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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i*)
open Util
open Term
open Names
open Globnames
open Mod_subst
open Pp (* debug *)
(*i*)
(* Representation/approximation of terms to use in the dnet:
*
* - no meta or evar (use ['a pattern] for that)
*
* - [Rel]s and [Sort]s are not taken into account (that's why we need
* a second pass of linear filterin on the results - it's not a perfect
* term indexing structure)
* - Foralls and LetIns are represented by a context DCtx (a list of
* generalization, similar to rel_context, and coded with DCons and
* DNil). This allows for matching under an unfinished context
*)
module DTerm =
struct
type 't t =
| DRel
| DSort
| DRef of global_reference
| DCtx of 't * 't (* (binding list, subterm) = Prods and LetIns *)
| DLambda of 't * 't
| DApp of 't * 't (* binary app *)
| DCase of case_info * 't * 't * 't array
| DFix of int array * int * 't array * 't array
| DCoFix of int * 't array * 't array
(* special constructors only inside the left-hand side of DCtx or
DApp. Used to encode lists of foralls/letins/apps as contexts *)
| DCons of ('t * 't option) * 't
| DNil
(* debug *)
let pr_dconstr f : 'a t -> std_ppcmds = function
| DRel -> str "*"
| DSort -> str "Sort"
| DRef _ -> str "Ref"
| DCtx (ctx,t) -> f ctx ++ spc() ++ str "|-" ++ spc () ++ f t
| DLambda (t1,t2) -> str "fun"++ spc() ++ f t1 ++ spc() ++ str"->" ++ spc() ++ f t2
| DApp (t1,t2) -> f t1 ++ spc() ++ f t2
| DCase (_,t1,t2,ta) -> str "case"
| DFix _ -> str "fix"
| DCoFix _ -> str "cofix"
| DCons ((t,dopt),tl) -> f t ++ (match dopt with
Some t' -> str ":=" ++ f t'
| None -> str "") ++ spc() ++ str "::" ++ spc() ++ f tl
| DNil -> str "[]"
(*
* Functional iterators for the t datatype
* a.k.a boring and error-prone boilerplate code
*)
let map f = function
| (DRel | DSort | DNil | DRef _) as c -> c
| DCtx (ctx,c) -> DCtx (f ctx, f c)
| DLambda (t,c) -> DLambda (f t, f c)
| DApp (t,u) -> DApp (f t,f u)
| DCase (ci,p,c,bl) -> DCase (ci, f p, f c, Array.map f bl)
| DFix (ia,i,ta,ca) ->
DFix (ia,i,Array.map f ta,Array.map f ca)
| DCoFix(i,ta,ca) ->
DCoFix (i,Array.map f ta,Array.map f ca)
| DCons ((t,topt),u) -> DCons ((f t,Option.map f topt), f u)
let compare x y =
let make_name n =
match n with
| DRef(ConstRef con) ->
DRef(ConstRef(constant_of_kn(canonical_con con)))
| DRef(IndRef (kn,i)) ->
DRef(IndRef(mind_of_kn(canonical_mind kn),i))
| DRef(ConstructRef ((kn,i),j ))->
DRef(ConstructRef((mind_of_kn(canonical_mind kn),i),j))
| k -> k in
Pervasives.compare (make_name x) (make_name y)
let fold f acc = function
| (DRel | DNil | DSort | DRef _) -> acc
| DCtx (ctx,c) -> f (f acc ctx) c
| DLambda (t,c) -> f (f acc t) c
| DApp (t,u) -> f (f acc t) u
| DCase (ci,p,c,bl) -> Array.fold_left f (f (f acc p) c) bl
| DFix (ia,i,ta,ca) ->
Array.fold_left f (Array.fold_left f acc ta) ca
