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|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
open Util
open Names
open Libnames
open Nameops
open Term
open Termops
open Reductionops
open Rawterm
open Environ
open Nametab
type constr_pattern =
| PRef of global_reference
| PVar of identifier
| PEvar of existential_key
| PRel of int
| PApp of constr_pattern * constr_pattern array
| PSoApp of int * constr_pattern list
| PLambda of name * constr_pattern * constr_pattern
| PProd of name * constr_pattern * constr_pattern
| PLetIn of name * constr_pattern * constr_pattern
| PSort of rawsort
| PMeta of int option
| PCase of case_style * constr_pattern option * constr_pattern *
constr_pattern array
| PFix of fixpoint
| PCoFix of cofixpoint
let rec occur_meta_pattern = function
| PApp (f,args) ->
(occur_meta_pattern f) or (array_exists occur_meta_pattern args)
| PLambda (na,t,c) -> (occur_meta_pattern t) or (occur_meta_pattern c)
| PProd (na,t,c) -> (occur_meta_pattern t) or (occur_meta_pattern c)
| PLetIn (na,t,c) -> (occur_meta_pattern t) or (occur_meta_pattern c)
| PCase(_,None,c,br) ->
(occur_meta_pattern c) or (array_exists occur_meta_pattern br)
| PCase(_,Some p,c,br) ->
(occur_meta_pattern p) or
(occur_meta_pattern c) or (array_exists occur_meta_pattern br)
| PMeta _ | PSoApp _ -> true
| PEvar _ | PVar _ | PRef _ | PRel _ | PSort _ | PFix _ | PCoFix _ -> false
let rec subst_pattern subst pat = match pat with
| PRef ref ->
let ref' = subst_global subst ref in
if ref' == ref then pat else
PRef ref'
| PVar _
| PEvar _
| PRel _ -> pat
| PApp (f,args) ->
let f' = subst_pattern subst f in
let args' = array_smartmap (subst_pattern subst) args in
if f' == f && args' == args then pat else
PApp (f',args')
| PSoApp (i,args) ->
let args' = list_smartmap (subst_pattern subst) args in
if args' == args then pat else
PSoApp (i,args')
| PLambda (name,c1,c2) ->
let c1' = subst_pattern subst c1 in
let c2' = subst_pattern subst c2 in
if c1' == c1 && c2' == c2 then pat else
PLambda (name,c1',c2')
| PProd (name,c1,c2) ->
let c1' = subst_pattern subst c1 in
let c2' = subst_pattern subst c2 in
if c1' == c1 && c2' == c2 then pat else
PProd (name,c1',c2')
| PLetIn (name,c1,c2) ->
let c1' = subst_pattern subst c1 in
let c2' = subst_pattern subst c2 in
if c1' == c1 && c2' == c2 then pat else
PLetIn (name,c1',c2')
| PSort _
| PMeta _ -> pat
| PCase (cs,typ, c, branches) ->
let typ' = option_smartmap (subst_pattern subst) typ in
let c' = subst_pattern subst c in
let branches' = array_smartmap (subst_pattern subst) branches in
if typ' == typ && c' == c && branches' == branches then pat else
PCase(cs,typ', c', branches')
| PFix fixpoint ->
let cstr = mkFix fixpoint in
let fixpoint' = destFix (subst_mps subst cstr) in
if fixpoint' == fixpoint then pat else
PFix fixpoint'
| PCoFix cofixpoint ->
let cstr = mkCoFix cofixpoint in
let cofixpoint' = destCoFix (subst_mps subst cstr) in
if cofixpoint' == cofixpoint then pat else
PCoFix cofixpoint'
type constr_label =
| ConstNode of constant
| IndNode of inductive
| CstrNode of constructor
| VarNode of identifier
exception BoundPattern;;
let label_of_ref = function
| ConstRef sp -> ConstNode sp
| IndRef sp -> IndNode sp
| ConstructRef sp -> CstrNode sp
| VarRef id -> VarNode id
let ref_of_label = function
| ConstNode sp -> ConstRef sp
| IndNode sp -> IndRef sp
| CstrNode sp -> ConstructRef sp
| VarNode id -> VarRef id
let subst_label subst cstl =
let ref = ref_of_label cstl in
let ref' = subst_global subst ref in
if ref' == ref then cstl else
label_of_ref ref'
let rec head_pattern_bound t =
match t with
| PProd (_,_,b) -> head_pattern_bound b
| PLetIn (_,_,b) -> head_pattern_bound b
| PApp (c,args) -> head_pattern_bound c
| PCase (_,p,c,br) -> head_pattern_bound c
| PRef r -> label_of_ref r
| PVar id -> VarNode id
| PEvar _ | PRel _ | PMeta _ | PSoApp _ | PSort _ | PFix _
-> raise BoundPattern
(* Perhaps they were arguments, but we don't beta-reduce *)
| PLambda _ -> raise BoundPattern
| PCoFix _ -> anomaly "head_pattern_bound: not a type"
let head_of_constr_reference c = match kind_of_term c with
| Const sp -> ConstNode sp
| Construct sp -> CstrNode sp
| Ind sp -> IndNode sp
| Var id -> VarNode id
| _ -> anomaly "Not a rigid reference"
(* Second part : Given a term with second-order variables in it,
represented by Meta's, and possibly applied using [SOAPP] to
terms, this function will perform second-order, binding-preserving,
matching, in the case where the pattern is a pattern in the sense
of Dale Miller.
