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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Hipattern
open Names
open Term
open Vars
open Termops
open Tacmach
open Util
open Declarations
open Globnames
module RelDecl = Context.Rel.Declaration
let qflag=ref true
let red_flags=ref CClosure.betaiotazeta
let (=?) f g i1 i2 j1 j2=
let c=f i1 i2 in
if Int.equal c 0 then g j1 j2 else c
let (==?) fg h i1 i2 j1 j2 k1 k2=
let c=fg i1 i2 j1 j2 in
if Int.equal c 0 then h k1 k2 else c
type ('a,'b) sum = Left of 'a | Right of 'b
type counter = bool -> metavariable
exception Is_atom of constr
let meta_succ m = m+1
let rec nb_prod_after n c=
match kind_of_term c with
| Prod (_,_,b) ->if n>0 then nb_prod_after (n-1) b else
1+(nb_prod_after 0 b)
| _ -> 0
let construct_nhyps ind gls =
let nparams = (fst (Global.lookup_inductive (fst ind))).mind_nparams in
let constr_types = Inductiveops.arities_of_constructors (pf_env gls) ind in
let hyp = nb_prod_after nparams in
Array.map hyp constr_types
(* indhyps builds the array of arrays of constructor hyps for (ind largs)*)
let ind_hyps nevar ind largs gls=
let types= Inductiveops.arities_of_constructors (pf_env gls) ind in
let myhyps t =
let t1=prod_applist t largs in
let t2=snd (decompose_prod_n_assum nevar t1) in
fst (decompose_prod_assum t2) in
Array.map myhyps types
let special_nf gl=
let infos=CClosure.create_clos_infos !red_flags (pf_env gl) in
(fun t -> CClosure.norm_val infos (CClosure.inject t))
let special_whd gl=
let infos=CClosure.create_clos_infos !red_flags (pf_env gl) in
(fun t -> CClosure.whd_val infos (CClosure.inject t))
type kind_of_formula=
Arrow of constr*constr
| False of pinductive*constr list
| And of pinductive*constr list*bool
| Or of pinductive*constr list*bool
| Exists of pinductive*constr list
| Forall of constr*constr
| Atom of constr
let kind_of_formula gl term =
let normalize=special_nf gl in
let cciterm=special_whd gl term in
match match_with_imp_term cciterm with
Some (a,b)-> Arrow(a,(pop b))
|_->
match match_with_forall_term cciterm with
Some (_,a,b)-> Forall(a,b)
|_->
match match_with_nodep_ind cciterm with
Some (i,l,n)->
let ind,u=destInd i in
let (mib,mip) = Global.lookup_inductive ind in
let nconstr=Array.length mip.mind_consnames in
if Int.equal nconstr 0 then
False((ind,u),l)
else
let has_realargs=(n>0) in
let is_trivial=
let is_constant c =
Int.equal (nb_prod c) mib.mind_nparams in
Array.exists is_constant mip.mind_nf_lc in
if Inductiveops.mis_is_recursive (ind,mib,mip) ||
(has_realargs && not is_trivial)
then
Atom cciterm
else
if Int.equal nconstr 1 then
And((ind,u),l,is_trivial)
else
Or((ind,u),l,is_trivial)
| _ ->
match match_with_sigma_type cciterm with
Some (i,l)-> Exists((destInd i),l)
|_-> Atom (normalize cciterm)
type atoms = {positive:constr list;negative:constr list}
type side = Hyp | Concl | Hint
let no_atoms = (false,{positive=[];negative=[]})
let dummy_id=VarRef (Id.of_string "_") (* "_" cannot be parsed *)
let build_atoms gl metagen side cciterm =
let trivial =ref false
and positive=ref []
and negative=ref [] in
let normalize=special_nf gl in
let rec build_rec env polarity cciterm=
match kind_of_formula gl cciterm with
False(_,_)->if not polarity then trivial:=true
