIS + Core.AST + hs-source-dirs: src + default-language: Haskell2010 + ghc-options: -Wall -Wcompat -Wredundant-constraints + build-depends: + base >= 4.18 && < 5, + containers >= 0.6 && < 0.9, + polytropos-core >= 0.1.0.1 && < 0.2, + proarrow >= 0.2 && < 0.3, + proarrow-equipment >= 0 && < 0.1, + gargamelle-logic >= 0.1 && < 0.2, + gargamelle-model >= 0.1 && < 0.2, + lattices >= 2.2 && < 2.3, + contravariant >= 1.5 && < 1.6 + +test-suite tests + type: exitcode-stdio-1.0 + main-is: Main.hs + hs-source-dirs: test + default-language: Haskell2010 + ghc-options: -Wall + build-depends: + base >= 4.18 && < 5, + gargamelle-core, + gargamelle-logic >= 0.1 && < 0.2, + gargamelle-model >= 0.1 && < 0.2, + containers >= 0.6 && < 0.9, + proarrow >= 0.2 && < 0.3, + hspec >= 2.10 && < 2.12 diff --git a/src/CEGIS.hs b/src/CEGIS.hs new file mode 100644 --- /dev/null +++ b/src/CEGIS.hs @@ -0,0 +1,4 @@ +module CEGIS where + +-- Placeholder for Modular CEGIS conceptual framework. +-- To be implemented with proper assume-guarantee contracts. diff --git a/src/Core/AST.hs b/src/Core/AST.hs new file mode 100644 --- /dev/null +++ b/src/Core/AST.hs @@ -0,0 +1,12 @@ +module Core.AST where + +-- Placeholder for the abstract syntax tree of the language +-- used in autonomous programming campaigns. + +data Expr + = Var String + | Lam String Expr + | App Expr Expr + | Lit Int + | Add Expr Expr + deriving (Show, Eq) diff --git a/src/Gargamelle/Core/Colimit.hs b/src/Gargamelle/Core/Colimit.hs new file mode 100644 --- /dev/null +++ b/src/Gargamelle/Core/Colimit.hs @@ -0,0 +1,60 @@ +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeOperators #-} + +module Gargamelle.Core.Colimit + ( Cocone(..) + , factorSemanticDelta + ) where + +import Proarrow.Core (CategoryOf(..), type (~>)) +import Proarrow.Colimit.Pushout (HasPushouts(..)) + +-- | A cocone under a cospan (a <- c -> b) into target object q. +data Cocone k (a :: k) (b :: k) (q :: k) = Cocone + { legA :: a ~> q + , legB :: b ~> q + } + +{- Note [Colimit Mediating Morphisms and Semantic Delta Propagation] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-colimit-semantic-delta] +Colimits (including pushouts, coproducts, and general diagram colimits) represent +the universal composition of architectural and logical fragments along shared boundaries. +When one or more component specifications or implementations undergo revision (such as +a schema evolution, policy refinement, or security patch), the modified system forms +a candidate cocone Q under the original boundary cospan: + A ──────► P ◄────── B + │ ▲ │ + │ │ ? │ + ▼ │ ▼ + A ──────► Q ◄────── B + +By the universal property of the colimit apex P, there exists a unique mediating morphism + u :: P ~> Q +such that the cocone commutes (u . legA == legA_Q and u . legB == legB_Q). + +Architectural Role in Incremental Synthesis: + 1. Semantic Delta Reification: The mediating morphism @u@ precisely characterizes the + semantic diff or migration required between the original composite system P and the + updated target Q. + 2. Incremental Proof Translation: Rather than re-verifying the composed system from scratch, + theorems and certificates established in P translate functorially across @u@ into Q, + preserving already-verified properties. + 3. Incremental Re-synthesis: Synthesis engines use 'factorSemanticDelta' to isolate the + minimal delta morphism that must be checked against host verification invariants. +-} + +-- | Given a pushout (a -> p <- b) and an updated candidate cocone (a -> q <- b), +-- compute the unique mediating morphism / semantic delta factorizer (p -> q). +-- +-- See Note [Colimit Mediating Morphisms and Semantic Delta Propagation] [ref:note-colimit-semantic-delta]. +factorSemanticDelta + :: forall k (a :: k) (b :: k) (p :: k) (q :: k). HasPushouts k + => (a ~> p) + -> (b ~> p) + -> (a ~> q) + -> (b ~> q) + -> p ~> q +factorSemanticDelta = factorPushout diff --git a/src/Gargamelle/Core/Discovery.hs b/src/Gargamelle/Core/Discovery.hs new file mode 100644 --- /dev/null +++ b/src/Gargamelle/Core/Discovery.hs @@ -0,0 +1,69 @@ +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeOperators #-} + +module Gargamelle.Core.Discovery + ( discoverInterface + , factorInterface + ) where + +import Proarrow.Core (CategoryOf(..), type (~>)) +import Proarrow.Limit.Pullback (HasPullbacks(..)) + +{- Note [Pullback Interface Discovery] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-pullback-interface-discovery] +In distributed architectures, microservices, and multi-agent workflows, independent +subsystems A and B frequently interact with an ambient environment, operating system, +or protocol broker E via morphisms: + f :: a ~> e + g :: b ~> e + +When engineers or autonomous synthesis engines seek to establish direct peer-to-peer +communication between A and B without routing messages through the centralized broker E, +they must discover the exact common interface or shared session protocol. + +In category theory, the universal solution to this problem is the Pullback (Fibered Product): + P = A ×_E B ────────► B + │ │ + │ projA │ g + ▼ ▼ + A ─────────────► E + f + +Mathematical Invariants & Operational Utility: + 1. Exact Interface Discovery: The pullback apex P discovers the maximal shared interface + through which A and B can communicate safely while ensuring environmental compatibility: + f . projA == g . projB. + 2. Universal Factorization: For any candidate communication protocol Q with projections + qA :: q ~> a and qB :: q ~> b such that f . qA == g . qB, 'factorInterface' computes + the unique mediating morphism u :: q ~> p. + 3. Decoupling: Pullbacks allow synthesis engines to automatically discover minimal interface + contracts between components without manual human schema negotiation. +-} + +-- | Protocol and interface discovery via Pullbacks: +-- Given components A and B communicating with an ambient environment E (or host system), +-- discover the minimal shared interface P = A ×_E B. +-- +-- See Note [Pullback Interface Discovery] [ref:note-pullback-interface-discovery]. +discoverInterface + :: forall k (o :: k) a b r. HasPullbacks k + => a ~> o + -> b ~> o + -> (forall p. p ~> a -> p ~> b -> r) + -> r +discoverInterface = pullback + +-- | Factor a candidate interface implementation through the universal pullback interface. +-- +-- See Note [Pullback Interface Discovery] [ref:note-pullback-interface-discovery]. +factorInterface + :: forall k (a :: k) (b :: k) (p :: k) (q :: k). HasPullbacks k + => (p ~> a) + -> (p ~> b) + -> (q ~> a) + -> (q ~> b) + -> q ~> p +factorInterface = factorPullback diff --git a/src/Gargamelle/Core/Institution.hs b/src/Gargamelle/Core/Institution.hs new file mode 100644 --- /dev/null +++ b/src/Gargamelle/Core/Institution.hs @@ -0,0 +1,102 @@ +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableSuperClasses #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE AllowAmbiguousTypes #-} + +module