044bfdb098
This PR deprecates `let_fun` syntax in favor of `have` and removes `letFun` support from WHNF and `simp`.
105 lines
3.1 KiB
Text
105 lines
3.1 KiB
Text
example : (λ x => x)
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=
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(λ x : Nat =>
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have foo := λ y => id (id y)
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foo (0 + x)) := by
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simp -zeta only [id]
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guard_target =ₛ
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(λ x => x)
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=
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(λ x : Nat =>
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have foo := λ y => y
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foo (0 + x))
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simp
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example (a : Nat) (h : a = b) : (have x := 1*a; 0 + x) = 0 + b := by
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simp -zeta only [Nat.zero_add]
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guard_target =ₛ
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(have x := 1 * a; x) = b
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simp -zeta only [Nat.one_mul]
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guard_target =ₛ
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(have x := a; x) = b
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simp [h]
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example (a : Nat) (h : a = b) : (have x := 1*a; 0 + x) = 0 + b := by
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simp -zeta only [Nat.zero_add, Nat.one_mul]
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guard_target =ₛ
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(have x := a; x) = b
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simp [h]
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example (a : Nat) (h : a = b) : (have _y := 0; have x := 1*a; 0 + x) = 0 + b := by
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simp -zeta only [Nat.zero_add, Nat.one_mul]
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guard_target =ₛ
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(have x := a; x) = b
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simp [h]
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example (a : Nat) (h : a = b) : (have y := 0; have x := y*0 + 1*a; 0 + x) = 0 + b := by
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simp -zeta only [Nat.zero_add, Nat.one_mul, Nat.mul_zero]
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guard_target =ₛ
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(have x := a; x) = b
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simp [h]
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example (a : Nat) (h : a = b) : (have y := 0; have x := y*0 + 1*a; 0 + x) = 0 + b := by
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simp -zeta only [Nat.zero_add, Nat.one_mul]
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guard_target =ₛ
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(have y := 0; have x := y*0 + a; x) = b
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fail_if_success simp -zeta only [Nat.zero_add, Nat.one_mul] -- Should not make progress
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simp -zeta only [Nat.mul_zero]
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guard_target =ₛ
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(have x := 0 + a; x) = b
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simp -zeta only [Nat.zero_add]
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guard_target =ₛ
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(have x := a; x) = b
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simp [h]
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def f (n : Nat) (e : Nat) :=
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match n with
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| 0 => e
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| n+1 => have _y := true; have x := 1*e; f n x
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example (a b : Nat) (h : a = b) : f 2 (0 + a) = b := by
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simp -zeta only [f]
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guard_target =ₛ
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(have x := 1 * (0 + a); have x := 1 * x; x) = b
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fail_if_success simp -zeta only [f]
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simp -zeta only [Nat.one_mul]
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guard_target =ₛ
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(have x := 0 + a; have x := x; x) = b
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simp [h]
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example (a b : Nat) (h : a = b) : f 20 (0 + a) = b := by
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simp -zeta only [f]
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fail_if_success simp -zeta only [f]
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simp -zeta only [Nat.one_mul]
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simp [h]
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example (a b : Nat) (h : a = b) : f 50 (0 + a) = b := by
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simp -zeta only [f]
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fail_if_success simp -zeta only [f]
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simp -zeta only [Nat.one_mul]
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simp [h]
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def g (n : Nat) (b : Bool) (e : Nat) :=
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match n with
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| 0 => if b then e else 0
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| n+1 => have b' := !b; have x := 1*e; g n b' x
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example (a b : Nat) (h : a = b) : g 2 true (0 + a) = b := by
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simp -zeta only [g]
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guard_target =ₛ
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(have b' := !true; have x := 1 * (0 + a); have b' := !b';
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have x := 1 * x; if b' = true then x else 0) = b
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simp -zeta only [Bool.not_true, Nat.one_mul]
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guard_target =ₛ
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(have b' := false; have x := 0 + a; have b' := !b';
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have x := x; if b' = true then x else 0) = b
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simp [h]
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example (a : Nat) : g 33 true (0 + a) = 0 := by
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simp -zeta only [g]
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fail_if_success simp -zeta only [g]
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simp -zeta only [Bool.not_true, Nat.one_mul]
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fail_if_success simp -zeta only [Bool.not_true, Nat.one_mul]
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simp -zeta only [Nat.zero_add]
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fail_if_success simp -zeta only [Nat.zero_add]
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simp
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