80 lines
2.8 KiB
Text
80 lines
2.8 KiB
Text
example (n : nat) (h : n < 5) : n < 5 :=
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begin
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revert h n, -- user provided a "bad" order, then we must sort
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intro n, intro h, exact h
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end
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constant p {n m : nat} : n < m → Prop
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example (n m : nat) (h1 : n < 5) (h2 : p h1) : p h1 :=
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begin
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revert n h2, -- there is an extra dependency that must be reverted too
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intro n, intro h1, intro h2, exact h2
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end
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example (n m : nat) (h1 : n < 5) (h2 : p h1) : p h1 :=
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begin
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revert n, -- there are extra dependencies that must be reverted too
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intro n, intro h1, intro h2, exact h2
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end
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-- set_option pp.purify_metavars false
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example : let n := 5 in ∀ (m : nat) (h1 : n < 5) (h2 : p h1), p h1 :=
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begin
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intros n m h1 h2,
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/-
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The goal is `?M1 : (n : ℕ := 5) (m : ℕ) (h1 : n < 5) (h2 : p h1) ⊢ p h1`
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-/
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(do g ← list.head <$> tactic.get_goals, tactic.trace g, n ← tactic.get_local `n, tactic.revert n, tactic.instantiate_mvars g >>= tactic.trace),
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/-
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The goal is now `?M1' : (m : ℕ) ⊢ let n : ℕ := 5 in ∀ (h1 : n < 5) (h2 : p h1), p h1`
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and we performed the assignment
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`?M1 := ?M1' h1 h2`
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-/
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intros n h1 h2,
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exact h2
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end
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constant f (g : nat → nat) (h : ∀ x, g x = x) (n m : nat) (g n = m) : n = m
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example (n m : nat) (h : n = m) : n = m :=
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begin
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fapply f,
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/- main goal is
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?M1 : (n m : ℕ) ⊢ ℕ → ℕ -/
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intro a,
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/- main goal is now
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`?M1' : (n m : ℕ) (a : ℕ) ⊢ ℕ`
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and (in Lean3) we perform the assignment
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`?M1 := fun a, ?M1'[a]` where
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`?M1'[a]` denotes a delayed abstraction.
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In Lean4, we don't have delayed abstractions anymore, and the assignment above is represented as
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`?M1 := (lctx, [a], ?M1')`
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Remark: `lctx` is the local context that contains `a` definition.
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-/
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(tactic.rotate_left 1),
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/- We moved to the second goal:
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`?M2 : (n m : ℕ) ⊢ ∀ (x : ℕ), ?M1 x = x`
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In Lean3, the goal would be
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`?M2 : (n m : ℕ) ⊢ ∀ (x : ℕ), ?M1'[x] x = x`
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In Lean4, we only substitute `?M1` when `?M1'` is fully assigned, and we can abstract `a` since we have
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`?M1 := (lctx, [a], ?M1')` -/
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intro b,
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/-
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`?M2' : (n m : ℕ) (b : ℕ) ⊢ ?M1 b = b`
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and we perform the assignment
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`?M2 := (lctx, [b], ?M2')`
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-/
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exact (eq.refl b),
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/- The `exact` tactic should produce an error in Lean4.
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Reason: the goal contains a metavariable that was partially assigned (`?M1`) by an `intro` tactic.
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Remark: this is a bizarre case, and it can only happen if the user tried to solve a goal `G1` a little bit,
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and then uses rotate to work on a goal `G2` that depends on `G1`.
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On the other hand, we don't have delayed abstractions in Lean4, and users will never see (and by confused by) them in goals.
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The error is detected at `type_context::is_def_eq`, when it finds a metavariable that is delayed assigned.
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-/
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exact n, exact m,
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exact rfl,
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exact h
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end
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