cbba783bcf
This improves Lean’s capabilities to guess the termination measure for
well-founded
recursion, by also trying lexicographic orders. For example:
def ackermann (n m : Nat) := match n, m with
| 0, m => m + 1
| .succ n, 0 => ackermann n 1
| .succ n, .succ m => ackermann n (ackermann (n + 1) m)
now just works.
The module docstring of `Lean.Elab.PreDefinition.WF.GuessLex` tells the
technical story.
Fixes #2837
23 lines
534 B
Text
23 lines
534 B
Text
/-!
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Another “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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Works out of the box!
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-/
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mutual
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def pedal : Nat → Nat → Nat → Nat
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| 0, _m, c => c
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| _n, 0, c => c
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| n+1, m+1, c =>
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if n < m
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then coast n m (c + m + 1)
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else pedal n (m + 1) (c + m + 1)
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def coast : Nat → Nat → Nat → Nat
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| n, m , c =>
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if n < m
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then coast n (m - 1) (c + n)
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else pedal n m (c + n)
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end
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