https://github.com/llelf/cocoricoogle

https://github.com/llelf/cocoricoogle

coq perl6 raku

Last synced: about 1 month ago
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• Host: GitHub
• URL: https://github.com/llelf/cocoricoogle
• Owner: llelf
• Created: 2019-10-18T20:45:43.000Z (about 5 years ago)
• Default Branch: master
• Last Pushed: 2019-10-21T16:52:45.000Z (about 5 years ago)
• Last Synced: 2024-09-29T10:41:44.037Z (about 2 months ago)
• Topics: coq, perl6, raku
• Language: Perl 6
• Size: 14.6 KB
• Stars: 6
• Watchers: 3
• Forks: 0
• Open Issues: 1
• Metadata Files:
  • Readme: README.org

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README

        
#+title: An evening experiment in finding lemmas

Why? Because normal ~Search~ won’t find it.

How to use: =cocoricoogle --help=, this README.

You would probably need to do ~apt/pkg/… install rakudo~.

#+begin_src coq

~/H/cocoricoogle› ./cocoricoogle -in=ssrnat 'a + b - _ = b'

(* HI.                            *)

(* Loading.                       *)

(* Searching (ssrnat).            *)

(* 453 entries. 4077 to search.   *)

addKn

     : forall n : nat, cancel (addn n) (subn^~ n)

     : forall a b : nat, a + b - a = b

(* 1 found. THXBYE.               *)

#+end_src

* V1 (master branch)

Get a list of definitions by doing ~Search _ in ⟨modules⟩~.  Try to match each using

~Check~.

Speed: ≈10000/minute.

** mode A

Query is =forall a b…, …= or =… -> forall a b…, …=.

: ./cocoricoogle -in=ssrnat  'forall x y z, x*_ = x*y + x*z'

** mode B

Query doesn’t contain =forall=. Then =--arity= / =-a= comes into play. Default is

=1-3=.  Free variables are assumed to be =a=, =b=, =c=, and so forth.

=Cocoricoogle= then will try all variants of arities and all permutations of

variables, i. e.

#+begin_src coq

(forall a b) (forall b a) (forall a b c) …

#+end_src

Gotchas (~Check~ is too clever):

- [[https://github.com/coq/coq/issues/10849#issuecomment-544257122][WTF#1]]. Search for ~addnAC~ and get ~PeanoNat.Nat.add_shuffle0~ for free.

- ~addnC~ matches ~forall a b, _ + b = _ + _ b~.

- ~(1 * a)%coq_nat = a~ matches ~a + 0 = a~.

* V2

Match using =Ltac=. Does works and is measurably faster.  Gothas:

- low boundary of arity cannot be arbitrary, because =Ltac= is defined once and

  ~match ty with forall a, a+b=_ => _ end~ is an error.

- different results of V1

* V3

Get the definition list and do everything else in Ltac. Needs a way pass a large(ish)

(at least 1000, but 50000 would be nice) list of definitions as an argument.

* V4

Just fix ~Search~.

* TODO¹

- subterms/coercions

- =ssr.ssrbool= vs =ssrbool=

- ~a→b~ vs ~a==b~ vs ~reflect a b~

¹) is because github doesn't render it if it's just a «TODO».