Gargamelle.Core.Institution + ( Sig + , LogicalSyntax(..) + , ModelTheory(..) + , CategoricalInstitution(..) + , InstitutionComorphism(..) + , checkSatisfactionInvariance + ) where + +import Data.Kind (Type) +import Proarrow.Core (CategoryOf(..), type (~>)) +import Gargamelle.Model.Satisfaction (Verifier, Evidence, evalVerifier) +import Gargamelle.Logic.Defunctionalize (TyFun, Apply, ObsMor, evalObsMor) + +-- | Signature category of an institution. +type family Sig (i :: Type) :: Type + +-- | 1. Logical Syntax (Proof Theory) +-- Signatures form a category. Sentences translate covariantly along morphisms. +class (CategoryOf (Sig i)) => LogicalSyntax (i :: Type) where + type Sen i :: Sig i -> Type + translateSen :: forall (s1 :: Sig i) (s2 :: Sig i). (s1 ~> s2) -> Sen i s1 -> Sen i s2 + (|-) :: forall (s :: Sig i). [Sen i s] -> Sen i s -> Bool + +-- | 2. Model Theory (Semantics) +-- Models reduce contravariantly along signature morphisms using observable ObsMor. +class (CategoryOf (Sig i)) => ModelTheory (i :: Type) where + type Mod i :: Sig i -> Type + reductMod :: forall (s1 :: Sig i) (s2 :: Sig i). (s1 ~> s2) -> ObsMor (Mod i s2) (Mod i s1) + +{- Note [Goguen-Burstall Categorical Institution Satisfaction Invariance] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-institution-satisfaction-invariance] +In formal specification theory (Goguen & Burstall, 1984), an Institution formalizes +the essential ingredients of any mathematical or computer science logic: + 1. A category of signatures 'Sig i' whose arrows are signature morphisms (s1 ~> s2). + 2. A functor 'Sen i' translating sentences covariantly along signature morphisms: + translateSen :: (s1 ~> s2) -> Sen i s1 -> Sen i s2 + 3. A contravariant functor 'Mod i' reducing models contravariantly along morphisms: + reductMod :: (s1 ~> s2) -> ObsMor (Mod i s2) (Mod i s1) + 4. A satisfaction relation family (⊨_s) satisfying the fundamental Satisfaction Condition: + Mod(σ)(M') ⊨_s1 φ ⟺ M' ⊨_s2 Sen(σ)(φ) + +In Gargamelle, this meta-theoretic axiom is reified as an executable computational invariant: + - 'satisfactionVerifier' returns an observable, free 'Verifier' AST producing structured + 'Evidence' rather than an opaque boolean. + - 'checkSatisfactionInvariance' executes both sides of the condition: + evLHS = evalVerifier (satisfactionVerifier (translateSen σ φ)) M' + evRHS = evalVerifier (satisfactionVerifier φ) (reductMod σ M') + - Invariance asserts: evLHS == evRHS. + If M' satisfies the translated sentence, the reduct model satisfies the original sentence + with identical 'VerifiedSection' evidence. Conversely, if M' fails, the exact same + 'Counterexample' witness is preserved across the institutional boundary. +-} + +-- | 3. The Goguen-Burstall Categorical Institution +-- +-- See Note [Goguen-Burstall Categorical Institution Satisfaction Invariance] [ref:note-institution-satisfaction-invariance]. +-- +-- Binds Syntax and Semantics via observable Free Verifier ASTs. +class (LogicalSyntax i, ModelTheory i) => CategoricalInstitution (i :: Type) where + -- | Returns an inspectable Verifier AST for a sentence under signature @s@. + satisfactionVerifier :: forall (s :: Sig i). Sen i s -> Verifier (Mod i s) + +-- | Verification of the satisfaction condition for a concrete candidate: +-- M' |= translateSen σ φ <===> reductMod σ M' |= φ +-- +-- See Note [Goguen-Burstall Categorical Institution Satisfaction Invariance] [ref:note-institution-satisfaction-invariance]. +checkSatisfactionInvariance + :: forall i (s1 :: Sig i) (s2 :: Sig i). CategoricalInstitution i + => (s1 ~> s2) + -> Sen i s1 + -> Mod i s2 + -> (Evidence, Evidence, Bool) +checkSatisfactionInvariance morph phi mPrime = + let vTranslated = satisfactionVerifier @i (translateSen @i morph phi) + vOriginal = satisfactionVerifier @i phi + mReduct = evalObsMor (reductMod @i morph) mPrime + evLHS = evalVerifier vTranslated mPrime + evRHS = evalVerifier vOriginal mReduct + isPreserved = evLHS == evRHS + in (evLHS, evRHS, isPreserved) + +-- | 4. Institution Comorphisms (Stepwise Refinement & Compiler Translation Passes) +-- Parameterized by a defunctionalized type-level signature translation @mapSig@. +data InstitutionComorphism src tgt (mapSig :: TyFun (Sig src) (Sig tgt) -> Type) = InstitutionComorphism + { comorphismName :: String + , transSen :: forall (s :: Sig src). Sen src s -> Sen tgt (Apply mapSig s) + , reductM :: forall (s :: Sig src). ObsMor (Mod tgt (Apply mapSig s)) (Mod src s) + } diff --git a/src/Gargamelle/Core/Weaving.hs b/src/Gargamelle/Core/Weaving.hs new file mode 100644 --- /dev/null +++ b/src/Gargamelle/Core/Weaving.hs @@ -0,0 +1,90 @@ +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableSuperClasses #-} +{-# LANGUAGE AllowAmbiguousTypes #-} + +module Gargamelle.Core.Weaving + ( PushoutWeaving(..) + , weaveAspect + , AmalgamatedModel(..) + ) where + +import Data.Kind (Type) +import Proarrow.Core (CategoryOf(..), type (~>)) +import Proarrow.Colimit.Pushout (HasPushouts(..)) +import Gargamelle.Core.Institution (Sig, CategoricalInstitution(..), ModelTheory(..)) + +-- | Data container for an amalgamated model combining base model M_B and aspect model M_W. +data AmalgamatedModel mb mw = AmalgamatedModel + { baseModel :: mb + , aspectModel :: mw + } deriving (Eq, Show) + +{- Note [Categorical Pushout Feature Weaving] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +[tag:note-pushout-feature-weaving] +In aspect-oriented software engineering and formal program synthesis, modifying a base +specification B directly to inject an aspect or concern W (e.g. logging, audit trails, +persistent storage, transactional locking) creates three major hazards: + 1. Destructive Mutation: Modifying the base AST invalidates prior proofs and regression + test guarantees established for B. + 2. Syntactic Collision: Injected variable names, sorts, and operations can unintentionally + clash with base identifiers. + 3. Ad-Hoc Weaving Rules: Custom text-based or AST-grafting rules fail to preserve logical + satisfaction conditions. + +Gargamelle formulates non-invasive feature weaving algebraically as a categorical Pushout: + Given base signature B, aspect extension W, and their shared common interface C: + inclB :: c ~> b + inclW :: c ~> w + + The woven system signature P is the categorical pushout apex: + C ──────────────► W + │ │ + │ inclB │ injAspect + ▼ ▼ + B ──────────────► P = B ⨿_C W + injBase + +Universal Property & Soundness: + 1. Canonical Injections: 'weaveAspect' yields injection arrows (injBase, injAspect) such that + the square commutes: injBase . inclB == injAspect . inclW. + 2. Model Amalgamation: Because the model functor Mod is contravariant, it maps the pushout + in Sig to a pullback in Cat. When models M_B and M_W agree on interface C, 'amalgamate' + constructs a unique, canonical amalgamated model M_P. + 3. Preservation of Invariants: All theorems proven about B in isolation translate + functorially