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.
129 lines
2.9 KiB
Text
129 lines
2.9 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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· 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 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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· 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 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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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 `decreasing_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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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)
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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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· 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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· 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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· apply dec2_lt
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end Ex10
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