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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 *)
(************************************************************************)
open Pp
open Util
open Names
open Term
open Vars
open Mod_subst
open Environ
open Globnames
open Nameops
open Libobject
open Lib
(** Characterization of the head of a term *)
(* We only compute an approximation to ensure the computation is not
arbitrary long (e.g. the head constant of [h] defined to be
[g (fun x -> phi(x))] where [g] is [fun f => g O] does not launch
the evaluation of [phi(0)] and the head of [h] is declared unknown). *)
type rigid_head_kind =
| RigidParameter of constant (* a Const without body *)
| RigidVar of variable (* a Var without body *)
| RigidType (* an inductive, a product or a sort *)
type head_approximation =
| RigidHead of rigid_head_kind
| ConstructorHead
| FlexibleHead of int * int * int * bool (* [true] if a surrounding case *)
| NotImmediatelyComputableHead
(** Registration as global tables and rollback. *)
module Evalreford = struct
type t = evaluable_global_reference
let compare gr1 gr2 = match gr1, gr2 with
| EvalVarRef id1, EvalVarRef id2 -> Id.compare id1 id2
| EvalVarRef _, EvalConstRef _ -> -1
| EvalConstRef c1, EvalConstRef c2 ->
Constant.CanOrd.compare c1 c2
| EvalConstRef _, EvalVarRef _ -> 1
end
module Evalrefmap =
Map.Make (Evalreford)
let head_map = Summary.ref Evalrefmap.empty ~name:"Head_decl"
let variable_head id = Evalrefmap.find (EvalVarRef id) !head_map
let constant_head cst = Evalrefmap.find (EvalConstRef cst) !head_map
let kind_of_head env t =
let rec aux k l t b = match kind_of_term (Reduction.whd_betaiotazeta env t) with
| Rel n when n > k -> NotImmediatelyComputableHead
| Rel n -> FlexibleHead (k,k+1-n,List.length l,b)
| Var id ->
(try on_subterm k l b (variable_head id)
with Not_found ->
(* a goal variable *)
match pi2 (lookup_named id env) with
| Some c -> aux k l c b
| None -> NotImmediatelyComputableHead)
| Const (cst,_) ->
(try on_subterm k l b (constant_head cst)
with Not_found -> assert false)
| Construct _ | CoFix _ ->
if b then NotImmediatelyComputableHead else ConstructorHead
| Sort _ | Ind _ | Prod _ -> RigidHead RigidType
| Cast (c,_,_) -> aux k l c b
| Lambda (_,_,c) ->
begin match l with
| [] ->
let () = assert (not b) in
aux (k + 1) [] c b
| h :: l -> aux k l (subst1 h c) b
end
| LetIn _ -> assert false
| Meta _ | Evar _ -> NotImmediatelyComputableHead
| App (c,al) -> aux k (Array.to_list al @ l) c b
| Proj (p,c) ->
(try on_subterm k (c :: l) b (constant_head p)
with Not_found -> assert false)
| Case (_,_,c,_) -> aux k [] c true
| Fix ((i,j),_) ->
let n = i.(j) in
try aux k [] (List.nth l n) true
with Failure _ -> FlexibleHead (k + n + 1, k + n + 1, 0, true)
and on_subterm k l with_case = function
| FlexibleHead (n,i,q,with_subcase) ->
let m = List.length l in
let k',rest,a =
if n > m then
(* eta-expansion *)
let a =
if i <= m then
(* we pick the head in the existing arguments *)
lift (n-m) (List.nth l (i-1))
else
(* we pick the head in the added arguments *)
mkRel (n-i+1) in
k+n-m,[],a
else
(* enough arguments to [cst] *)
k,List.skipn n l,List.nth l (i-1) in
let l' = List.make q (mkMeta 0) @ rest in
aux k' l' a (with_subcase || with_case)
| ConstructorHead when with_case -> NotImmediatelyComputableHead
| x -> x
in aux 0 [] t false
(* FIXME: maybe change interface here *)
let compute_head = function
| EvalConstRef cst ->
let env = Global.env() in
let cb = Environ.lookup_constant cst env in
let is_Def = function Declarations.Def _ -> true | _ -> false in
let body =
if cb.Declarations.const_proj = None && is_Def cb.Declarations.const_body
then Declareops.body_of_constant cb else None
in
(match body with
| None -> RigidHead (RigidParameter cst)
| Some c -> kind_of_head env c)
| EvalVarRef id ->
(match pi2 (Global.lookup_named id) with
| Some c when not (Decls.variable_opacity id) ->
kind_of_head (Global.env()) c
| _ ->
RigidHead (RigidVar id))
let is_rigid env t =
match kind_of_head env t with
| RigidHead _ | ConstructorHead -> true
| _ -> false
(** Registration of heads as an object *)
let load_head _ (_,(ref,(k:head_approximation))) =
head_map := Evalrefmap.add ref k !head_map
let cache_head o =
load_head 1 o
let subst_head_approximation subst = function
| RigidHead (RigidParameter cst) as k ->
let cst,c = subst_con_kn subst cst in
if isConst c && eq_constant (fst (destConst c)) cst then
(* A change of the prefix of the constant *)
k
else
(* A substitution of the constant by a functor argument *)
kind_of_head (Global.env()) c
| x -> x
let subst_head (subst,(ref,k)) =
(subst_evaluable_reference subst ref, subst_head_approximation subst k)
let discharge_head (_,(ref,k)) =
match ref with
| EvalConstRef cst -> Some (EvalConstRef (pop_con cst), k)
| EvalVarRef id -> None
let rebuild_head (ref,k) =
(ref, compute_head ref)
type head_obj = evaluable_global_reference * head_approximation
let inHead : head_obj -> obj =
declare_object {(default_object "HEAD") with
cache_function = cache_head;
load_function = load_head;
subst_function = subst_head;
classify_function = (fun x -> Substitute x);
discharge_function = discharge_head;
rebuild_function = rebuild_head }
let declare_head c =
let hd = compute_head c in
add_anonymous_leaf (inHead (c,hd))
(** Printing *)
let pr_head = function
| RigidHead (RigidParameter cst) -> str "rigid constant " ++ pr_con cst
| RigidHead (RigidType) -> str "rigid type"
| RigidHead (RigidVar id) -> str "rigid variable " ++ pr_id id
| ConstructorHead -> str "constructor"
| FlexibleHead (k,n,p,b) -> int n ++ str "th of " ++ int k ++ str " binders applied to " ++ int p ++ str " arguments" ++ (if b then str " (with case)" else mt())
| NotImmediatelyComputableHead -> str "unknown"
|
