55 lines
1.6 KiB
Lean4
55 lines
1.6 KiB
Lean4
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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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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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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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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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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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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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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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