| DCoFix(i,ta,ca) ->
Array.fold_left f (Array.fold_left f acc ta) ca
| DCons ((t,topt),u) -> f (Option.fold_left f (f acc t) topt) u
let choose f = function
| (DRel | DSort | DNil | DRef _) -> invalid_arg "choose"
| DCtx (ctx,c) -> f ctx
| DLambda (t,c) -> f t
| DApp (t,u) -> f u
| DCase (ci,p,c,bl) -> f c
| DFix (ia,i,ta,ca) -> f ta.(0)
| DCoFix (i,ta,ca) -> f ta.(0)
| DCons ((t,topt),u) -> f u
let fold2 (f:'a -> 'b -> 'c -> 'a) (acc:'a) (c1:'b t) (c2:'c t) : 'a =
let head w = map (fun _ -> ()) w in
if not (Int.equal (compare (head c1) (head c2)) 0)
then invalid_arg "fold2:compare" else
match c1,c2 with
| (DRel, DRel | DNil, DNil | DSort, DSort | DRef _, DRef _) -> acc
| (DCtx (c1,t1), DCtx (c2,t2)
| DApp (c1,t1), DApp (c2,t2)
| DLambda (c1,t1), DLambda (c2,t2)) -> f (f acc c1 c2) t1 t2
| DCase (ci,p1,c1,bl1),DCase (_,p2,c2,bl2) ->
Array.fold_left2 f (f (f acc p1 p2) c1 c2) bl1 bl2
| DFix (ia,i,ta1,ca1), DFix (_,_,ta2,ca2) ->
Array.fold_left2 f (Array.fold_left2 f acc ta1 ta2) ca1 ca2
| DCoFix(i,ta1,ca1), DCoFix(_,ta2,ca2) ->
Array.fold_left2 f (Array.fold_left2 f acc ta1 ta2) ca1 ca2
| DCons ((t1,topt1),u1), DCons ((t2,topt2),u2) ->
f (Option.fold_left2 f (f acc t1 t2) topt1 topt2) u1 u2
| _ -> assert false
let map2 (f:'a -> 'b -> 'c) (c1:'a t) (c2:'b t) : 'c t =
let head w = map (fun _ -> ()) w in
if not (Int.equal (compare (head c1) (head c2)) 0)
then invalid_arg "map2_t:compare" else
match c1,c2 with
| (DRel, DRel | DSort, DSort | DNil, DNil | DRef _, DRef _) as cc ->
let (c,_) = cc in c
| DCtx (c1,t1), DCtx (c2,t2) -> DCtx (f c1 c2, f t1 t2)
| DLambda (t1,c1), DLambda (t2,c2) -> DLambda (f t1 t2, f c1 c2)
| DApp (t1,u1), DApp (t2,u2) -> DApp (f t1 t2,f u1 u2)
| DCase (ci,p1,c1,bl1), DCase (_,p2,c2,bl2) ->
DCase (ci, f p1 p2, f c1 c2, Array.map2 f bl1 bl2)
| DFix (ia,i,ta1,ca1), DFix (_,_,ta2,ca2) ->
DFix (ia,i,Array.map2 f ta1 ta2,Array.map2 f ca1 ca2)
| DCoFix (i,ta1,ca1), DCoFix (_,ta2,ca2) ->
DCoFix (i,Array.map2 f ta1 ta2,Array.map2 f ca1 ca2)
| DCons ((t1,topt1),u1), DCons ((t2,topt2),u2) ->
DCons ((f t1 t2,Option.lift2 f topt1 topt2), f u1 u2)
| _ -> assert false
let terminal = function
| (DRel | DSort | DNil | DRef _) -> true
| _ -> false
end
(*
* Terms discrimination nets
* Uses the general dnet datatype on DTerm.t
* (here you can restart reading)
*)
(*
* Construction of the module
*)
module type IDENT =
sig
type t
val compare : t -> t -> int
val subst : substitution -> t -> t
val constr_of : t -> constr
end
module type OPT =
sig
val reduce : constr -> constr
val direction : bool
end
module Make =
functor (Ident : IDENT) ->
functor (Opt : OPT) ->
struct
module TDnet : Dnet.S with type ident=Ident.t
and type 'a structure = 'a DTerm.t
and type meta = metavariable
= Dnet.Make(DTerm)(Ident)
(struct
type t = metavariable
let compare = Pervasives.compare
end)
type t = TDnet.t
