|
(************************************************************************)
(* * 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 Pp
open CErrors
open Util
open Names
open Nameops
open Term
open Constr
open Context
open Vars
open Environ
module RelDecl = Context.Rel.Declaration
module NamedDecl = Context.Named.Declaration
module CompactedDecl = Context.Compacted.Declaration
module Internal = struct
let pr_sort_family = Sorts.pr_sort_family
[@@ocaml.deprecated "Use [Sorts.pr_sort_family]"]
let pr_fix = Constr.debug_print_fix
[@@ocaml.deprecated "Use [Constr.debug_print_fix]"]
let debug_print_constr c = Constr.debug_print EConstr.Unsafe.(to_constr c)
let debug_print_constr_env env sigma c = Constr.debug_print EConstr.(to_constr sigma c)
let term_printer = ref debug_print_constr_env
let print_constr_env env sigma t = !term_printer (env:env) sigma (t:Evd.econstr)
let set_print_constr f = term_printer := f
module EvMap = Evar.Map
let evar_suggested_name evk sigma =
let open Evd in
let base_id evk' evi =
match evar_ident evk' sigma with
| Some id -> id
| None -> match evi.evar_source with
| _,Evar_kinds.ImplicitArg (c,(n,Some id),b) -> id
| _,Evar_kinds.VarInstance id -> id
| _,Evar_kinds.QuestionMark {Evar_kinds.qm_name = Name id} -> id
| _,Evar_kinds.GoalEvar -> Id.of_string "Goal"
| _ ->
let env = reset_with_named_context evi.evar_hyps (Global.env()) in
Namegen.id_of_name_using_hdchar env sigma evi.evar_concl Anonymous
in
let names = EvMap.mapi base_id (undefined_map sigma) in
let id = EvMap.find evk names in
let fold evk' id' (seen, n) =
if seen then (seen, n)
else if Evar.equal evk evk' then (true, n)
else if Id.equal id id' then (seen, succ n)
else (seen, n)
in
let (_, n) = EvMap.fold fold names (false, 0) in
if n = 0 then id else Nameops.add_suffix id (string_of_int (pred n))
let pr_existential_key sigma evk =
let open Evd in
match evar_ident evk sigma with
| None ->
str "?" ++ Id.print (evar_suggested_name evk sigma)
| Some id ->
str "?" ++ Id.print id
let pr_instance_status (sc,typ) =
let open Evd in
begin match sc with
| IsSubType -> str " [or a subtype of it]"
| IsSuperType -> str " [or a supertype of it]"
| Conv -> mt ()
end ++
begin match typ with
| CoerceToType -> str " [up to coercion]"
| TypeNotProcessed -> mt ()
| TypeProcessed -> str " [type is checked]"
end
let protect f x =
try f x
with e -> str "EXCEPTION: " ++ str (Printexc.to_string e)
let print_kconstr env sigma a =
protect (fun c -> print_constr_env env sigma c) a
let pr_meta_map env sigma =
let open Evd in
let print_constr = print_kconstr in
let pr_name = function
Name id -> str"[" ++ Id.print id ++ str"]"
| _ -> mt() in
let pr_meta_binding = function
| (mv,Cltyp (na,b)) ->
hov 0
(pr_meta mv ++ pr_name na ++ str " : " ++
print_constr env sigma b.rebus ++ fnl ())
| (mv,Clval(na,(b,s),t)) ->
hov 0
(pr_meta mv ++ pr_name na ++ str " := " ++
print_constr env sigma b.rebus ++
str " : " ++ print_constr env sigma t.rebus ++
spc () ++ pr_instance_status s ++ fnl ())
in
prlist pr_meta_binding (meta_list sigma)
let pr_decl env sigma (decl,ok) =
let open NamedDecl in
let print_constr = print_kconstr in
match decl with
| LocalAssum ({binder_name=id},_) -> if ok then Id.print id else (str "{" ++ Id.print id ++ str "}")
| LocalDef ({binder_name=id},c,_) -> str (if ok then "(" else "{") ++ Id.print id ++ str ":=" ++
print_constr env sigma c ++ str (if ok then ")" else "}")
let pr_evar_source env sigma = function
| Evar_kinds.NamedHole id -> Id.print id
| Evar_kinds.QuestionMark _ -> str "underscore"
| Evar_kinds.CasesType false -> str "pattern-matching return predicate"
| Evar_kinds.CasesType true ->
str "subterm of pattern-matching return predicate"
| Evar_kinds.BinderType (Name id) -> str "type of " ++ Id.print id
| Evar_kinds.BinderType Anonymous -> str "type of anonymous binder"
| Evar_kinds.ImplicitArg (c,(n,ido),b) ->
let open Globnames in
let print_constr = print_kconstr in
let id = Option.get ido in
str "parameter " ++ Id.print id ++ spc () ++ str "of" ++
spc () ++ print_constr env sigma (EConstr.of_constr @@ printable_constr_of_global c)
| Evar_kinds.InternalHole -> str "internal placeholder"
| Evar_kinds.TomatchTypeParameter (ind,n) ->
let print_constr = print_kconstr in
pr_nth n ++ str " argument of type " ++ print_constr env sigma (EConstr.mkInd ind)
| Evar_kinds.GoalEvar -> str "goal evar"
| Evar_kinds.ImpossibleCase -> str "type of impossible pattern-matching clause"
| Evar_kinds.MatchingVar _ -> str "matching variable"
| Evar_kinds.VarInstance id -> str "instance of " ++ Id.print id
| Evar_kinds.SubEvar (where,evk) ->
(match where with
| None -> str "subterm of "
| Some Evar_kinds.Body -> str "body of "
| Some Evar_kinds.Domain -> str "domain of "
