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
3.6 KiB
Text
113 lines
3.6 KiB
Text
/-!
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# Tests exercising basic behaviour of `rw`.
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See also `tests/lean/run/rewrite.lean`.
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-/
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axiom appendNil {α} (as : List α) : as ++ [] = as
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axiom appendAssoc {α} (as bs cs : List α) : (as ++ bs) ++ cs = as ++ (bs ++ cs)
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axiom reverseEq {α} (as : List α) : as.reverse.reverse = as
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theorem ex1 {α} (as bs : List α) : as.reverse.reverse ++ [] ++ [] ++ bs ++ bs = as ++ (bs ++ bs) := by
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rw [appendNil, appendNil, reverseEq];
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trace_state;
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rw [←appendAssoc];
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theorem ex2 {α} (as bs : List α) : as.reverse.reverse ++ [] ++ [] ++ bs ++ bs = as ++ (bs ++ bs) := by
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rewrite [reverseEq, reverseEq]; -- Error on second reverseEq
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done
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axiom zeroAdd (x : Nat) : 0 + x = x
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theorem ex2a (x y z) (h₁ : 0 + x = y) (h₂ : 0 + y = z) : x = z := by
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rewrite [zeroAdd] at h₁ h₂;
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trace_state;
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subst x;
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subst y;
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exact rfl
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theorem ex3 (x y z) (h₁ : 0 + x = y) (h₂ : 0 + y = z) : x = z := by
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rewrite [zeroAdd] at *;
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subst x;
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subst y;
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exact rfl
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theorem ex4 (x y z) (h₁ : 0 + x = y) (h₂ : 0 + y = z) : x = z := by
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rewrite [appendAssoc] at *; -- Error
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done
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theorem ex5 (m n k : Nat) (h : 0 + n = m) (h : k = m) : k = n := by
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rw [zeroAdd] at *;
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trace_state; -- `h` is still a name for `h : k = m`
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refine Eq.trans h ?hole;
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apply Eq.symm;
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assumption
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theorem ex6 (p q r : Prop) (h₁ : q → r) (h₂ : p ↔ q) (h₃ : p) : r := by
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rw [←h₂] at h₁;
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exact h₁ h₃
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theorem ex7 (p q r : Prop) (h₁ : q → r) (h₂ : p ↔ q) (h₃ : p) : r := by
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rw [h₂] at h₃;
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exact h₁ h₃
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example (α : Type) (p : Prop) (a b c : α) (h : p → a = b) : a = c := by
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rw [h _] -- should manifest goal `⊢ p`, like `rw [h]` would
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/-!
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Testing the `occs` configuration argument.
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-/
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variable (f : Nat → Nat) (w : ∀ n, f n = 0)
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example : [f 1, f 2, f 1, f 2] = [0, 0, 0, 0] := by
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rw (config := {occs := .pos [2]}) [w]
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trace_state -- make sure we rewrote the first `f 2`, rather than the second `f 1`.
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rw [w, w]
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example : [f 1, f 2, f 1, f 2] = [0, 0, 0, 0] := by
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rw (config := {occs := .all}) [w]
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trace_state -- expecting [0, f 2, 0, f 2] = [0, 0, 0, 0]
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rw [w]
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example : [f 1, f 2, f 1, f 2] = [0, 0, 0, 0] := by
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rw (config := {occs := .pos [1, 2]}) [w]
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trace_state -- expecting [0, f 2, 0, f 2] = [0, 0, 0, 0]
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-- After the first rewrite, the argument of `w` have been instantiated as `1`,
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-- so the second eligible rewrite is the second `f 1`.
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rw [w]
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example : [f 1, f 2, f 1, f 2] = [0, 0, 0, 0] := by
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rw (config := {occs := .neg [1]}) [w]
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trace_state -- expecting [f 1, 0, f 1, 0] = [0, 0, 0, 0]
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rw [w]
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example : [f 1, f 2, f 1, f 2] = [0, 0, 0, 0] := by
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rw (config := {occs := .neg [1, 2]}) [w]
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trace_state -- expecting [f 1, f 2, 0, f 2] = [0, 0, 0, 0]
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rw [w, w]
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example : [f 1, f 2, f 1, f 2] = [0, 0, 0, 0] := by
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rw (config := {occs := .neg [1, 3]}) [w]
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trace_state -- expecting [f 1, 0, f 1, f 2] = [0, 0, 0, 0]
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-- This one is slightly confusing:
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-- We skipped the first `f 1`, because `1 ∈ [1,3]`.
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-- We then rewrite the first `f 2 = 0`, because it is the second match.
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-- Now the second `f 1` is no longer eligible, because we have instantiated the argument of `w` to `2`.
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-- Finally we skip the second `f 2` because of `3 ∈ [1,3]`.
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rw [w, w]
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-- A slightly trickier example, where there are already metavariables in the goal,
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-- and we ensure that we don't unify metavariables in positions skipped by `occs`.
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example : { x : Nat × Nat // x.1 = 0 ∧ x.2 = 0 } := by
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refine ⟨(f ?_, f ?_), ?_⟩
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rotate_right
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dsimp
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rw (config := {occs := .pos [2]}) [w]
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-- TODO: note that `rw` duplicates goals when there are metavariables.
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-- This should be fixed.
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rw [w]
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exact ⟨rfl, rfl⟩
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exact 37
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exact 0
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