type ident = TDnet.ident
type result = ident * (constr*existential_key) * Termops.subst
open DTerm
open TDnet
let rec pat_of_constr c : term_pattern =
match kind_of_term c with
| Rel _ -> Term DRel
| Sort _ -> Term DSort
| Var i -> Term (DRef (VarRef i))
| Const c -> Term (DRef (ConstRef c))
| Ind i -> Term (DRef (IndRef i))
| Construct c -> Term (DRef (ConstructRef c))
| Term.Meta _ -> assert false
| Evar (i,_) -> Meta i
| Case (ci,c1,c2,ca) ->
Term(DCase(ci,pat_of_constr c1,pat_of_constr c2,Array.map pat_of_constr ca))
| Fix ((ia,i),(_,ta,ca)) ->
Term(DFix(ia,i,Array.map pat_of_constr ta, Array.map pat_of_constr ca))
| CoFix (i,(_,ta,ca)) ->
Term(DCoFix(i,Array.map pat_of_constr ta,Array.map pat_of_constr ca))
| Cast (c,_,_) -> pat_of_constr c
| Lambda (_,t,c) -> Term(DLambda (pat_of_constr t, pat_of_constr c))
| (Prod (_,_,_) | LetIn(_,_,_,_)) ->
let (ctx,c) = ctx_of_constr (Term DNil) c in Term (DCtx (ctx,c))
| App (f,ca) ->
Array.fold_left (fun c a -> Term (DApp (c,a)))
(pat_of_constr f) (Array.map pat_of_constr ca)
and ctx_of_constr ctx c : term_pattern * term_pattern =
match kind_of_term c with
| Prod (_,t,c) -> ctx_of_constr (Term(DCons((pat_of_constr t,None),ctx))) c
| LetIn(_,d,t,c) -> ctx_of_constr (Term(DCons((pat_of_constr t, Some (pat_of_constr d)),ctx))) c
| _ -> ctx,pat_of_constr c
let empty_ctx : term_pattern -> term_pattern = function
| Meta _ as c -> c
| Term (DCtx(_,_)) as c -> c
| c -> Term (DCtx (Term DNil, c))
(*
* Basic primitives
*)
let empty = TDnet.empty
let subst s t =
let sleaf id = Ident.subst s id in
let snode = function
| DTerm.DRef gr -> DTerm.DRef (fst (subst_global s gr))
| n -> n in
TDnet.map sleaf snode t
let union = TDnet.union
let add (c:constr) (id:Ident.t) (dn:t) =
let c = Opt.reduce c in
let c = empty_ctx (pat_of_constr c) in
TDnet.add dn c id
let new_meta_no = Evarutil.new_untyped_evar
let neutral_meta = new_meta_no()
let new_meta () = Meta (new_meta_no())
let new_evar () = mkEvar(new_meta_no(),[||])
let rec remove_cap : term_pattern -> term_pattern = function
| Term (DCons (t,u)) -> Term (DCons (t,remove_cap u))
| Term DNil -> new_meta()
| Meta _ as m -> m
| _ -> assert false
let under_prod : term_pattern -> term_pattern = function
| Term (DCtx (t,u)) -> Term (DCtx (remove_cap t,u))
| Meta m -> Term (DCtx(new_meta(), Meta m))
| _ -> assert false
let init = let e = new_meta_no() in (mkEvar (e,[||]),e)
let rec e_subst_evar i (t:unit->constr) c =
match kind_of_term c with
| Evar (j,_) when Int.equal i j -> t()
| _ -> map_constr (e_subst_evar i t) c
let subst_evar i c = e_subst_evar i (fun _ -> c)
(* debug *)
let rec pr_term_pattern p =
(fun pr_t -> function
| Term t -> pr_t t
| Meta m -> str"["++Pp.int (Obj.magic m)++str"]"
) (pr_dconstr pr_term_pattern) p
let search_pat cpat dpat dn (up,plug) =
let whole_c = subst_evar plug cpat up in
