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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* $Id:$ *)
(*i camlp4deps: "parsing/grammar.cma" i*)
open Decl_expr
open Names
open Term
open Genarg
open Pcoq
open Pcoq.Constr
open Pcoq.Tactic
open Pcoq.Vernac_
let none_is_empty = function
None -> []
| Some l -> l
GEXTEND Gram
GLOBAL: proof_instr;
thesis :
[[ "thesis" -> Plain
| "thesis"; "for"; i=ident -> (For i)
| "thesis"; "["; n=INT ;"]" -> (Sub (int_of_string n))
]];
statement :
[[ i=ident ; ":" ; c=constr -> {st_label=Name i;st_it=c}
| i=ident -> {st_label=Anonymous;
st_it=Topconstr.CRef (Libnames.Ident (loc, i))}
| c=constr -> {st_label=Anonymous;st_it=c}
]];
constr_or_thesis :
[[ t=thesis -> Thesis t ] |
[ c=constr -> This c
]];
statement_or_thesis :
[
[ t=thesis -> {st_label=Anonymous;st_it=Thesis t} ]
|
[ i=ident ; ":" ; cot=constr_or_thesis -> {st_label=Name i;st_it=cot}
| i=ident -> {st_label=Anonymous;
st_it=This (Topconstr.CRef (Libnames.Ident (loc, i)))}
| c=constr -> {st_label=Anonymous;st_it=This c}
]
];
justification :
[[ -> Automated []
| IDENT "by"; l=LIST1 constr SEP "," -> Automated l
| IDENT "by"; IDENT "tactic"; tac=tactic -> By_tactic tac ]]
;
simple_cut_or_thesis :
[[ ls = statement_or_thesis;
j=justification -> {cut_stat=ls;cut_by=j} ]]
;
simple_cut :
[[ ls = statement;
j=justification -> {cut_stat=ls;cut_by=j} ]]
;
elim_type:
[[ IDENT "induction" -> ET_Induction
| IDENT "cases" -> ET_Case_analysis ]]
;
block_type :
[[ IDENT "claim" -> B_claim
| IDENT "focus" -> B_focus
| IDENT "proof" -> B_proof
| et=elim_type -> B_elim et ]]
;
elim_obj:
[[ IDENT "on"; c=constr -> Real c
| IDENT "of"; c=simple_cut -> Virtual c ]]
;
elim_step:
[[ IDENT "consider" ; h=vars ; IDENT "from" ; c=constr -> Pconsider (c,h)
| IDENT "per"; et=elim_type; obj=elim_obj -> Pper (et,obj)]]
;
rew_step :
[[ "~=" ; c=simple_cut -> (Rhs,c)
| "=~" ; c=simple_cut -> (Lhs,c)]]
;
cut_step:
[[ "then"; tt=elim_step -> Pthen tt
| "then"; c=simple_cut_or_thesis -> Pthen (Pcut c)
| IDENT "thus"; tt=rew_step -> Pthus (let s,c=tt in Prew (s,c))
| IDENT "thus"; c=simple_cut_or_thesis -> Pthus (Pcut c)
| IDENT "hence"; c=simple_cut_or_thesis -> Phence (Pcut c)
| tt=elim_step -> tt
| tt=rew_step -> let s,c=tt in Prew (s,c);
| IDENT "have"; c=simple_cut_or_thesis -> Pcut c;
| IDENT "claim"; c=statement -> Pclaim c;
| IDENT "focus"; IDENT "on"; c=statement -> Pfocus c;
| "end"; bt = block_type -> Pend bt;
| IDENT "escape" -> Pescape ]]
;
(* examiner s'il est possible de faire R _ et _ R pour R une relation qcq*)
loc_id:
[[ id=ident -> fun x -> (loc,(id,x)) ]];
hyp:
[[ id=loc_id -> id None ;
| id=loc_id ; ":" ; c=constr -> id (Some c)]]
;
vars:
[[ name=hyp -> [Hvar name]
| name=hyp; ","; v=vars -> (Hvar name) :: v
| name=hyp; IDENT "be";
IDENT "such"; IDENT "that"; h=hyps -> (Hvar name)::h
| name=hyp;
IDENT "such"; IDENT "that"; h=hyps -> (Hvar name)::h
]]
;
hyps:
[[ IDENT "we"; IDENT "have"; v=vars -> v
| st=statement; IDENT "and"; h=hyps -> Hprop st::h
| st=statement; IDENT "and"; v=vars -> Hprop st::v
| st=statement -> [Hprop st]
]]
;
vars_or_thesis:
[[name=hyp -> [Hvar name]
|name=hyp; ","; v=vars_or_thesis -> (Hvar name) :: v
|name=hyp; OPT[IDENT "be"];
IDENT "such"; IDENT "that"; h=hyps_or_thesis -> (Hvar name)::h
]]
;
hyps_or_thesis:
[[ IDENT "we"; IDENT "have"; v=vars_or_thesis -> v
| st=statement_or_thesis; IDENT "and"; h=hyps_or_thesis -> Hprop st::h
| st=statement_or_thesis; IDENT "and"; v=vars_or_thesis -> Hprop st::v
| st=statement_or_thesis -> [Hprop st];
]]
;
intro_step:
[[ IDENT "suppose" ; h=hyps -> Psuppose h
| IDENT "suppose" ; IDENT "it"; IDENT "is" ; c=pattern LEVEL "0" ;
po=OPT[ IDENT "with"; p=LIST1 hyp -> p ] ;
ho=OPT[ IDENT "and" ; h=hyps_or_thesis -> h ] ->
Pcase (none_is_empty po,c,none_is_empty ho)
| "let" ; v=vars -> Plet v
| IDENT "take"; witnesses = LIST1 constr SEP "," -> Ptake witnesses
| IDENT "assume"; h=hyps -> Passume h
| IDENT "given"; h=vars -> Pgiven h
| IDENT "define"; id=ident; args=LIST0 hyp;
"as"; body=constr -> Pdefine(id,args,body)
| IDENT "reconsider"; id=ident; "as" ; typ=constr -> Pcast (This id,typ)
| IDENT "reconsider"; t=thesis; "as" ; typ=constr -> Pcast (Thesis t ,typ)
]]
;
emphasis :
[[ -> 0
| "*" -> 1
| "**" -> 2
| "***" -> 3
]]
;
bare_proof_instr:
[[ c = cut_step -> c ;
| i = intro_step -> i ]]
;
proof_instr :
[[ e=emphasis;i=bare_proof_instr -> {emph=e;instr=i}]]
;
END;;
|
