Find the definition and notations like ++ in Coq

Question

How can we get the definition/type for those notations like "+", or "++" of List?

I have tried : Search ++, Search "++", Search (++), SearchAbout ... and Check ++, Check "++", Check(++).

None of them work however...

SearchAbout "++" does show some info, but not the definition of "++".

score 26 · Accepted Answer · answered Sep 25 '14 at 06:50

26

Do:

Locate "++".

To lookup for notations.

Then you can Print/Check the actual term being denoted.

answered Sep 25 '14 at 06:50

Ptival

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Thanks, this is very useful. But I'm still wondering is there a convenient command to do this in emacs & proof general ? – luochen1990 Sep 29 '18 at 06:59
@luochen1990 In ProofGeneral, the default shortcuts are `C-c C-a C-c` for Check, and `C-c C-a C-p` for Print. If you use menus, they are somewhere in the ProofGeneral menus too. – Ptival Sep 29 '18 at 17:01
Thanks, but is there a shortcut for "Locate" ? – luochen1990 Oct 09 '18 at 02:52
Shortcut for Locate is `C-c C-a C-n` – lelf Jun 24 '19 at 16:56

score 8 · Answer 2 · answered Sep 25 '14 at 07:28

8

In addition to previous answer, you can use Unfold "++" to unfold it's definition without locating it first.

Example:

Coq < Goal forall A (l : list A), l ++ [] = [].
1 subgoal

  ============================
   forall (A : Type) (l : list A), l ++ [] = []

Unnamed_thm < unfold "++".
1 subgoal

  ============================
   forall (A : Type) (l : list A),
   (fix app (l0 m : list A) {struct l0} : list A :=
      match l0 with
      | [] => m
      | a :: l1 => a :: app l1 m
      end) l [] = []

answered Sep 25 '14 at 07:28

sinan

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Nit: presumably you meant `l ++ [] = l`, not `l ++ [] = []`? – Mark Dickinson Sep 27 '14 at 07:48
@MarkDickinson that would make it provable, yes. :) – sinan Sep 27 '14 at 17:13

Find the definition and notations like ++ in Coq

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