b5122b6a7b
This change * moves `termination_by` and `decreasing_by` next to the function they apply to * simplify the syntax of `termination_by` * apply the `decreasing_by` goal to all goals at once, for better interactive use. See the section in `RELEASES.md` for more details and migration advise. This is a hard breaking change, requiring developers to touch every `termination_by` in their code base. We decided to still do it as a hard-breaking change, because supporting both old and new syntax at the same time would be non-trivial, and not save that much. Moreover, this requires changes to some metaprograms that developers might have written, and supporting both syntaxes at the same time would make _their_ migration harder.
138 lines
3 KiB
Text
138 lines
3 KiB
Text
/-!
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Various tests about `decreasing_by`.
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-/
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-- For concise recursive definition that need well-founded recursion
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-- and `decreasing_by` tactics that would fail if run on the subgoal
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opaque dec1 : Nat → Nat
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axiom dec1_lt (n : Nat) : dec1 n < n
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opaque dec2 : Nat → Nat
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axiom dec2_lt (n : Nat) : dec2 n < n
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def simple (n : Nat) := n + simple (dec1 n)
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decreasing_by apply dec1_lt
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namespace Ex1
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-- Multiple goals, explicit termination_By
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
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termination_by (n, m)
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decreasing_by
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· simp_wf
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apply Prod.Lex.right
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apply dec2_lt
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· simp_wf
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apply Prod.Lex.left
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apply dec1_lt
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end Ex1
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namespace Ex2
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-- Multiple goals, no termination_By
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-- This does *not* work, because GuessLex does not pass multiple goals to the tactic.
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-- so this tactic script fails.
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
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decreasing_by
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· simp_wf
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apply Prod.Lex.right
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apply dec2_lt
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· simp_wf
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apply Prod.Lex.left
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apply dec1_lt
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end Ex2
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namespace Ex3
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-- Using `all_goals`, explicit termination_By
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
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termination_by (n, m)
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decreasing_by all_goals
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simp_wf
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first
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| apply Prod.Lex.right
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apply dec2_lt
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| apply Prod.Lex.left
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apply dec1_lt
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end Ex3
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namespace Ex4
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-- Multiple goals, no termination_By
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-- This does work, because the tactic is flexible enough
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-- (Not a recommended way; complex `decrasing_by` should go along with `termination_by`.)
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
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decreasing_by all_goals
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simp_wf
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first
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| apply Prod.Lex.right
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apply dec2_lt
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| apply Prod.Lex.left
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apply dec1_lt
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end Ex4
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namespace Ex5
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-- Empty proof. Produces parse error and unsolved goals.
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
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termination_by n m => (n, m)
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decreasing_by -- Error
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end Ex5
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namespace Ex6
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-- Incomplete tactic
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-- Unsolved goals reported
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
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termination_by (n, m)
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decreasing_by apply id -- Error
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end Ex6
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namespace Ex7
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-- Incomplete tactic, no termination_by
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-- Shows guess-lex matrix
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
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decreasing_by apply id
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end Ex7
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namespace Ex8
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-- tactic solving just one goal
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-- unsolved goals
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
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termination_by (n, m)
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decreasing_by -- Error
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· simp_wf
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apply Prod.Lex.right
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apply dec2_lt
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end Ex8
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namespace Ex9
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-- Incomplete tactic, no termination_by
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-- Shows guess-lex matrix
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def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
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decreasing_by
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· simp_wf
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apply Prod.Lex.right
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apply dec2_lt
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end Ex9
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namespace Ex10
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-- This checks that guess-lex does not run tactics in “recover” mode.
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-- (If it would it would produce the wrong termination order and then we should see errors)
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def foo (n m : Nat) : Nat := foo (n - 1) (dec2 m)
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decreasing_by all_goals
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· simp_wf
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apply dec2_lt
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end Ex10
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