Danila Fedorin
8ce6e5e4e4
LatticeInterpretation now extends Interp L (Value → Prop), so each analysis defines only its LatticeInterpretation instance and gets the ⟦⟧ notation for free. Drops the standalone per-analysis Interp instances (signInterp and the anonymous constInterp). The Interp class is kept for other uses. The interp*_mk_disjoint bootstrap lemmas now state on the raw interp function since they feed the instance and run before any Interp instance exists; the trivial sup/inf wrappers are inlined into the instance. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
67 lines
2.9 KiB
Lean4
67 lines
2.9 KiB
Lean4
import Spa.Language.Base
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import Spa.Lattice
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import Spa.Interp
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namespace Spa
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inductive Value where
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| int (z : ℤ)
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deriving DecidableEq
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def Env : Type := List (String × Value)
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inductive Env.Mem : String × Value → Env → Prop
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| here (s : String) (v : Value) (ρ : Env) : Env.Mem (s, v) ((s, v) :: ρ)
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| there (s s' : String) (v v' : Value) (ρ : Env) :
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¬(s = s') → Env.Mem (s, v) ρ → Env.Mem (s, v) ((s', v') :: ρ)
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inductive EvalExpr : Env → Expr → Value → Prop
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| num (ρ : Env) (n : ℕ) : EvalExpr ρ (.num n) (.int n)
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| var (ρ : Env) (x : String) (v : Value) :
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Env.Mem (x, v) ρ → EvalExpr ρ (.var x) v
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| add (ρ : Env) (e₁ e₂ : Expr) (z₁ z₂ : ℤ) :
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EvalExpr ρ e₁ (.int z₁) → EvalExpr ρ e₂ (.int z₂) →
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EvalExpr ρ (.add e₁ e₂) (.int (z₁ + z₂))
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| sub (ρ : Env) (e₁ e₂ : Expr) (z₁ z₂ : ℤ) :
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EvalExpr ρ e₁ (.int z₁) → EvalExpr ρ e₂ (.int z₂) →
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EvalExpr ρ (.sub e₁ e₂) (.int (z₁ - z₂))
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inductive EvalBasicStmt : Env → BasicStmt → Env → Prop
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| noop (ρ : Env) : EvalBasicStmt ρ .noop ρ
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| assign (ρ : Env) (x : String) (e : Expr) (v : Value) :
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EvalExpr ρ e v → EvalBasicStmt ρ (.assign x e) ((x, v) :: ρ)
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inductive EvalBasicStmts : Env → List BasicStmt → Env → Prop
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| nil {ρ : Env} : EvalBasicStmts ρ [] ρ
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| cons {ρ₁ ρ₂ ρ₃ : Env} {bs : BasicStmt} {bss : List BasicStmt} :
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EvalBasicStmt ρ₁ bs ρ₂ → EvalBasicStmts ρ₂ bss ρ₃ →
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EvalBasicStmts ρ₁ (bs :: bss) ρ₃
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inductive EvalStmt : Env → Stmt → Env → Prop
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| basic (ρ₁ ρ₂ : Env) (bs : BasicStmt) :
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EvalBasicStmt ρ₁ bs ρ₂ → EvalStmt ρ₁ (.basic bs) ρ₂
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| andThen (ρ₁ ρ₂ ρ₃ : Env) (s₁ s₂ : Stmt) :
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EvalStmt ρ₁ s₁ ρ₂ → EvalStmt ρ₂ s₂ ρ₃ →
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EvalStmt ρ₁ (.andThen s₁ s₂) ρ₃
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| ifTrue (ρ₁ ρ₂ : Env) (e : Expr) (z : ℤ) (s₁ s₂ : Stmt) :
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EvalExpr ρ₁ e (.int z) → ¬(z = 0) → EvalStmt ρ₁ s₁ ρ₂ →
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EvalStmt ρ₁ (.ifElse e s₁ s₂) ρ₂
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| ifFalse (ρ₁ ρ₂ : Env) (e : Expr) (s₁ s₂ : Stmt) :
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EvalExpr ρ₁ e (.int 0) → EvalStmt ρ₁ s₂ ρ₂ →
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EvalStmt ρ₁ (.ifElse e s₁ s₂) ρ₂
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| whileTrue (ρ₁ ρ₂ ρ₃ : Env) (e : Expr) (z : ℤ) (s : Stmt) :
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EvalExpr ρ₁ e (.int z) → ¬(z = 0) → EvalStmt ρ₁ s ρ₂ →
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EvalStmt ρ₂ (.whileLoop e s) ρ₃ →
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EvalStmt ρ₁ (.whileLoop e s) ρ₃
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| whileFalse (ρ : Env) (e : Expr) (s : Stmt) :
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EvalExpr ρ e (.int 0) →
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EvalStmt ρ (.whileLoop e s) ρ
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class LatticeInterpretation (L : Type*) [Lattice L] extends Interp L (Value → Prop) where
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interp_sup : ∀ {l₁ l₂ : L} (v : Value),
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interp l₁ v ∨ interp l₂ v → interp (l₁ ⊔ l₂) v
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interp_inf : ∀ {l₁ l₂ : L} (v : Value),
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interp l₁ v ∧ interp l₂ v → interp (l₁ ⊓ l₂) v
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end Spa
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