Danila Fedorin
2cfd0a2fb7
- 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>
79 lines
2.6 KiB
Lean4
79 lines
2.6 KiB
Lean4
/-
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Port of `Language/Base.agda`.
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`StringSet` (built on `Lattice/MapSet.agda`, itself on `Lattice/Map.agda`) is
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lifted to mathlib's `Finset String`: `insertˢ ↦ insert`, `emptyˢ ↦ ∅`,
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`singletonˢ ↦ {·}`, `_⊔ˢ_ ↦ ∪`, `to-List ↦ Finset.toList` (with
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`Finset.nodup_toList` standing in for the intrinsic `Unique` proof).
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Constructor renaming (Agda mixfix has no direct Lean counterpart):
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_+_ ↦ Expr.add _-_ ↦ Expr.sub `_ ↦ Expr.var #_ ↦ Expr.num
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_←_ ↦ BasicStmt.assign noop ↦ BasicStmt.noop
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⟨_⟩ ↦ Stmt.basic _then_ ↦ Stmt.andThen
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if_then_else_ ↦ Stmt.ifElse while_repeat_ ↦ Stmt.whileLoop
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The `_∈ᵉ_` / `_∈ᵇ_` variable-occurrence relations are ported as
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`Expr.HasVar` / `BasicStmt.HasVar`; the commented-out lemmas relating them to
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`Expr-vars` remain unported (they were commented out in the Agda, too).
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-/
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import Mathlib.Data.Finset.Basic
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namespace Spa
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inductive Expr where
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| add (e₁ e₂ : Expr)
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| sub (e₁ e₂ : Expr)
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| var (x : String)
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| num (n : ℕ)
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deriving DecidableEq
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inductive BasicStmt where
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| assign (x : String) (e : Expr)
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| noop
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deriving DecidableEq
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inductive Stmt where
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| basic (bs : BasicStmt)
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| andThen (s₁ s₂ : Stmt)
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| ifElse (e : Expr) (s₁ s₂ : Stmt)
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| whileLoop (e : Expr) (s : Stmt)
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deriving DecidableEq
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/-- Agda: `_∈ᵉ_`. -/
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inductive Expr.HasVar : String → Expr → Prop
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| addLeft {e₁ e₂ k} : Expr.HasVar k e₁ → Expr.HasVar k (.add e₁ e₂)
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| addRight {e₁ e₂ k} : Expr.HasVar k e₂ → Expr.HasVar k (.add e₁ e₂)
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| subLeft {e₁ e₂ k} : Expr.HasVar k e₁ → Expr.HasVar k (.sub e₁ e₂)
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| subRight {e₁ e₂ k} : Expr.HasVar k e₂ → Expr.HasVar k (.sub e₁ e₂)
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| here {k} : Expr.HasVar k (.var k)
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/-- Agda: `_∈ᵇ_`. -/
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inductive BasicStmt.HasVar : String → BasicStmt → Prop
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| assignLeft {k e} : BasicStmt.HasVar k (.assign k e)
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| assignRight {k k' e} : Expr.HasVar k e → BasicStmt.HasVar k (.assign k' e)
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/-- Agda: `Expr-vars`. -/
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def Expr.vars : Expr → Finset String
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| .add l r => l.vars ∪ r.vars
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| .sub l r => l.vars ∪ r.vars
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| .var s => {s}
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| .num _ => ∅
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/-- Agda: `BasicStmt-vars`. -/
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def BasicStmt.vars : BasicStmt → Finset String
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| .assign x e => {x} ∪ e.vars
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| .noop => ∅
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/-- Agda: `Stmt-vars`. -/
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def Stmt.vars : Stmt → Finset String
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| .basic bs => bs.vars
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| .andThen s₁ s₂ => s₁.vars ∪ s₂.vars
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| .ifElse e s₁ s₂ => (e.vars ∪ s₁.vars) ∪ s₂.vars
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| .whileLoop e s => e.vars ∪ s.vars
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/-- Agda: `Stmts-vars`. -/
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def Stmt.varsList (ss : List Stmt) : Finset String :=
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ss.foldr (fun s acc => s.vars ∪ acc) ∅
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end Spa
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