gargamelle-core (empty) → 0.1.0.0

raw patch · 15 files changed

+1130/−0 lines, 15 filesdep +basedep +containersdep +contravariant

Dependencies added: base, containers, contravariant, gargamelle-core, gargamelle-logic, gargamelle-model, hspec, lattices, polytropos-core, proarrow, proarrow-equipment

Files

CHANGELOG.md +7/−0
LICENSE +189/−0
README.md +193/−0
gargamelle-core.cabal +71/−0
src/CEGIS.hs +4/−0
src/Core/AST.hs +12/−0
src/Gargamelle/Core/Colimit.hs +60/−0
src/Gargamelle/Core/Discovery.hs +69/−0
src/Gargamelle/Core/Institution.hs +102/−0
src/Gargamelle/Core/Weaving.hs +90/−0
src/Institution.hs +32/−0
src/Propositional.hs +57/−0
src/SessionTypes.hs +50/−0
src/Sheaf.hs +46/−0
test/Main.hs +148/−0

+ CHANGELOG.md view

@@ -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.

+ LICENSE view

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+ README.md view

@@ -0,0 +1,193 @@+# `gargamelle-core` — Categorical Institutions, Colimit Pushout Weaving & Interface Discovery++[![Haskell](https://img.shields.io/badge/Language-Haskell2010-purple.svg)](https://haskell.org)+[![License: EUPL-1.2](https://img.shields.io/badge/License-EUPL--1.2-blue.svg)](https://spdx.org/licenses/EUPL-1.2.html)+[![Tier 3 Logic Engine](https://img.shields.io/badge/Tier-3%20Logic%20%26%20Institution%20Engine-teal.svg)](../../README.md#architectural-tier-map)++---++## 1. 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+```++<!-- See Note [Goguen-Burstall Categorical Institution Satisfaction Invariance] [ref:note-institution-satisfaction-invariance] -->++### 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.++<!-- See Note [Categorical Pushout Feature Weaving] [ref:note-pushout-feature-weaving] -->++### 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 $u : Q \to P$.++<!-- See Note [Pullback Interface Discovery] [ref:note-pullback-interface-discovery] -->++### 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.++<!-- See Note [Colimit Mediating Morphisms and Semantic Delta Propagation] [ref:note-colimit-semantic-delta] -->++---++## 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).*

+ gargamelle-core.cabal view

@@ -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

+ src/CEGIS.hs view

@@ -0,0 +1,4 @@+module CEGIS where++-- Placeholder for Modular CEGIS conceptual framework.+-- To be implemented with proper assume-guarantee contracts.

+ src/Core/AST.hs view

@@ -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)

+ src/Gargamelle/Core/Colimit.hs view

@@ -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

+ src/Gargamelle/Core/Discovery.hs view

@@ -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

+ src/Gargamelle/Core/Institution.hs view

@@ -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)+  }

+ src/Gargamelle/Core/Weaving.hs view

@@ -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

+ src/Institution.hs view

@@ -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

+ src/Propositional.hs view

@@ -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 _ = "<model>"++-- | 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

+ src/SessionTypes.hs view

@@ -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

+ src/Sheaf.hs view

@@ -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

+ test/Main.hs view

@@ -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