feat(CombinatoryLogic): Partrec → SKI computability#403
feat(CombinatoryLogic): Partrec → SKI computability#403jessealama wants to merge 7 commits intoleanprover:mainfrom
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Looks pretty good to me! The title should probably say that only one direction of the equivalence is proven here (Partrec -> SKI). If I have time I can do a more thorough review but my only real concern would be whether the new version of primitive recursion could use the original one in Recursion.lean any more (though I would believe that the pair/unpair dance makes that impossible)
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jessealama
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In an earlier version of this proof, I tried to apply the original recursor directly but gave up because it was getting too bulky. The new |
Makes sense! happy for you to leave as-is and/or hide the definition as you & the maintainers prefer. I suppose the ideal outcome would be for the definition of the term to mirror what the function looks like in |
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Converting to draft — splitting out the Sqrt/NatPair/NatUnpair layer as a smaller PR first: #445. |
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@jessealama Can you resolve the merge conflicts here please? |
Prove that every Nat.Partrec function on ℕ is SKI-computable (nat_partrec_ski_computable). Translates all eight Nat.Partrec.Code constructors to SKI terms and proves correctness, exercising the Recursion.lean infrastructure: primitive recursion (Rec), μ-recursion (RFind/RFindAbove), Nat pairing/unpairing, and integer square root.
…ntions Shorten verbose docstrings, collapse rw/have/subst patterns to obtain rfl, extract inline calc blocks, and rename to camelCase (natPartrec_skiComputable, rfindAbove_induction).
Only one direction (Partrec → SKI) is proven; rename file and section header to avoid overclaiming equivalence. Remove unrelated SKIPartrec stub (converse direction) to a separate branch.
Add computes_of_total and RFindAbove_unfold helpers to eliminate repeated proof patterns. Simplify comp/pair_computes Part.mem chains and rfindAbove_induction via early subst + local helper. Remove dormant @[scoped grind] attributes from nil_correct and neg_correct.
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Split the conjunction into `rfind_eval_root` (f evaluates to 0 at the root) and `rfind_eval_pos_below` (f evaluates to nonzero below k).
Done! I'd like to leave this as a draft for now; I'm a bit unhappy with a couple of the proofs and will spend some time cleaning them up. I'm open to any suggestions, of course, but just as a matter of review priority, I'm happy to put this on your backburner. |
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Prove that every Nat.Partrec function on ℕ is SKI-computable (nat_partrec_ski_computable). Translates all eight Nat.Partrec.Code constructors to SKI terms and proves correctness, exercising the Recursion.lean infrastructure: primitive recursion (Rec), μ-recursion (RFind/RFindAbove), Nat pairing/unpairing, and integer square root.