33aaabaed7
This PR improves the generation of `.induct_unfolding` by rewriting `match` statements more reliably, using the new “congruence equations” introduced in #8284. Fixes #8195.
112 lines
4.2 KiB
Text
112 lines
4.2 KiB
Text
-- set_option trace.Meta.FunInd true in
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def foo (n m : Nat) (h : n < m) : Nat :=
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match m with
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| 0 => by contradiction -- This case should not show up in the principles below
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| m+1 => match n with
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| 0 => 0
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| n+1 => foo n m (Nat.succ_lt_succ_iff.mp h)
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/--
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info: foo.induct (motive : (n m : Nat) → n < m → Prop) (case1 : ∀ (m : Nat) (h : 0 < m + 1), 0 < m.succ → motive 0 m.succ h)
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(case2 : ∀ (m n : Nat) (h : n + 1 < m + 1), n.succ < m.succ → motive n m ⋯ → motive n.succ m.succ h) (n m : Nat)
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(h : n < m) : motive n m h
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-/
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#guard_msgs(pass trace, all) in
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#check foo.induct
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/--
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info: foo.induct_unfolding (motive : (n m : Nat) → n < m → Nat → Prop)
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(case1 : ∀ (m : Nat) (h : 0 < m + 1), 0 < m.succ → motive 0 m.succ h 0)
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(case2 :
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∀ (m n : Nat) (h : n + 1 < m + 1), n.succ < m.succ → motive n m ⋯ (foo n m ⋯) → motive n.succ m.succ h (foo n m ⋯))
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(n m : Nat) (h : n < m) : motive n m h (foo n m h)
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-/
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#guard_msgs(pass trace, all) in
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#check foo.induct_unfolding
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/--
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info: foo.fun_cases (motive : (n m : Nat) → n < m → Prop)
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(case1 : ∀ (m : Nat) (h : 0 < m + 1), 0 < m + 1 → 0 < m.succ → motive 0 m.succ h)
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(case2 : ∀ (m n : Nat) (h : n + 1 < m + 1), n.succ < m + 1 → n.succ < m.succ → motive n.succ m.succ h) (n m : Nat)
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(h : n < m) : motive n m h
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-/
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#guard_msgs(pass trace, all) in
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#check foo.fun_cases
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def bar (n m : Nat) (h : n = m) : Nat :=
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match m with
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| 0 => 0
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| m+1 => match n with
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| 0 => by contradiction
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| n+1 => bar n m (Nat.succ.inj h)
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/--
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info: bar.induct (motive : (n m : Nat) → n = m → Prop) (case1 : ∀ (h : 0 = 0), motive 0 0 h)
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(case2 : ∀ (m n : Nat) (h : n + 1 = m + 1), m.succ = n.succ → motive n m ⋯ → motive n.succ m.succ h) (n m : Nat)
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(h : n = m) : motive n m h
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-/
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#guard_msgs(pass trace, all) in
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#check bar.induct
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/--
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info: bar.induct_unfolding (motive : (n m : Nat) → n = m → Nat → Prop) (case1 : ∀ (h : 0 = 0), motive 0 0 h 0)
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(case2 :
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∀ (m n : Nat) (h : n + 1 = m + 1), m.succ = n.succ → motive n m ⋯ (bar n m ⋯) → motive n.succ m.succ h (bar n m ⋯))
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(n m : Nat) (h : n = m) : motive n m h (bar n m h)
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-/
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#guard_msgs(pass trace, all) in
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#check bar.induct_unfolding
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/--
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info: bar.fun_cases (motive : (n m : Nat) → n = m → Prop) (case1 : ∀ (h : 0 = 0), motive 0 0 h)
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(case2 : ∀ (m n : Nat) (h : n + 1 = m + 1), m.succ = m + 1 → m.succ = n.succ → motive n.succ m.succ h) (n m : Nat)
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(h : n = m) : motive n m h
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-/
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#guard_msgs(pass trace, all) in
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#check bar.fun_cases
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def baz (n : Nat) (h : n ≠ 0) : Nat :=
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match n with
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| 0 => by contradiction
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| k + 1 => if h : k = 0 then 0 else baz k h
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/--
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info: baz.induct (motive : (n : Nat) → n ≠ 0 → Prop) (case1 : ∀ (h : 0 + 1 ≠ 0), motive (Nat.succ 0) h)
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(case2 : ∀ (k : Nat) (h : k + 1 ≠ 0) (h_1 : ¬k = 0), motive k h_1 → motive k.succ h) (n : Nat) (h : n ≠ 0) :
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motive n h
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-/
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#guard_msgs(pass trace, all) in
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#check baz.induct
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/--
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info: baz.induct_unfolding (motive : (n : Nat) → n ≠ 0 → Nat → Prop) (case1 : ∀ (h : 0 + 1 ≠ 0), motive (Nat.succ 0) h 0)
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(case2 : ∀ (k : Nat) (h : k + 1 ≠ 0) (h_1 : ¬k = 0), motive k h_1 (baz k h_1) → motive k.succ h (baz k h_1)) (n : Nat)
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(h : n ≠ 0) : motive n h (baz n h)
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-/
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#guard_msgs(pass trace, all) in
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#check baz.induct_unfolding
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/--
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info: baz.fun_cases (motive : (n : Nat) → n ≠ 0 → Prop) (case1 : ∀ (h : 0 + 1 ≠ 0), Nat.succ 0 ≠ 0 → motive (Nat.succ 0) h)
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(case2 : ∀ (k : Nat) (h : k + 1 ≠ 0), ¬k = 0 → k.succ ≠ 0 → motive k.succ h) (n : Nat) (h : n ≠ 0) : motive n h
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-/
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#guard_msgs(pass trace, all) in
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#check baz.fun_cases
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def mean (n m : Nat) (h : n = m) : Nat :=
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match m with
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| 0 => 0
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| m+1 => match n with
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| 0 => (by contradiction : Bool → Nat) true -- overapplied `noConfusion`
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| n+1 => Nat.noConfusion h fun h' => mean n m h' -- non-contradictory `noConfusion`
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/--
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info: mean.fun_cases (motive : (n m : Nat) → n = m → Prop) (case1 : ∀ (h : 0 = 0), motive 0 0 h)
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(case2 : ∀ (m n : Nat) (h : n + 1 = m + 1), m.succ = m + 1 → m.succ = n.succ → motive n.succ m.succ h) (n m : Nat)
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(h : n = m) : motive n m h
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-/
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#guard_msgs(pass trace, all) in
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#check mean.fun_cases
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