88 lines
2.5 KiB
Text
88 lines
2.5 KiB
Text
@[simp] def f1 (i : Int) (a b : Nat) : Nat :=
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match i, a with
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| -1, _ => b
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| _, 0 => b+1
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| _, a+1 => f1 (i-1) a (b*2)
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#check f1.eq_1
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#check f1.eq_2
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example : f1 (-1) a b = b := by simp -- should work
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example : f1 (-2) 0 b = b+1 := by simp
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example : f1 (-2) (a+1) b = f1 (-3) a (b*2) := by simp
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example (h : i ≠ -1) : f1 i (a+1) b = f1 (i-1) a (b*2) := by simp -- should work
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@[simp] def f2 (c : Char) (a b : Nat) : Nat :=
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match c, a with
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| 'a', _ => b
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| _, 0 => b+1
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| _, a+1 => f2 c a (b*2)
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example : f2 'a' a b = b := by simp
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example : f2 'b' 0 b = b+1 := by simp
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example : f2 'b' (a+1) b = f2 'b' a (b*2) := by simp
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example (h : c ≠ 'a') : f2 c (a+1) b = f2 c a (b*2) := by simp
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@[simp] def f3 (i : Fin 5) (a b : Nat) : Nat :=
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match i, a with
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| 2, _ => b
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| _, 0 => b+1
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| _, a+1 => f3 (i+1) a (b*2)
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#check f3.eq_1
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#check f3.eq_2
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example : f3 2 a b = b := by simp -- should work
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example : f3 3 0 b = b+1 := by simp
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example : f3 1 (a+1) b = f3 2 a (b*2) := by simp
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example (h : i ≠ 2) : f3 i (a+1) b = f3 (i+1) a (b*2) := by simp; done -- should work
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@[simp] def f4 (i : UInt16) (a b : Nat) : Nat :=
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match i, a with
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| 2, _ => b
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| _, 0 => b+1
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| _, a+1 => f4 (i+1) a (b*2)
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#check f4.eq_1
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#check f4.eq_2
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example : f4 2 a b = b := by simp -- should work
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example : f4 3 0 b = b+1 := by simp
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example : f4 1 (a+1) b = f4 2 a (b*2) := by simp
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example (h : i ≠ 2) : f4 i (a+1) b = f4 (i+1) a (b*2) := by simp -- should work
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@[simp] def f5 (i : BitVec 8) (a b : Nat) : Nat :=
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match i, a with
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| 2, _ => b
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| _, 0 => b+1
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| _, a+1 => f5 (i+1) a (b*2)
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#check f5.eq_1
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#check f5.eq_2
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open BitVec
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example : f5 2 a b = b := by simp -- should work
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example : f5 2#8 a b = b := by simp -- should work
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example : f5 3 0 b = b+1 := by simp
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example : f5 3#8 0 b = b+1 := by simp
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example : f5 1 (a+1) b = f5 2 a (b*2) := by simp
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example : f5 1#8 (a+1) b = f5 2 a (b*2) := by simp
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example (h : i ≠ 2#8) : f5 i (a+1) b = f5 (i+1) a (b*2) := by simp -- should work
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@[simp] def f6 (i : BitVec 8) (a b : Nat) : Nat :=
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match i, a with
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| 2#8, _ => b
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| _, 0 => b+1
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| _, a+1 => f6 (i+1) a (b*2)
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#check f6.eq_1
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#check f6.eq_2
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example : f6 2#8 a b = b := by simp -- should work
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example : f6 2#8 a b = b := by simp -- should work
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example : f6 3 0 b = b+1 := by simp
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example : f6 3#8 0 b = b+1 := by simp
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example : f6 1 (a+1) b = f6 2 a (b*2) := by simp
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example : f6 1#8 (a+1) b = f6 2 a (b*2) := by simp
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example (h : i ≠ 2#8) : f6 i (a+1) b = f6 (i+1) a (b*2) := by simp -- should work
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