ALGORITHM:
Given a pattern, we decompose it, flattening Cast's and apply's,
recursing on all operators, and pushing the name of the binder each
time we descend a binder.
When we reach a first-order variable, we ask that the corresponding
term's free-rels all be higher than the depth of the current stack.
When we reach a second-order application, we ask that the
intersection of the free-rels of the term and the current stack be
contained in the arguments of the application, and in that case, we
construct a LAMBDA with the names on the stack.
*)
exception PatternMatchingFailure
let constrain ((n : int),(m : constr)) sigma =
if List.mem_assoc n sigma then
if eq_constr m (List.assoc n sigma) then sigma
else raise PatternMatchingFailure
else
(n,m)::sigma
let build_lambda toabstract stk (m : constr) =
let rec buildrec m p_0 p_1 = match p_0,p_1 with
| (_, []) -> m
| (n, (na,t)::tl) ->
if List.mem n toabstract then
buildrec (mkLambda (na,t,m)) (n+1) tl
else
buildrec (pop m) (n+1) tl
in
buildrec m 1 stk
let memb_metavars m n =
match (m,n) with
| (None, _) -> true
| (Some mvs, n) -> List.mem n mvs
let eq_context ctxt1 ctxt2 = array_for_all2 eq_constr ctxt1 ctxt2
let matches_core convert allow_partial_app pat c =
let rec sorec stk sigma p t =
let cT = strip_outer_cast t in
match p,kind_of_term cT with
| PSoApp (n,args),m ->
let relargs =
List.map
(function
| PRel n -> n
| _ -> error "Only bound indices are currently allowed in second order pattern matching")
args in
let frels = Intset.elements (free_rels cT) in
if list_subset frels relargs then
constrain (n,build_lambda relargs stk cT) sigma
else
raise PatternMatchingFailure
| PMeta (Some n), m ->
let depth = List.length stk in
let frels = Intset.elements (free_rels cT) in
if List.for_all (fun i -> i > depth) frels then
constrain (n,lift (-depth) cT) sigma
else
raise PatternMatchingFailure
| PMeta None, m -> sigma
| PRef (VarRef v1), Var v2 when v1 = v2 -> sigma
| PVar v1, Var v2 when v1 = v2 -> sigma
| PRef ref, _ when constr_of_reference ref = cT -> sigma
| PRel n1, Rel n2 when n1 = n2 -> sigma
| PSort (RProp c1), Sort (Prop c2) when c1 = c2 -> sigma
| PSort (RType _), Sort (Type _) -> sigma
| PApp (PMeta (Some n),args1), App (c2,args2) when allow_partial_app ->
let p = Array.length args2 - Array.length args1 in
if p>=0 then
let args21, args22 = array_chop p args2 in
let sigma =
let depth = List.length stk in
let c = mkApp(c2,args21) in
let frels = Intset.elements (free_rels c) in
if List.for_all (fun i -> i > depth) frels then
constrain (n,lift (-depth) c) sigma
else
raise PatternMatchingFailure in
array_fold_left2 (sorec stk) sigma args1 args22
else raise PatternMatchingFailure
| PApp (c1,arg1), App (c2,arg2) ->
(try array_fold_left2 (sorec stk) (sorec stk sigma c1 c2) arg1 arg2
with Invalid_argument _ -> raise PatternMatchingFailure)
| PProd (na1,c1,d1), Prod(na2,c2,d2) ->
sorec ((na2,c2)::stk) (sorec stk sigma c1 c2) d1 d2
| PLambda (na1,c1,d1), Lambda(na2,c2,d2) ->
sorec ((na2,c2)::stk) (sorec stk sigma c1 c2) d1 d2
| PLetIn (na1,c1,d1), LetIn(na2,c2,t2,d2) ->
sorec ((na2,t2)::stk) (sorec stk sigma c1 c2) d1 d2
| PRef (ConstRef _ as ref), _ when convert <> None ->
let (env,evars) = out_some convert in
let c = constr_of_reference ref in
if is_conv env evars c cT then sigma
else raise PatternMatchingFailure
| PCase (_,_,a1,br1), Case (_,_,a2,br2) ->
(* On ne teste pas le prédicat *)
if (Array.length br1) = (Array.length br2) then
array_fold_left2 (sorec stk) (sorec stk sigma a1 a2) br1 br2
else
raise PatternMatchingFailure
(* À faire *)
| PFix f0, Fix f1 when f0 = f1 -> sigma
| PCoFix c0, CoFix c1 when c0 = c1 -> sigma
| _ -> raise PatternMatchingFailure
in
Sort.list (fun (a,_) (b,_) -> a<b) (sorec [] [] pat c)
let matches = matches_core None false
let pmatches = matches_core None true
(* To skip to the next occurrence *)
exception NextOccurrence of int
(* Tells if it is an authorized occurrence *)
let authorized_occ nocc mres =
