73 lines
2.1 KiB
Text
73 lines
2.1 KiB
Text
inductive Expr
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| Var : Nat → Expr
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| Val : Nat → Expr
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| Add : Expr → Expr → Expr
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| Mul : Expr → Expr → Expr
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open Expr Nat
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def mkExpr : Nat → Nat → Expr
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| 0 v := if v = 0 then Var 1 else Val v
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| (n+1) v := Add (mkExpr n (v+1)) (mkExpr n (v-1))
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def appendAdd : Expr → Expr → Expr
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| (Add e₁ e₂) e₃ := Add e₁ (appendAdd e₂ e₃)
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| e₁ e₂ := Add e₁ e₂
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def appendMul : Expr → Expr → Expr
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| (Mul e₁ e₂) e₃ := Mul e₁ (appendMul e₂ e₃)
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| e₁ e₂ := Mul e₁ e₂
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def reassoc : Expr → Expr
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| (Add e₁ e₂) :=
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let e₁' := reassoc e₁;
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let e₂' := reassoc e₂;
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appendAdd e₁' e₂'
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| (Mul e₁ e₂) :=
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let e₁' := reassoc e₁;
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let e₂' := reassoc e₂;
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appendMul e₁' e₂'
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| e := e
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def constFolding : Expr → Expr
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| (Add e₁ e₂) :=
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let e₁ := constFolding e₁;
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let e₂ := constFolding e₂;
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(match e₁, e₂ with
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| Val a, Val b => Val (a+b)
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| Val a, Add e (Val b) => Add (Val (a+b)) e
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| Val a, Add (Val b) e => Add (Val (a+b)) e
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| _, _ => Add e₁ e₂)
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| (Mul e₁ e₂) :=
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let e₁ := constFolding e₁;
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let e₂ := constFolding e₂;
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(match e₁, e₂ with
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| Val a, Val b => Val (a*b)
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| Val a, Mul e (Val b) => Mul (Val (a*b)) e
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| Val a, Mul (Val b) e => Mul (Val (a*b)) e
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| _, _ => Mul e₁ e₂)
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| e := e
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def size : Expr → Nat
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| (Add l r) := size l + size r + 1
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| (Mul l r) := size l + size r + 1
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| e := 1
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def toStringAux : Expr → String → String
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| (Var v) r := r ++ "#" ++ toString v
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| (Val v) r := r ++ toString v
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| (Add e₁ e₂) r := (toStringAux e₂ ((toStringAux e₁ (r ++ "(")) ++ " + ")) ++ ")"
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| (Mul e₁ e₂) r := (toStringAux e₂ ((toStringAux e₁ (r ++ "(")) ++ " * ")) ++ ")"
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def eval : Expr → Nat
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| (Var x) := 0
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| (Val v) := v
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| (Add l r) := eval l + eval r
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| (Mul l r) := eval l * eval r
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def main : IO UInt32 :=
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let e := (mkExpr 23 1);
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let v₁ := eval e;
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let v₂ := eval (constFolding (reassoc e));
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IO.println (toString v₁ ++ " " ++ toString v₂) *>
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pure 0
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