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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Names
module RelDecl = Context.Rel.Declaration
(*********************)
(* Occurring *)
(*********************)
exception LocalOccur
(* (closedn n M) raises FreeVar if a variable of height greater than n
occurs in M, returns () otherwise *)
let closedn n c =
let rec closed_rec n c = match Constr.kind c with
| Constr.Rel m -> if m>n then raise LocalOccur
| _ -> Constr.iter_with_binders succ closed_rec n c
in
try closed_rec n c; true with LocalOccur -> false
(* [closed0 M] is true iff [M] is a (de Bruijn) closed term *)
let closed0 c = closedn 0 c
(* (noccurn n M) returns true iff (Rel n) does NOT occur in term M *)
let noccurn n term =
let rec occur_rec n c = match Constr.kind c with
| Constr.Rel m -> if Int.equal m n then raise LocalOccur
| _ -> Constr.iter_with_binders succ occur_rec n c
in
try occur_rec n term; true with LocalOccur -> false
(* (noccur_between n m M) returns true iff (Rel p) does NOT occur in term M
for n <= p < n+m *)
let noccur_between n m term =
let rec occur_rec n c = match Constr.kind c with
| Constr.Rel p -> if n<=p && p<n+m then raise LocalOccur
| _ -> Constr.iter_with_binders succ occur_rec n c
in
try occur_rec n term; true with LocalOccur -> false
(* Checking function for terms containing existential variables.
The function [noccur_with_meta] considers the fact that
each existential variable (as well as each isevar)
in the term appears applied to its local context,
which may contain the CoFix variables. These occurrences of CoFix variables
are not considered *)
let isMeta c = match Constr.kind c with
| Constr.Meta _ -> true
| _ -> false
let noccur_with_meta n m term =
let rec occur_rec n c = match Constr.kind c with
| Constr.Rel p -> if n<=p && p<n+m then raise LocalOccur
| Constr.App(f,_cl) ->
(match Constr.kind f with
| Constr.Cast (c,_,_) when isMeta c -> ()
| Constr.Meta _ -> ()
| _ -> Constr.iter_with_binders succ occur_rec n c)
| Constr.Evar (_, _) -> ()
| _ -> Constr.iter_with_binders succ occur_rec n c
in
try (occur_rec n term; true) with LocalOccur -> false
(*********************)
(* Lifting *)
(*********************)
let exliftn = Constr.exliftn
let liftn = Constr.liftn
let lift = Constr.lift
(*********************)
(* Substituting *)
(*********************)
(* (subst1 M c) substitutes M for Rel(1) in c
we generalise it to (substl [M1,...,Mn] c) which substitutes in parallel
M1,...,Mn for respectively Rel(1),...,Rel(n) in c *)
(* 1st : general case *)
type info = Closed | Open | Unknown
type 'a substituend = { mutable sinfo: info; sit: 'a }
let lift_substituend depth s =
match s.sinfo with
| Closed -> s.sit
| Open -> lift depth s.sit
| Unknown ->
let sit = s.sit in
if closed0 sit then
let () = s.sinfo <- Closed in
sit
else
let () = s.sinfo <- Open in
lift depth sit
let make_substituend c = { sinfo=Unknown; sit=c }
let substn_many lamv n c =
let lv = Array.length lamv in
if Int.equal lv 0 then c
else
let rec substrec depth c = match Constr.kind c with
| Constr.Rel k ->
if k<=depth then c
else if k-depth <= lv then lift_substituend depth (Array.unsafe_get lamv (k-depth-1))
else Constr.mkRel (k-lv)
| _ -> Constr.map_with_binders succ substrec depth c in
substrec n c
(*
let substkey = CProfile.declare_profile "substn_many";;
let substn_many lamv n c = CProfile.profile3 substkey substn_many lamv n c;;
*)
let make_subst = function
| [] -> [||]
| hd :: tl ->
let len = List.length tl in
let subst = Array.make (1 + len) (make_substituend hd) in
let s = ref tl in
for i = 1 to len do
match !s with
| [] -> assert false
| x :: tl ->
Array.unsafe_set subst i (make_substituend x);
s := tl
done;
subst
(* The type of substitutions, with term substituting most recent
binder at the head *)
type substl = Constr.t list
let substnl laml n c = substn_many (make_subst laml) n c
let substl laml c = substn_many (make_subst laml) 0 c
let subst1 lam c = substn_many [|make_substituend lam|] 0 c
let substnl_decl laml k r = RelDecl.map_constr (fun c -> substnl laml k c) r
let substl_decl laml r = RelDecl.map_constr (fun c -> substnl laml 0 c) r
let subst1_decl lam r = RelDecl.map_constr (fun c -> subst1 lam c) r
(* Build a substitution from an instance, inserting missing let-ins *)
let subst_of_rel_context_instance sign l =
let rec aux subst sign l =
let open RelDecl in
match sign, l with
| LocalAssum _ :: sign', a::args' -> aux (a::subst) sign' args'
| LocalDef (_,c,_)::sign', args' ->
aux (substl subst c :: subst) sign' args'
| [], [] -> subst
| _ -> CErrors.anomaly (Pp.str "Instance and signature do not match.")
