Rice's theorem #57
Rice's theorem #57
Conversation
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There seem to be conflicts? |
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oops my mistake! i've fixed the conflicts but it doesn't want to build remotely (it goes through on my computer) i think because of the linter warnings — i'll come back to this soon but it seems to want no space after the transition arrows (ie |
Depending on how your terminal displays certain Unicode, what appears as roughly a single space after an arrow may actually be multiple spaces |
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Hmm I don't think that's it, it's definitely asking for no spaces. It's only complaining about hypotheses of the form "blank reduces to blank" (eg I expect it's because in the declaration |
For this branch with a symbol after the arrow, I think this makes sense. I see though that for the notation without a symbol it is also like this, is that what is being linted for you? This should be changed, probably not noticed previously because we don't use it much. |
Ahh yes you're absolutely right — I've changed it and replaced the spaces after the transitions now |
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Hi @thomaskwaring, |
* add tensor zero eqv * add parr top eqv * use notation for zero and top * add parr and tensor scoped notation
* confluence * non-terminal simps * style * use reduction_sys * non-terminal simp * remove redundant lemma * update TODO * style * fix Trans instances * use Trans instance for brevity * add a reference * para_lc_l and para_lc_r as * naming conventions * change confusing names * aesop ruleset * rm unused lemma * ASCII arrows * missed rule_sets * use proof irrelevance * style * namespace rule set
* Switch to the standard type for relations. * Missing changes
* Activate mathlib linters and fix some warnings. * Add lint & suggest action
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Thanks! I'm doing that now — sorry for the noise I'm not much up on my git-yoga |
This pull request extends the development of SKI combinatory logic — adding notions of evaluation and normal forms, and proving a version of Rice's theorem. The results and definitions are contained in the new file
CombinatoryLogic/Evaluation.lean, which is based heavily on the following development by Bhavik Mehta.Notes
The definitions and results of this PR allows us to define normal-order evaluation as a
PFun, in the sense of Mathlib. The missing piece to make this useful is the so-called Standardisation theorem, saying that normal-order reduction will find a normal form, if there is one. The proof of Theorem T9 of Section C in A Mathematical Logic Without Variables (Rosser, 1935) should be amenable to formalization. This would be very interesting, as it ought to define a surjection from SKI terms to, for instance, partial recursive functions on the natural numbers, demonstrating that SKI terms are Turing-complete.