1311e36a98
This adds support for mutual structural recursive functions. For now this is opt-in: The functions must have a `termination_by structural …` annotation (new since #4542) for this to work: ```lean mutual inductive A | self : A → A | other : B → A | empty inductive B | self : B → B | other : A → B | empty end mutual def A.size : A → Nat | .self a => a.size + 1 | .other b => b.size + 1 | .empty => 0 termination_by structural x => x def B.size : B → Nat | .self b => b.size + 1 | .other a => a.size + 1 | .empty => 0 termination_by structural x => x end ``` The recursive functions don’t have to be in a one-to-one relation to a set of mutually recursive inductive data types. It is possible to ignore some of the types: ```lean def A.self_size : A → Nat | .self a => a.self_size + 1 | .other _ => 0 | .empty => 0 termination_by structural x => x ``` or have more than one function per argument type: ```lean def isEven : Nat → Prop | 0 => True | n+1 => ¬ isOdd n termination_by structural x => x def isOdd : Nat → Prop | 0 => False | n+1 => ¬ isEven n termination_by structural x => x ``` This does not include * Support for nested inductive data types or nested recursion * Inferring mutual structural recursion in the absence of `termination_by`. * Functional induction principles for these. * Mutually recursive functions that live in different universes. This may be possible, maybe after beefing up the `.below` and `.brecOn` functions; we can look into this some other time, maybe when there are concrete use cases. --------- Co-authored-by: Richard Kiss <him@richardkiss.com> Co-authored-by: Tobias Grosser <tobias@grosser.es>
98 lines
2.5 KiB
Text
98 lines
2.5 KiB
Text
Inferred termination argument:
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termination_by n - i
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Inferred termination argument:
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termination_by xs.size - i
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Inferred termination argument:
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termination_by xs.size - i
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Inferred termination argument:
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termination_by (xs.size - i, ys.size - j)
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Inferred termination argument:
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termination_by (xs.size - i, i - j)
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Inferred termination argument:
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termination_by (xs.size - i, i)
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guessLexDiff.lean:84:4-84:11: error: fail to show termination for
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failure
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with errors
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structural recursion cannot be used:
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argument #1 cannot be used for structural recursion
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it is unchanged in the recursive calls
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argument #2 cannot be used for structural recursion
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failed to eliminate recursive application
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_root_.failure xs i
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Could not find a decreasing measure.
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The arguments relate at each recursive call as follows:
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(<, ≤, =: relation proved, ? all proofs failed, _: no proof attempted)
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i #1 #2 i + i
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1) 85:26-38 = = = =
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2) 85:58-76 ? < _ _
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3) 85:26-38 = = = =
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4) 88:26-42 _ < _ _
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5) 88:26-42 ? ≤ ≤ ?
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6) 88:26-42 _ < _ _
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7) 88:26-42 _ < _ _
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8) 88:26-42 _ < _ _
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9) 97:8-20 _ < _ _
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#1: xs.size - i
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#2: xs.size - (i + 1)
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Please use `termination_by` to specify a decreasing measure.
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guessLexDiff.lean:102:4-102:18: error: fail to show termination for
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mutual_failure
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mutual_failure2
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with errors
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mutual structural recursion requires explicit `termination_by` clauses
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Could not find a decreasing measure.
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The arguments relate at each recursive call as follows:
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(<, ≤, =: relation proved, ? all proofs failed, _: no proof attempted)
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Call from mutual_failure to mutual_failure2 at 104:4-24:
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i #1 #2
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i = ? ?
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#3 ? = ?
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Call from mutual_failure to mutual_failure2 at 104:52-78:
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i #1 #2
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i ? _ _
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#3 _ < _
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Call from mutual_failure to mutual_failure2 at 104:4-24:
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i #1 #2
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i _ _ _
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#3 _ = _
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Call from mutual_failure to mutual_failure2 at 111:4-28:
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i #1 #2
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i _ _ _
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#3 _ < _
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Call from mutual_failure to mutual_failure2 at 117:8-28:
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i #1 #2
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i _ _ _
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#3 _ ? _
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Call from mutual_failure2 to mutual_failure at 123:4-23:
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i #3
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i _ _
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#1 _ _
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#2 _ _
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Call from mutual_failure2 to mutual_failure at 123:50-75:
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i #3
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i _ _
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#1 _ _
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#2 _ _
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Call from mutual_failure2 to mutual_failure at 127:4-27:
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i #3
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i _ _
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#1 _ _
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#2 _ _
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Call from mutual_failure2 to mutual_failure at 133:8-27:
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i #3
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i _ _
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#1 _ _
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#2 _ _
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#1: xs.size - i
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#2: xs.size - (i + 1)
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#3: xs.size - i
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Please use `termination_by` to specify a decreasing measure.
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