in aux [] (List.rev sign) l
let adjust_subst_to_rel_context sign l =
List.rev (subst_of_rel_context_instance sign l)
let adjust_rel_to_rel_context sign n =
let rec aux sign =
let open RelDecl in
match sign with
| LocalAssum _ :: sign' -> let (n',p) = aux sign' in (n'+1,p)
| LocalDef (_,_c,_)::sign' -> let (n',p) = aux sign' in (n'+1,if n'
| [] -> (0,n)
in snd (aux sign)
(* (thin_val sigma) removes identity substitutions from sigma *)
let rec thin_val = function
| [] -> []
| (id, c) :: tl ->
match Constr.kind c with
| Constr.Var v ->
if Id.equal id v then thin_val tl
else (id, make_substituend c) :: (thin_val tl)
| _ -> (id, make_substituend c) :: (thin_val tl)
let rec find_var id = function
| [] -> raise Not_found
| (idc, c) :: subst ->
if Id.equal id idc then c
else find_var id subst
(* (replace_vars sigma M) applies substitution sigma to term M *)
let replace_vars var_alist x =
let var_alist = thin_val var_alist in
match var_alist with
| [] -> x
| _ ->
let rec substrec n c = match Constr.kind c with
| Constr.Var x ->
(try lift_substituend n (find_var x var_alist)
with Not_found -> c)
| _ -> Constr.map_with_binders succ substrec n c
in
substrec 0 x
(* (subst_var str t) substitute (Var str) by (Rel 1) in t *)
let subst_var str t = replace_vars [(str, Constr.mkRel 1)] t
(* (subst_vars [id1;...;idn] t) substitute (Var idj) by (Rel j) in t *)
let substn_vars p vars c =
let _,subst =
List.fold_left (fun (n,l) var -> ((n+1),(var,Constr.mkRel n)::l)) (p,[]) vars
in replace_vars (List.rev subst) c
let subst_vars subst c = substn_vars 1 subst c
(** Universe substitutions *)
open Constr
let subst_univs_level_constr subst c =
if Univ.is_empty_level_subst subst then c
else
let f = Univ.Instance.subst_fn (Univ.subst_univs_level_level subst) in
let changed = ref false in
let rec aux t =
match kind t with
| Const (c, u) ->
if Univ.Instance.is_empty u then t
else
let u' = f u in
if u' == u then t
else (changed := true; mkConstU (c, u'))
| Ind (i, u) ->
if Univ.Instance.is_empty u then t
else
let u' = f u in
if u' == u then t
else (changed := true; mkIndU (i, u'))
| Construct (c, u) ->
if Univ.Instance.is_empty u then t
else
let u' = f u in
if u' == u then t
else (changed := true; mkConstructU (c, u'))
| Sort (Sorts.Type u) ->
let u' = Univ.subst_univs_level_universe subst u in
if u' == u then t else
(changed := true; mkSort (Sorts.sort_of_univ u'))
| _ -> Constr.map aux t
in
let c' = aux c in
if !changed then c' else c
let subst_univs_level_context s =
Context.Rel.map (subst_univs_level_constr s)
let subst_instance_constr subst c =
if Univ.Instance.is_empty subst then c
else
let f u = Univ.subst_instance_instance subst u in
let rec aux t =
match kind t with
| Const (c, u) ->
if Univ.Instance.is_empty u then t
else
let u' = f u in
if u' == u then t
else (mkConstU (c, u'))
| Ind (i, u) ->
if Univ.Instance.is_empty u then t
else
let u' = f u in
if u' == u then t
else (mkIndU (i, u'))
| Construct (c, u) ->
if Univ.Instance.is_empty u then t
else
let u' = f u in
if u' == u then t
else (mkConstructU (c, u'))
| Sort (Sorts.Type u) ->
let u' = Univ.subst_instance_universe subst u in
if u' == u then t else
(mkSort (Sorts.sort_of_univ u'))
| _ -> Constr.map aux t
in
aux c
let univ_instantiate_constr u c =
let open Univ in
assert (Int.equal (Instance.length u) (AUContext.size c.univ_abstracted_binder));
subst_instance_constr u c.univ_abstracted_value
(* let substkey = CProfile.declare_profile "subst_instance_constr";; *)
(* let subst_instance_constr inst c = CProfile.profile2 substkey subst_instance_constr inst c;; *)
let subst_instance_context s ctx =
if Univ.Instance.is_empty s then ctx
else Context.Rel.map (fun x -> subst_instance_constr s x) ctx
let universes_of_constr c =
let open Univ in
let rec aux s c =
match kind c with
| Const (_c, u) ->
LSet.fold LSet.add (Instance.levels u) s
| Ind ((_mind,_), u) | Construct (((_mind,_),_), u) ->
LSet.fold LSet.add (Instance.levels u) s
| Sort u when not (Sorts.is_small u) ->
let u = Sorts.univ_of_sort u in
LSet.fold LSet.add (Universe.levels u) s
| _ -> Constr.fold aux s c
in aux LSet.empty c
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