08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
113 lines
1.8 KiB
Text
113 lines
1.8 KiB
Text
/-!
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# Tests of the `subst` tactic when `let`s are present.
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-/
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/-!
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Eliminates `a` even though `e : id a = m`.
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-/
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/--
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trace: case intro
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n : Nat
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m : Nat := n
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a : Nat
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e : id a = m
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⊢ 0 + n = n
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---
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trace: case intro
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a : Nat
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m : Nat := id a
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⊢ 0 + id a = id a
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-/
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#guard_msgs in
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theorem ex1 (n : Nat) : 0 + n = n := by
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let m := n
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have h : ∃ k, id k = m := ⟨m, rfl⟩
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cases h with
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| intro a e =>
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trace_state
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subst e
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trace_state
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apply Nat.zero_add
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/-!
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Eliminates `a` even though `e : m = id a`.
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-/
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/--
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trace: case intro
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n : Nat
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m : Nat := n
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a : Nat
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e : m = id a
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⊢ 0 + n = n
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---
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trace: case intro
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n : Nat
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m : Nat := n
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⊢ 0 + n = n
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-/
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#guard_msgs in
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theorem ex2 (n : Nat) : 0 + n = n := by
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let m := n
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have h : ∃ k, m = id k := ⟨m, rfl⟩
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cases h with
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| intro a e =>
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trace_state
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subst e
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trace_state
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apply Nat.zero_add
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/-!
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Since `v` is a let binding, the `subst v` tactic instead
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zeta delta reduces it everywhere and then clears it.
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-/
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/--
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trace: n : Nat
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h : n = 0
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m : Nat := n + 1
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v : Nat := m + 1
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this : v = n + 2
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⊢ 0 + n = 0
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---
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trace: n : Nat
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h : n = 0
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m : Nat := n + 1
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this : m + 1 = n + 2
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⊢ 0 + n = 0
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---
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trace: m : Nat := 0 + 1
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this : m + 1 = 0 + 2
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⊢ 0 + 0 = 0
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-/
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#guard_msgs in
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theorem ex3 (n : Nat) (h : n = 0) : 0 + n = 0 := by
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let m := n + 1
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let v := m + 1
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have : v = n + 2 := rfl
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trace_state
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subst v
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trace_state
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subst n
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trace_state
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rfl
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/-!
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Can't do `subst this` with `this : v = n + 2` since `v` is a let binding.
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The tactic sees `m + 1 = n + 2` and fails.
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-/
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/--
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error: Tactic `subst` failed: invalid equality proof, it is not of the form (x = t) or (t = x)
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v = n + 2
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n : Nat
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h : n = 0
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m : Nat := n + 1
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v : Nat := m + 1
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this : v = n + 2
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⊢ 0 + n = 0
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-/
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#guard_msgs in
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theorem ex4 (n : Nat) (h : n = 0) : 0 + n = 0 := by
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let m := n + 1
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let v := m + 1
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have : v = n + 2 := rfl
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subst this
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