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.
63 lines
2 KiB
Text
63 lines
2 KiB
Text
/-!
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A “tricky” example from “Finding Lexicographic Orders for Termination Proofs in
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Isabelle/HOL” by Lukas Bulwahn, Alexander Krauss, and Tobias Nipkow,
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10.1007/978-3-540-74591-4_5
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At the time of writing, Lean is able to find the lexicographic order
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just fine, but only if the tactic is powerful enough. In partiuclar,
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the default `decreasing_tactic` can only handle lexicographic descend when either
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the left gets smaller, or the left stays equal and the right gets smaller.
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But here we need to allow the general form, where the left is ≤ and the right
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gets smaller. This needs a backtracking proof search, it seems, which we build here
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(`search_lex`).
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-/
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set_option showInferredTerminationBy true
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macro_rules | `(tactic| decreasing_trivial) =>
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`(tactic| apply Nat.le_refl)
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macro_rules | `(tactic| decreasing_trivial) =>
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`(tactic| apply Nat.succ_lt_succ; decreasing_trivial)
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macro_rules | `(tactic| decreasing_trivial) =>
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`(tactic| apply Nat.sub_le)
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macro_rules | `(tactic| decreasing_trivial) =>
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`(tactic| apply Nat.div_le_self)
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syntax "search_lex " tacticSeq : tactic
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macro_rules | `(tactic|search_lex $ts:tacticSeq) => `(tactic| (
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solve
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| apply Prod.Lex.right'
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· $ts
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· search_lex $ts
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| apply Prod.Lex.left
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· $ts
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| $ts
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))
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-- set_option trace.Elab.definition.wf true in
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mutual
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def prod (x y z : Nat) : Nat :=
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if y % 2 = 0 then eprod x y z else oprod x y z
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-- termination_by (y, 1, 0)
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decreasing_by
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all_goals
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search_lex solve
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| decreasing_trivial
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| apply Nat.bitwise_rec_lemma; assumption
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def oprod (x y z : Nat) := eprod x (y - 1) (z + x)
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-- termination_by (y, 0, 1)
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decreasing_by
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search_lex solve
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| decreasing_trivial
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| apply Nat.bitwise_rec_lemma; assumption
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def eprod (x y z : Nat) := if y = 0 then z else prod (2 * x) (y / 2) z
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-- termination_by (y, 0, 0)
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decreasing_by
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search_lex solve
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| decreasing_trivial
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| apply Nat.bitwise_rec_lemma; assumption
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end
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