76799db032
This modification was suggested by @kha. TODO: - Use `simp [-f]` instead of `simp without f` - Allow users to remove hypothesis from `*`. Example: `simp [*, -h]` for simplify using all hypotheses but `h`.
43 lines
1.1 KiB
Text
43 lines
1.1 KiB
Text
/- "Proving in the Large" chapter of CPDT -/
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inductive exp : Type
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| Const (n : nat) : exp
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| Plus (e1 e2 : exp) : exp
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| Mult (e1 e2 : exp) : exp
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open exp
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def eeval : exp → nat
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| (Const n) := n
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| (Plus e1 e2) := eeval e1 + eeval e2
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| (Mult e1 e2) := eeval e1 * eeval e2
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def times (k : nat) : exp → exp
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| (Const n) := Const (k * n)
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| (Plus e1 e2) := Plus (times e1) (times e2)
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| (Mult e1 e2) := Mult (times e1) e2
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def reassoc : exp → exp
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| (Const n) := (Const n)
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| (Plus e1 e2) :=
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let e1' := reassoc e1 in
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let e2' := reassoc e2 in
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match e2' with
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| (Plus e21 e22) := Plus (Plus e1' e21) e22
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| _ := Plus e1' e2'
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end
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| (Mult e1 e2) :=
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let e1' := reassoc e1 in
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let e2' := reassoc e2 in
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match e2' with
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| (Mult e21 e22) := Mult (Mult e1' e21) e22
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| _ := Mult e1' e2'
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end
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attribute [simp] mul_add times reassoc eeval
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theorem eeval_times (k e) : eeval (times k e) = k * eeval e :=
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by induction e; simp [*]
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theorem reassoc_correct (e) : eeval (reassoc e) = eeval e :=
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by induction e; simp [*]; cases (reassoc e2); rsimp
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