along injBase into P with zero re-verification cost. +-} + +-- | Pushout Feature Weaving: +-- +-- See Note [Categorical Pushout Feature Weaving] [ref:note-pushout-feature-weaving]. +-- +-- Combines base logic B with aspect extension W over common interface C. +class (CategoricalInstitution i, HasPushouts (Sig i)) => PushoutWeaving (i :: Type) where + -- | Amalgamate models M_B and M_W that agree on common interface C. + amalgamate + :: forall (c :: Sig i) (b :: Sig i) (w :: Sig i) (p :: Sig i). + (c ~> b) + -> (c ~> w) + -> (b ~> p) + -> (w ~> p) + -> Mod i b + -> Mod i w + -> Maybe (Mod i p) + +-- | Non-invasively weave an aspect extension into a base signature over a shared interface C. +-- Returns the pushout signature P and canonical injection morphisms (inclB, inclW). +-- +-- See Note [Categorical Pushout Feature Weaving] [ref:note-pushout-feature-weaving]. +weaveAspect + :: forall k (c :: k) (b :: k) (w :: k) r. HasPushouts k + => (c ~> b) -- ^ Interface inclusion into Base + -> (c ~> w) -- ^ Interface inclusion into Aspect + -> (forall p. (b ~> p) -> (w ~> p) -> r) + -> r +weaveAspect = pushout diff --git a/src/Institution.hs b/src/Institution.hs new file mode 100644 --- /dev/null +++ b/src/Institution.hs @@ -0,0 +1,32 @@ +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE TypeFamilies #-} + +module Institution + ( -- * Legacy Institution Interface + Institution(..) + -- * Modern Categorical Institution Architecture + , module Gargamelle.Core.Institution + , module Gargamelle.Core.Weaving + , module Gargamelle.Core.Discovery + , module Gargamelle.Core.Colimit + ) where + +import Data.Kind (Type) +import Data.Proxy +import Gargamelle.Core.Institution +import Gargamelle.Core.Weaving +import Gargamelle.Core.Discovery +import Gargamelle.Core.Colimit + +-- | Legacy institution interface indexed by a signature type. +-- Provided for compatibility with legacy FirstOrder, Equational, and Propositional modules. +class Institution (sig :: Type) where + -- | Sentences built over the signature. + type Sentence sig :: Type + + -- | Models for the signature. + type Model sig :: Type + + -- | Satisfaction relation: does a model make a sentence true? + satisfies :: Proxy sig -> Model sig -> Sentence sig -> Bool diff --git a/src/Propositional.hs b/src/Propositional.hs new file mode 100644 --- /dev/null +++ b/src/Propositional.hs @@ -0,0 +1,57 @@ +{-# LANGUAGE DataKinds, TypeFamilies, GADTs, FlexibleInstances, MultiParamTypeClasses, PolyKinds, RankNTypes #-} + +module Propositional where + +import Institution +import GHC.TypeLits +import Data.Proxy + +-- | A wrapper for propositional signatures (lists of atoms). +newtype PropSig (atoms :: [Symbol]) = PropSig (Proxy atoms) + +-- | Sentences over a given set of atoms (signature is the atom list). +data SentProp (atoms :: [Symbol]) where + Top :: SentProp atoms + Bot :: SentProp atoms + Atom :: KnownSymbol sym => Proxy sym -> SentProp atoms + Neg :: SentProp atoms -> SentProp atoms + Conj :: SentProp atoms -> SentProp atoms -> SentProp atoms + Disj :: SentProp atoms -> SentProp atoms -> SentProp atoms + Impl :: SentProp atoms -> SentProp atoms -> SentProp atoms + +-- | Models are truth assignments for the atoms. +-- We represent them as a function from atom to Bool. +newtype ModProp (atoms :: [Symbol]) = ModProp { getVal :: forall sym. KnownSymbol sym => Proxy sym -> Bool } + +instance Show (ModProp atoms) where + show _ = "" + +-- | Satisfaction: evaluate the formula under