25baf73005
Motivation: better `simp` cache behavior. Recall that `simp` cache uses `dischargeDepth`.
64 lines
1.4 KiB
Text
64 lines
1.4 KiB
Text
/-!
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Test support for `if-then-else` terms in the simplifier.
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The condition should be simplified before trying to apply congruence.
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We are currently accomplished that using pre-simp theorems.
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TODO: replace them with simprocs.
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In the following example, the term `g (a + <num>)` takes an
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exponential amount of time to be simplified without the pre-simp theorems.
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-/
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def myid (x : Nat) := 0 + x
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@[simp] theorem myid_eq : myid x = x := by simp [myid]
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namespace Ex1
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def f (x : Nat) (y z : Nat) : Nat :=
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if myid x = 0 then y else z
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def g (x : Nat) : Nat :=
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match x with
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| 0 => 1
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| a+1 => f x (g a + 1) (g a)
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theorem ex (h : a = 1) : g (a+32) = a := by
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simp [g, f, h]
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end Ex1
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namespace Ex2
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def f (x : Nat) (y z : Nat) : Nat :=
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if myid x > 0 then z else y
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def g (x : Nat) : Nat :=
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match x with
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| 0 => 1
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| a+1 => f x (g a + 1) (g a)
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theorem ex (h : a = 1) : g (a+32) = a := by
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simp [g, f, h]
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end Ex2
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namespace Ex3
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def f (x : Nat) (y z : Nat) : Nat :=
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if _ : myid x = 0 then y else z
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def g (x : Nat) : Nat :=
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match x with
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| 0 => 1
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| a+1 => f x (g a + 1) (g a)
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theorem ex (h : a = 1) : g (a+32) = a := by
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simp [g, f, h]
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end Ex3
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namespace Ex4
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def f (x : Nat) (y z : Nat) : Nat :=
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if _ : myid x > 0 then z else y
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def g (x : Nat) : Nat :=
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match x with
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| 0 => 1
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| a+1 => f x (g a + 1) (g a)
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theorem ex (h : a = 1) : g (a+32) = a := by
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simp [g, f, h]
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end Ex4
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