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agda-spa/lean/Spa.lean

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Lean migration: Phases 0-2 (core lattice/chain, fixpoint, transport) - lean/ lake project pinned to Lean v4.17.0 + mathlib v4.17.0 - Spa.Lattice: fold monotonicity, FixedHeight/BoundedChains (LTSeries-based), FiniteHeightLattice, chain-bottom-is-least; the rest of Lattice.agda, Chain.agda and Equivalence.agda lift into mathlib (see LEAN_MIGRATION.md) - Spa.Fixedpoint: gas-based least-fixpoint computation (doStep/fix/aFix) - Spa.Isomorphism: FixedHeight transport along monotone inverse pairs Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 18:36:43 -07:00
import Spa.Lattice
import Spa.Fixedpoint
Lean migration: Phase 3 (Unit, Prod, AboveBelow lattices) - Spa.Lattice.Unit: PUnit fixed height 0 (lattice lifted from mathlib) - Spa.Lattice.Prod: chain unzip + FixedHeight (h1+h2) on products (componentwise lattice lifted from mathlib's Prod.instLattice) - Spa.Lattice.AboveBelow: flat lattice via Lattice.mk' (mirrors the Agda semilattices+absorption construction), boundedness via rank into Nat, Plain x ↦ plainFixedHeight x, height 2 Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 18:48:02 -07:00
import Spa.Lattice.Unit
import Spa.Lattice.AboveBelow
Lean migration: Phase 4 (IterProd + FiniteMap lattices) - Spa.Lattice.IterProd: k-fold product, recursive Lattice instance, fixed height k*hA + hB, bot = build of bottoms - Spa.Lattice.FiniteMap: spine-pinned assoc lists ({l // l.map fst = ks}); with = the 1100-line Map.agda collapses into positional 'combine'. Same lemma inventory (membership, locate, updating, GeneralizedUpdate, valuesAt, Provenance-union, le_of_mem_mem) — Nodup is now an explicit hypothesis where the Agda Map carried it intrinsically. Fixed height |ks|*hB still via transport along the IterProd isomorphism, which no longer needs Unique ks (representation is canonical). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 19:12:39 -07:00
import Spa.Lattice.FiniteMap
Add computational reaching-definitions analysis Introduce a finite-height lattice instance for Bool, then build the reaching-definitions analysis on top of the forward framework: * Spa/Lattice/Bool.lean: FiniteHeightLattice Bool (the two-element lattice false ≤ true), making FiniteMap A Bool ks a finite-height "power set" lattice for free. * Spa/Analysis/Reaching.lean: DefSet prog = FiniteMap prog.State Bool prog.states as the per-variable lattice of definition sites, with a StmtEvaluator whose transfer function performs a strong update (assignment to k at node s sets k's def-set to {s}). The analysis computes a least fixed point and produces correct reaching-definitions sets. Soundness (relating def-sets to actual execution provenance) is deferred; not yet exposed in Spa.lean. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-06-23 15:12:37 -05:00
import Spa.Lattice.Bool
Lean migration: Phase 5 (language, CFGs, traces, Program) - Spa.Language.Base: Expr/BasicStmt/Stmt + HasVar relations; StringSet lifts to Finset String - Spa.Language.Semantics: Value/Env/Env.Mem, big-step relations, LatticeInterpretation (respects-≈ field drops out with =) - Spa.Language.Graphs: Graph with nodes : Fin size → List BasicStmt (Vec lookup lemmas lift to Fin.append_left/right), comp/link/loop/ skipto/singleton/wrap/buildCfg, predecessors via List.finRange - Spa.Language.Traces: Trace + EndToEndTrace (Prop-valued) - Spa.Language.Properties: trace embeddings, loop lemmas, buildCfg_sufficient; the 80-line Fin-disjointness block reduces to castAdd_ne_natAdd + mathlib list lemmas - Spa.Language: Program (vars via Finset.sort — toList is noncomputable) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 19:30:42 -07:00
import Spa.Language.Base
Add scoped quotation syntax for object-language programs Introduce [spa_e| ... ] for Expr and [spa| ... ] for Stmt, scoped to the Spa namespace via a dedicated syntax category and macro_rules. This removes the deeply nested .andThen / .basic (.assign ...) boilerplate when writing programs; Main.lean's test programs are rewritten to use it. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-06-23 14:17:11 -05:00
import Spa.Language.Notation
Lean migration: Phase 5 (language, CFGs, traces, Program) - Spa.Language.Base: Expr/BasicStmt/Stmt + HasVar relations; StringSet lifts to Finset String - Spa.Language.Semantics: Value/Env/Env.Mem, big-step relations, LatticeInterpretation (respects-≈ field drops out with =) - Spa.Language.Graphs: Graph with nodes : Fin size → List BasicStmt (Vec lookup lemmas lift to Fin.append_left/right), comp/link/loop/ skipto/singleton/wrap/buildCfg, predecessors via List.finRange - Spa.Language.Traces: Trace + EndToEndTrace (Prop-valued) - Spa.Language.Properties: trace embeddings, loop lemmas, buildCfg_sufficient; the 80-line Fin-disjointness block reduces to castAdd_ne_natAdd + mathlib list lemmas - Spa.Language: Program (vars via Finset.sort — toList is noncomputable) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 19:30:42 -07:00
import Spa.Language.Semantics
import Spa.Language.Graphs
import Spa.Language.Traces
import Spa.Language.Properties
import Spa.Language
Lean migration: Phase 6 (forward analysis framework) - Spa.Analysis.Forward.Lattices: VariableValues/StateVariables (FiniteMap instantiations), fixed heights, variablesAt, joinForKey/joinAll, interpV and its sup/foldr lemmas - Spa.Analysis.Forward.Evaluation: StmtEvaluator/ExprEvaluator + validity (the Agda Valid* instance records become plain Props) - Spa.Analysis.Forward.Adapters: expr-to-stmt evaluator adapter + validity - Spa.Analysis.Forward: updateAll, analyze, result (least fixpoint via the gas-based Fixedpoint), walkTrace, analyze_correct — the framework's main soundness theorem Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 20:14:53 -07:00
import Spa.Analysis.Forward.Lattices
import Spa.Analysis.Forward.Evaluation
import Spa.Analysis.Forward.Adapters
import Spa.Analysis.Forward
Lean migration: Phase 7 (Sign + Constant analyses, executable) - Spa.Showable: port of Showable.agda (quoted strings, map format) for output parity - Spa.Analysis.Utils: eval_combine₂ - Spa.Lattice.AboveBelow.le_cases: order of the flat lattice by cases - Spa.Analysis.Sign / Spa.Analysis.Constant: the four monotonicity POSTULATES from the Agda files are now proved theorems (via le_cases); interpretations, evaluator validity, analyze_correct per analysis - Main + lake exe spa: runs both analyses on the Agda test program; constant analysis folds unknown=0, sign analysis gives unknown=⊤ Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09 20:52:08 -07:00
import Spa.Showable
import Spa.Analysis.Utils
import Spa.Analysis.Sign
import Spa.Analysis.Constant
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