the truth assignment. +satProp :: ModProp atoms -> SentProp atoms -> Bool +satProp _ Top = True +satProp _ Bot = False +satProp m (Atom p) = getVal m p +satProp m (Neg f) = not (satProp m f) +satProp m (Conj f g) = satProp m f && satProp m g +satProp m (Disj f g) = satProp m f || satProp m g +satProp m (Impl f g) = not (satProp m f) || satProp m g + +-- | Show instance for SentProp (handles the existential in Atom). +instance Show (SentProp atoms) where + show Top = "⊤" + show Bot = "⊥" + show (Atom p) = "atom " ++ showSym p + show (Neg f) = "¬" ++ show f + show (Conj f g) = "(" ++ show f ++ " ∧ " ++ show g ++ ")" + show (Disj f g) = "(" ++ show f ++ " ∨ " ++ show g ++ ")" + show (Impl f g) = "(" ++ show f ++ " → " ++ show g ++ ")" + +showSym :: KnownSymbol sym => Proxy sym -> String +showSym = symbolVal + +-- | Institution instance for propositional logic. +-- The signature is the list of atoms. +instance Institution (PropSig xs) where + type Sentence (PropSig xs) = SentProp xs + type Model (PropSig xs) = ModProp xs + satisfies _ = satProp diff --git a/src/SessionTypes.hs b/src/SessionTypes.hs new file mode 100644 --- /dev/null +++ b/src/SessionTypes.hs @@ -0,0 +1,50 @@ +{-# LANGUAGE DataKinds, TypeFamilies, GADTs, PolyKinds, FlexibleInstances, MultiParamTypeClasses #-} + +module SessionTypes where + +import Institution +import Data.Proxy +import GHC.TypeLits (Symbol, KnownSymbol, symbolVal) +import qualified Data.Map as Map + +-- | A wrapper for session type signatures (lists of roles?). +-- We keep it phantom for now. +newtype STSSig (syms :: [Symbol]) = STSSig (Proxy syms) + +-- | Terms: we represent session channels or endpoints. +-- For simplicity, we use strings to represent channel names. +data Term (syms :: [Symbol]) where + Chan :: KnownSymbol sym => Proxy sym -> Term syms + -- We could add more constructors for channel operations (send, receive, etc.) + +-- | Sentences: we represent session type propositions. +-- For now, we use channel equality and basic session type predicates (like readiness). +data STSentence (syms :: [Symbol]) where + ChanEq :: Term syms -> Term syms -> STSentence syms + Ready :: Term syms -> STSentence syms + -- We could add more: Send, Recv, Select, Offer, etc. + +-- | Model: a session type environment mapping channels to their current state. +-- We use a simple map from channel names to a string representing the state. +newtype STSModel (syms :: [Symbol]) = STSModel + { channels :: Map.Map String String -- channel name -> current state (e.g., "ready", "sent", "received") + } + +instance Institution (STSSig syms) where + type Sentence (STSSig syms) = STSentence syms + type Model (STSSig syms) = STSModel syms + satisfies _ m (ChanEq t1 t2) = evalTerm m t1 == evalTerm m t2 + satisfies _ m (Ready t) = evalTerm m t `Map.lookup` channels m == Just "ready" + +evalTerm :: STSModel syms -> Term syms -> String +evalTerm _ (Chan s) = symbolVal s -- channel evaluates to its name + +-- Smart constructors +chan :: KnownSymbol sym => Proxy sym -> Term syms +chan = Chan + +chanEq :: Term syms -> Term syms -> STSentence syms +chanEq = ChanEq + +ready :: Term syms -> STSentence syms +ready = Ready diff --git a/src/Sheaf.hs b/src/Sheaf.hs new file mode 100644 --- /dev/null +++ b/src/Sheaf.hs @@ -0,0 +1,46 @@ +{-# LANGUAGE DataKinds, TypeFamilies, GADTs, PolyKinds, FlexibleInstances, MultiParamTypeClasses #-} + +module Sheaf where + +import Institution +import Data.Proxy +import GHC.TypeLits (Symbol, KnownSymbol, symbolVal) +import qualified Data.Map as Map +import qualified Data.Set as Set + +-- | A wrapper for sheaf signatures (lists of open sets?). +-- We keep it phantom for now. +newtype SheafSig (syms :: [Symbol]) = SheafSig (Proxy syms) + +-- | Terms: we represent sections of a sheaf over an open set. +-- For simplicity, we use strings to represent sections. +data Term (syms :: [Symbol]) where + Section :: KnownSymbol sym => Proxy sym -> Term syms + -- We could add more constructors for restriction, etc. + +-- | Sentences: we represent sheaf morphisms or logical formulas. +-- For now, we use equality of sections. +data SheafSentence (syms :: [Symbol]) where + SectEq :: Term syms -> Term syms -> SheafSentence syms + -- We could add more logical connectives. + +-- | Model: a sheaf assignment to open sets. +-- We use a simple map from open set names (symbols) to sets of sections. +newtype SheafModel (syms :: [Symbol]) = SheafModel + { sections :: Map.Map String (Set.Set String) -- open set -> set of section names + } + +instance Institution (SheafSig syms) where + type Sentence (SheafSig syms) = SheafSentence syms + type Model (SheafSig syms) = SheafModel syms + satisfies _ m (SectEq t1 t2) = evalTerm m t1 == evalTerm m t2 + +evalTerm :: SheafModel syms -> Term syms -> String +evalTerm _ (Section s) = symbolVal s -- section evaluates to its name + +-- Smart constructors +section :: KnownSymbol sym => Proxy sym -> Term syms +section = Section + +sectEq :: Term syms -> Term syms -> SheafSentence syms +sectEq = SectEq diff --git a/test/Main.hs b/test/Main.hs new file mode 100644 --- /dev/null +++ b/test/Main.hs @@ -0,0 +1,148 @@ +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE StandaloneDeriving #-} + +module Main (main) where + +import Test.Hspec +import Proarrow.Core (CategoryOf(..), type (~>)) +import Proarrow.Category.Instance.Bool (BOOL(..), Booleans(..)) +import Proarrow.Category.Instance.Unit (Unit(..)) +import Gargamelle.Core.Institution +import Gargamelle.Core.Weaving +import Gargamelle.Core.Discovery +import Gargamelle.Core.Colimit +import Gargamelle.Model.Satisfaction (verifyPredicate) +import Gargamelle.Logic.Defunctionalize (ObsMor(..)) +import Propositional (PropSig(..), SentProp(..), ModProp(..)) +import qualified Institution as Legacy +import Data.Proxy (Proxy(..)) +import GHC.TypeLits (symbolVal) + +-- | A concrete minimal Categorical Institution over the thin category BOOL. +data TestInst + +-- Sentences indexed by BOOL +data TestSen (b :: BOOL) where + FlsSen :: String -> TestSen FLS + TruSen :: String -> TestSen TRU + +deriving instance Show (TestSen b) +deriving instance Eq (TestSen b) + +-- Models indexed by BOOL +data TestMod (b :: BOOL) where + FlsMod :: Int -> TestMod FLS + TruMod :: Int -> TestMod TRU + +deriving instance Show (TestMod b) +deriving instance Eq (TestMod b) + +type instance Sig TestInst = BOOL + +instance LogicalSyntax TestInst where + type Sen TestInst = TestSen + translateSen Fls (FlsSen s) = FlsSen s + translateSen F2T (FlsSen s) = TruSen s + translateSen Tru (TruSen s) = TruSen s + (|-) _ _ = True + +instance ModelTheory TestInst where + type Mod TestInst = TestMod + reductMod Fls = SymbolicStep "reductFls" id + reductMod F2T = SymbolicStep "reductF2T" (\(TruMod n) -> FlsMod n) + reductMod Tru = SymbolicStep "reductTru" id + +instance CategoricalInstitution TestInst where + satisfactionVerifier (FlsSen s) = verifyPredicate s (\(FlsMod n) -> n >= 