| Arrow (a,b)->
build_rec env (not polarity) a;
build_rec env polarity b
| And(i,l,b) | Or(i,l,b)->
if b then
begin
let unsigned=normalize (substnl env 0 cciterm) in
if polarity then
positive:= unsigned :: !positive
else
negative:= unsigned :: !negative
end;
let v = ind_hyps 0 i l gl in
let g i _ decl =
build_rec env polarity (lift i (RelDecl.get_type decl)) in
let f l =
List.fold_left_i g (1-(List.length l)) () l in
if polarity && (* we have a constant constructor *)
Array.exists (function []->true|_->false) v
then trivial:=true;
Array.iter f v
| Exists(i,l)->
let var=mkMeta (metagen true) in
let v =(ind_hyps 1 i l gl).(0) in
let g i _ decl =
build_rec (var::env) polarity (lift i (RelDecl.get_type decl)) in
List.fold_left_i g (2-(List.length l)) () v
| Forall(_,b)->
let var=mkMeta (metagen true) in
build_rec (var::env) polarity b
| Atom t->
let unsigned=substnl env 0 t in
if not (isMeta unsigned) then (* discarding wildcard atoms *)
if polarity then
positive:= unsigned :: !positive
else
negative:= unsigned :: !negative in
begin
match side with
Concl -> build_rec [] true cciterm
| Hyp -> build_rec [] false cciterm
| Hint ->
let rels,head=decompose_prod cciterm in
let env=List.rev_map (fun _->mkMeta (metagen true)) rels in
build_rec env false head;trivial:=false (* special for hints *)
end;
(!trivial,
{positive= !positive;
negative= !negative})
type right_pattern =
Rarrow
| Rand
| Ror
| Rfalse
| Rforall
| Rexists of metavariable*constr*bool
type left_arrow_pattern=
LLatom
| LLfalse of pinductive*constr list
| LLand of pinductive*constr list
| LLor of pinductive*constr list
| LLforall of constr
| LLexists of pinductive*constr list
| LLarrow of constr*constr*constr
type left_pattern=
Lfalse
| Land of pinductive
| Lor of pinductive
| Lforall of metavariable*constr*bool
| Lexists of pinductive
| LA of constr*left_arrow_pattern
type t={id:global_reference;
constr:constr;
pat:(left_pattern,right_pattern) sum;
atoms:atoms}
let build_formula side nam typ gl metagen=
let normalize = special_nf gl in
try
let m=meta_succ(metagen false) in
let trivial,atoms=
if !qflag then
build_atoms gl metagen side typ
else no_atoms in
let pattern=
match side with
Concl ->
let pat=
match kind_of_formula gl typ with
False(_,_) -> Rfalse
| Atom a -> raise (Is_atom a)
| And(_,_,_) -> Rand
| Or(_,_,_) -> Ror
| Exists (i,l) ->
let d = RelDecl.get_type (List.last (ind_hyps 0 i l gl).(0)) in
Rexists(m,d,trivial)
| Forall (_,a) -> Rforall
| Arrow (a,b) -> Rarrow in
Right pat
| _ ->
let pat=
match kind_of_formula gl typ with
False(i,_) -> Lfalse
| Atom a -> raise (Is_atom a)
| And(i,_,b) ->
if b then
let nftyp=normalize typ in raise (Is_atom nftyp)
else Land i
| Or(i,_,b) ->
if b then
let nftyp=normalize typ in raise (Is_atom nftyp)
else Lor i
| Exists (ind,_) -> Lexists ind
| Forall (d,_) ->
Lforall(m,d,trivial)
| Arrow (a,b) ->
let nfa=normalize a in
LA (nfa,
match kind_of_formula gl a with
False(i,l)-> LLfalse(i,l)
| Atom t-> LLatom
| And(i,l,_)-> LLand(i,l)
| Or(i,l,_)-> LLor(i,l)
| Arrow(a,c)-> LLarrow(a,c,b)
| Exists(i,l)->LLexists(i,l)
| Forall(_,_)->LLforall a) in
Left pat
in
Left {id=nam;
constr=normalize typ;
pat=pattern;
atoms=atoms}
with Is_atom a-> Right a (* already in nf *)
|