if nocc = 0 then mres
else raise (NextOccurrence nocc)
(* Tries to match a subterm of [c] with [pat] *)
let rec sub_match nocc pat c =
match kind_of_term c with
| Cast (c1,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta (-1)) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1] in
(lm,mkCast (List.hd lc, c2))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1] in
(lm,mkCast (List.hd lc, c2)))
| Lambda (x,c1,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta (-1)) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1;c2] in
(lm,mkLambda (x,List.hd lc,List.nth lc 1))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1;c2] in
(lm,mkLambda (x,List.hd lc,List.nth lc 1)))
| Prod (x,c1,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta (-1)) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1;c2] in
(lm,mkProd (x,List.hd lc,List.nth lc 1))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1;c2] in
(lm,mkProd (x,List.hd lc,List.nth lc 1)))
| LetIn (x,c1,t2,c2) ->
(try authorized_occ nocc ((matches pat c), mkMeta (-1)) with
| PatternMatchingFailure ->
let (lm,lc) = try_sub_match nocc pat [c1;t2;c2] in
(lm,mkLetIn (x,List.hd lc,List.nth lc 1,List.nth lc 2))
| NextOccurrence nocc ->
let (lm,lc) = try_sub_match (nocc - 1) pat [c1;t2;c2] in
(lm,mkLetIn (x,List.hd lc,List.nth lc 1,List.nth lc 2)))
| App (c1,lc) ->
(try authorized_occ nocc ((matches pat c), mkMeta (-1)) with
| PatternMatchingFailure ->
let (lm,le) = try_sub_match nocc pat (c1::(Array.to_list lc)) in
(lm,mkApp (List.hd le, Array.of_list (List.tl le)))
| NextOccurrence nocc ->
let (lm,le) = try_sub_match (nocc - 1) pat (c1::(Array.to_list lc)) in
(lm,mkApp (List.hd le, Array.of_list (List.tl le))))
| Case (ci,hd,c1,lc) ->
(try authorized_occ nocc ((matches pat c), mkMeta (-1)) with
| PatternMatchingFailure ->
let (lm,le) = try_sub_match nocc pat (c1::Array.to_list lc) in
(lm,mkCase (ci,hd,List.hd le,Array.of_list (List.tl le)))
| NextOccurrence nocc ->
let (lm,le) = try_sub_match (nocc - 1) pat (c1::Array.to_list lc) in
(lm,mkCase (ci,hd,List.hd le,Array.of_list (List.tl le))))
| Construct _ | Fix _ | Ind _|CoFix _ |Evar _|Const _
| Rel _|Meta _|Var _|Sort _ ->
(try authorized_occ nocc ((matches pat c),mkMeta (-1)) with
| PatternMatchingFailure -> raise (NextOccurrence nocc)
| NextOccurrence nocc -> raise (NextOccurrence (nocc - 1)))
(* Tries [sub_match] for all terms in the list *)
and try_sub_match nocc pat lc =
let rec try_sub_match_rec nocc pat lacc = function
| [] -> raise (NextOccurrence nocc)
| c::tl ->
(try
let (lm,ce) = sub_match nocc pat c in
(lm,lacc@(ce::tl))
with
| NextOccurrence nocc -> try_sub_match_rec nocc pat (lacc@[c]) tl) in
try_sub_match_rec nocc pat [] lc
let is_matching pat n =
try let _ = matches pat n in true
with PatternMatchingFailure -> false
let matches_conv env sigma = matches_core (Some (env,sigma)) false
let is_matching_conv env sigma pat n =
try let _ = matches_conv env sigma pat n in true
with PatternMatchingFailure -> false
let rec pattern_of_constr t =
match kind_of_term t with
| Rel n -> PRel n
| Meta n -> PMeta (Some n)
| Var id -> PVar id
| Sort (Prop c) -> PSort (RProp c)
| Sort (Type _) -> PSort (RType None)
| Cast (c,_) -> pattern_of_constr c
| LetIn (na,c,_,b) -> PLetIn (na,pattern_of_constr c,pattern_of_constr b)
| Prod (na,c,b) -> PProd (na,pattern_of_constr c,pattern_of_constr b)
| Lambda (na,c,b) -> PLambda (na,pattern_of_constr c,pattern_of_constr b)
| App (f,a) -> PApp (pattern_of_constr f,Array.map pattern_of_constr a)
| Const sp -> PRef (ConstRef sp)
| Ind sp -> PRef (IndRef sp)
| Construct sp -> PRef (ConstructRef sp)
| Evar (n,ctxt) ->
if ctxt = [||] then PEvar n
else PApp (PEvar n, Array.map pattern_of_constr ctxt)
| Case (ci,p,a,br) ->
PCase (ci.ci_pp_info.style,
Some (pattern_of_constr p),pattern_of_constr a,
Array.map pattern_of_constr br)
| Fix f -> PFix f
| CoFix _ ->
error "pattern_of_constr: (co)fix currently not supported"
|