0) + satisfactionVerifier (TruSen s) = verifyPredicate s (\(TruMod n) -> n >= 0) + +main :: IO () +main = hspec $ do + -- Tested against Note [Categorical Pushout Feature Weaving] [ref:note-pushout-feature-weaving] + describe "Pushout Feature Weaving (B ⨿_C W)" $ do + it "weaves aspect into base signature over a shared interface in Unit category" $ do + let inclBase = Unit + let inclAspect = Unit + weaveAspect inclBase inclAspect $ \injBase injAspect -> do + case (injBase, injAspect) of + (Unit, Unit) -> True `shouldBe` True + + it "weaves aspect into base signature over thin boolean category" $ do + -- C = FLS, Base = FLS, Aspect = TRU + let inclBase = Fls :: FLS ~> FLS + let inclAspect = F2T :: FLS ~> TRU + weaveAspect inclBase inclAspect $ \(injBase :: FLS ~> p) (injAspect :: TRU ~> p) -> do + -- By pushout of (FLS <- FLS -> TRU), the apex is TRU + -- with injBase = F2T and injAspect = Tru + case (injBase, injAspect) of + (F2T, Tru) -> True `shouldBe` True + _ -> expectationFailure "Unexpected pushout injection arrows" + + -- Tested against Note [Colimit Mediating Morphisms and Semantic Delta Propagation] [ref:note-colimit-semantic-delta] + it "computes mediating factorizer for semantic delta propagation" $ do + -- Pushout of (Unit <- Unit -> Unit) is Unit + let pBase = Unit + let pAspect = Unit + let candidateBase = Unit + let candidateAspect = Unit + let factorizer = factorSemanticDelta pBase pAspect candidateBase candidateAspect + case factorizer of + Unit -> True `shouldBe` True + + -- Tested against Note [Pullback Interface Discovery] [ref:note-pullback-interface-discovery] + describe "Pullback Interface Discovery (A ×_E B)" $ do + it "discovers minimal interface in Unit category" $ do + let f = Unit + let g = Unit + discoverInterface f g $ \projA projB -> do + case (projA, projB) of + (Unit, Unit) -> True `shouldBe` True + + it "factors candidate interfaces through the universal pullback" $ do + let p1 = Unit + let p2 = Unit + let q1 = Unit + let q2 = Unit + case factorInterface p1 p2 q1 q2 of + Unit -> True `shouldBe` True + + -- Tested against Note [Goguen-Burstall Categorical Institution Satisfaction Invariance] [ref:note-institution-satisfaction-invariance] + describe "Goguen-Burstall Categorical Institution Satisfaction Invariance" $ do + it "verifies satisfaction condition invariance across signature morphisms" $ do + let phi = FlsSen "x_non_negative" + let mPrime = TruMod 42 + let (evLHS, evRHS, isPreserved) = checkSatisfactionInvariance @TestInst F2T phi mPrime + isPreserved `shouldBe` True + evLHS `shouldBe` evRHS + + it "detects counterexample invariance across signature morphisms" $ do + let phi = FlsSen "x_non_negative" + let mInvalid = TruMod (-5) + let (evLHS, evRHS, isPreserved) = checkSatisfactionInvariance @TestInst F2T phi mInvalid + isPreserved `shouldBe` True + evLHS `shouldBe` evRHS + + describe "Legacy Institution Compatibility" $ do + it "evaluates propositional satisfaction relation" $ do + let formula :: SentProp '["p", "q"] + formula = Conj (Atom (Proxy @"p")) (Atom (Proxy @"q")) + let model :: ModProp '["p", "q"] + model = ModProp (\p -> case symbolVal p of + "p" -> True + "q" -> True + _ -> False) + Legacy.satisfies (Proxy @(PropSig '["p", "q"])) model formula `shouldBe` True + let badModel :: ModProp '["p", "q"] + badModel = ModProp (\p -> case symbolVal p of + "p" -> True + "q" -> False + _ -> False) + Legacy.satisfies (Proxy @(PropSig '["p", "q"])) badModel formula `shouldBe` False