2652cc18b8
This PR standardizes error messages by quoting names with backticks. The changes were automated, so some cases may still be missing.
200 lines
3.3 KiB
Text
200 lines
3.3 KiB
Text
/-!
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Tests of the `intro` tactic
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-/
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/-!
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No arguments, introduce one hypothesis.
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-/
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/--
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trace: n✝ : Nat
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⊢ n✝ = 1 → n✝ + 1 = 2
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---
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trace: n✝ : Nat
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a✝ : n✝ = 1
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⊢ n✝ + 1 = 2
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-/
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#guard_msgs in
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example : ∀ n : Nat, n = 1 → n + 1 = 2 := by
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intro
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trace_state
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intro
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trace_state
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subst_vars
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rfl
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/-!
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`_` uses hygienic name derived from binder name
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-/
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/--
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trace: n✝ : Nat
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h : n✝ = 1
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⊢ n✝ + 1 = 2
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-/
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#guard_msgs in
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example : ∀ n : Nat, n = 1 → n + 1 = 2 := by
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intro _ h
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trace_state
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subst_vars
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rfl
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/-!
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`rfl` pattern applies `substEq`.
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Order doesn't matter, and HEq is allowed.
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-/
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/-- trace: ⊢ 1 + 1 = 2 -/
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#guard_msgs in
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example : ∀ n : Nat, n = 1 → n + 1 = 2 := by
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intro _ rfl
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trace_state
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subst_vars
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rfl
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/-- trace: ⊢ 1 + 1 = 2 -/
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#guard_msgs in
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example : ∀ n : Nat, 1 = n → n + 1 = 2 := by
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intro _ rfl
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trace_state
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subst_vars
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rfl
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/-- trace: ⊢ 1 + 1 = 2 -/
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#guard_msgs in
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example : ∀ n : Nat, n ≍ 1 → n + 1 = 2 := by
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intro _ rfl
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trace_state
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subst_vars
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rfl
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/-- trace: ⊢ 1 + 1 = 2 -/
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#guard_msgs in
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example : ∀ n : Nat, 1 ≍ n → n + 1 = 2 := by
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intro _ rfl
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trace_state
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subst_vars
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rfl
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/-!
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Introduces `let`s and `have`s
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-/
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/--
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trace: x : Nat := 1
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y : Nat := 2
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⊢ x + y = 3
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-/
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#guard_msgs in
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example : let n := 1; have m := 2; n + m = 3 := by
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intro x y
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trace_state
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rfl
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/-!
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Unfolds definitions if necessary.
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-/
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/--
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trace: n : Nat
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⊢ n ≥ 0
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-/
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#guard_msgs in
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example : id (∀ n, n ≥ 0) := by
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intro n
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trace_state
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exact Nat.zero_le n
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/-!
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Patterns.
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-/
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/--
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trace: x : Nat
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y : Int
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⊢ (x, y) = (x, y)
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-/
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#guard_msgs in
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example : ∀ p : Nat × Int, p = p := by
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intro (x, y)
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trace_state
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rfl
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/--
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trace: x : Nat
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y : Int
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⊢ (x, y) = (x, y)
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-/
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#guard_msgs in
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example : ∀ p : Nat × Int, p = p := by
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intro ⟨x, y⟩
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trace_state
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rfl
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/-!
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Can give type ascriptions, and elaboration is interleaved with unification.
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Without interleaving, this test would fail because the ascription would elaborate to `(1 : Nat) = _`
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-/
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/--
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trace: h : (1 : Int) = (1 : Int)
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⊢ True
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-/
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#guard_msgs in
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set_option pp.numericTypes true in
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example : (1 : Int) = 1 → True := by
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intro (h : 1 = _)
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trace_state
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trivial
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/-!
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Error if there are too many arguments.
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-/
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/--
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error: Tactic `introN` failed: There are no additional binders or `let` bindings in the goal to introduce
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a : Nat
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b : a = 1
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⊢ a + 1 = 2
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-/
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#guard_msgs in
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example : ∀ n : Nat, n = 1 → n + 1 = 2 := by
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intro a b c
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/-!
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Error if substitution isn't between variables.
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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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1 = 2
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a✝ : 1 = 2
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⊢ False
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-/
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#guard_msgs in
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example : 1 = 2 → False := by
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intro rfl
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/-!
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Error if type ascription doesn't unify
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-/
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/--
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error: Type mismatch: Hypothesis `n` has type
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Nat
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but is expected to have type
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Int
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due to the provided type annotation
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-/
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#guard_msgs in
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example : ∀ (n : Nat), n = n := by
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intro (n : Int)
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/-!
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Error if type ascription has unsolved metavariables.
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-/
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/--
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error: don't know how to synthesize placeholder
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context:
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⊢ ?_
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---
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error: don't know how to synthesize placeholder for argument `β`
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context:
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⊢ Sort _
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---
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error: unsolved goals
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n : Nat
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⊢ n = n
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-/
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#guard_msgs in
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set_option pp.mvars false in
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example : ∀ (n : Nat), n = n := by
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intro (n : Function.const _ Nat _)
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