(* if we are at the root, add an empty context *)
let dpat = if isEvar_or_Meta up then under_prod (empty_ctx dpat) else dpat in
TDnet.Idset.fold
(fun id acc ->
let c_id = Opt.reduce (Ident.constr_of id) in
let (ctx,wc) =
try Termops.align_prod_letin whole_c c_id
with Invalid_argument _ -> [],c_id in
let up = it_mkProd_or_LetIn up ctx in
let wc,whole_c = if Opt.direction then whole_c,wc else wc,whole_c in
try (id,(up,plug),Termops.filtering ctx Reduction.CUMUL wc whole_c)::acc
with Termops.CannotFilter -> (* msgnl(str"recon "++Termops.print_constr_env (Global.env()) wc); *) acc
) (TDnet.find_match dpat dn) []
let fold_pattern_neutral f =
fold_pattern (fun acc (mset,m,dn) -> if Int.equal m neutral_meta then acc else f m dn acc)
let fold_pattern_nonlin f =
let defined = ref Int.Map.empty in
fold_pattern_neutral
( fun m dn acc ->
let dn = try TDnet.inter dn (Int.Map.find m !defined) with Not_found -> dn in
defined := Int.Map.add m dn !defined;
f m dn acc )
let fold_pattern_up f acc dpat cpat dn (up,plug) =
fold_pattern_nonlin
( fun m dn acc ->
f dn (subst_evar plug (e_subst_evar neutral_meta new_evar cpat) up, m) acc
) acc dpat dn
let possibly_under pat k dn (up,plug) =
let rec aux fst dn (up,plug) acc =
let cpat = pat() in
let dpat = pat_of_constr cpat in
let dpat = if fst then under_prod (empty_ctx dpat) else dpat in
(k dn (up,plug)) @
snd (fold_pattern_up (aux false) acc dpat cpat dn (up,plug)) in
aux true dn (up,plug) []
let eq_pat eq () = mkApp(eq,[|mkEvar(neutral_meta,[||]);new_evar();new_evar()|])
let app_pat () = mkApp(new_evar(),[|mkEvar(neutral_meta,[||])|])
(*
* High-level primitives describing specific search problems
*)
let search_pattern dn pat =
let pat = Opt.reduce pat in
search_pat pat (empty_ctx (pat_of_constr pat)) dn init
let search_concl dn pat =
let pat = Opt.reduce pat in
search_pat pat (under_prod (empty_ctx (pat_of_constr pat))) dn init
let search_eq_concl dn eq pat =
let pat = Opt.reduce pat in
let eq_pat = eq_pat eq () in
let eq_dpat = under_prod (empty_ctx (pat_of_constr eq_pat)) in
snd (fold_pattern_up
(fun dn up acc ->
search_pat pat (pat_of_constr pat) dn up @ acc
) [] eq_dpat eq_pat dn init)
let search_head_concl dn pat =
let pat = Opt.reduce pat in
possibly_under app_pat (search_pat pat (pat_of_constr pat)) dn init
let find_all dn = Idset.elements (TDnet.find_all dn)
let map f dn = TDnet.map f (fun x -> x) dn
end
module type S =
sig
type t
type ident
type result = ident * (constr*existential_key) * Termops.subst
val empty : t
val add : constr -> ident -> t -> t
val union : t -> t -> t
val subst : substitution -> t -> t
val search_pattern : t -> constr -> result list
val search_concl : t -> constr -> result list
val search_head_concl : t -> constr -> result list
val search_eq_concl : t -> constr -> constr -> result list
val find_all : t -> ident list
val map : (ident -> ident) -> t -> t
end
|