| Some Evar_kinds.Codomain -> str "codomain of ") ++ Evar.print evk
let pr_evar_info env sigma evi =
let open Evd in
let print_constr = print_kconstr in
let phyps =
try
let decls = match Filter.repr (evar_filter evi) with
| None -> List.map (fun c -> (c, true)) (evar_context evi)
| Some filter -> List.combine (evar_context evi) filter
in
prlist_with_sep spc (pr_decl env sigma) (List.rev decls)
with Invalid_argument _ -> str "Ill-formed filtered context" in
let pty = print_constr env sigma evi.evar_concl in
let pb =
match evi.evar_body with
| Evar_empty -> mt ()
| Evar_defined c -> spc() ++ str"=> " ++ print_constr env sigma c
in
let candidates =
match evi.evar_body, evi.evar_candidates with
| Evar_empty, Some l ->
spc () ++ str "{" ++
prlist_with_sep (fun () -> str "|") (print_constr env sigma) l ++ str "}"
| _ ->
mt ()
in
let src = str "(" ++ pr_evar_source env sigma (snd evi.evar_source) ++ str ")" in
hov 2
(str"[" ++ phyps ++ spc () ++ str"|- " ++ pty ++ pb ++ str"]" ++
candidates ++ spc() ++ src)
let compute_evar_dependency_graph sigma =
let open Evd in
(* Compute the map binding ev to the evars whose body depends on ev *)
let fold evk evi acc =
let fold_ev evk' acc =
let tab =
try EvMap.find evk' acc
with Not_found -> Evar.Set.empty
in
EvMap.add evk' (Evar.Set.add evk tab) acc
in
match evar_body evi with
| Evar_empty -> acc
| Evar_defined c -> Evar.Set.fold fold_ev (evars_of_term (EConstr.Unsafe.to_constr c)) acc
in
Evd.fold fold sigma EvMap.empty
let evar_dependency_closure n sigma =
let open Evd in
(* Create the DAG of depth [n] representing the recursive dependencies of
undefined evars. *)
let graph = compute_evar_dependency_graph sigma in
let rec aux n curr accu =
if Int.equal n 0 then Evar.Set.union curr accu
else
let fold evk accu =
try
let deps = EvMap.find evk graph in
Evar.Set.union deps accu
with Not_found -> accu
in
(* Consider only the newly added evars *)
let ncurr = Evar.Set.fold fold curr Evar.Set.empty in
(* Merge the others *)
let accu = Evar.Set.union curr accu in
aux (n - 1) ncurr accu
in
let undef = EvMap.domain (undefined_map sigma) in
aux n undef Evar.Set.empty
let evar_dependency_closure n sigma =
let open Evd in
let deps = evar_dependency_closure n sigma in
let map = EvMap.bind (fun ev -> find sigma ev) deps in
EvMap.bindings map
let has_no_evar sigma =
try let () = Evd.fold (fun _ _ () -> raise Exit) sigma () in true
with Exit -> false
let pr_evd_level sigma = UState.pr_uctx_level (Evd.evar_universe_context sigma)
let reference_of_level sigma l = UState.qualid_of_level (Evd.evar_universe_context sigma) l
let pr_evar_universe_context ctx =
let open UState in
let prl = pr_uctx_level ctx in
if UState.is_empty ctx then mt ()
else
(str"UNIVERSES:"++brk(0,1)++
h 0 (Univ.pr_universe_context_set prl (UState.context_set ctx)) ++ fnl () ++
str"ALGEBRAIC UNIVERSES:"++brk(0,1)++
h 0 (Univ.LSet.pr prl (UState.algebraics ctx)) ++ fnl() ++
str"UNDEFINED UNIVERSES:"++brk(0,1)++
h 0 (UnivSubst.pr_universe_opt_subst (UState.subst ctx)) ++ fnl() ++
str "WEAK CONSTRAINTS:"++brk(0,1)++
h 0 (UState.pr_weak prl ctx) ++ fnl ())
let print_env_short env sigma =
let print_constr = print_kconstr in
let pr_rel_decl = function
| RelDecl.LocalAssum (n,_) -> Name.print n.binder_name
| RelDecl.LocalDef (n,b,_) -> str "(" ++ Name.print n.binder_name ++ str " := "
++ print_constr env sigma (EConstr.of_constr b) ++ str ")"
in
let pr_named_decl = NamedDecl.to_rel_decl %> pr_rel_decl in
let nc = List.rev (named_context env) in
let rc = List.rev (rel_context env) in
str "[" ++ pr_sequence pr_named_decl nc ++ str "]" ++ spc () ++
str "[" ++ pr_sequence pr_rel_decl rc ++ str "]"
let pr_evar_constraints sigma pbs =
let pr_evconstr (pbty, env, t1, t2) =
let env =
(* We currently allow evar instances to refer to anonymous de
Bruijn indices, so we protect the error printing code in this
case by giving names to every de Bruijn variable in the
rel_context of the conversion problem. MS: we should rather
stop depending on anonymous variables, they can be used to
indicate independency. Also, this depends on a strategy for
naming/renaming. *)
Namegen.make_all_name_different env sigma
in
print_env_short env sigma ++ spc () ++ str "|-" ++ spc () ++
protect (print_constr_env env sigma) t1 ++ spc () ++
str (match pbty with
| Reduction.CONV -> "=="
| Reduction.CUMUL -> "<=") ++
spc () ++ protect (print_constr_env env @@ Evd.from_env env) t2
in
prlist_with_sep fnl pr_evconstr pbs
let pr_evar_map_gen with_univs pr_evars env sigma =
let uvs = Evd.evar_universe_context sigma in
let (_, conv_pbs) = Evd.extract_all_conv_pbs sigma in
let evs = if has_no_evar sigma then mt () else pr_evars sigma ++ fnl ()
and svs = if with_univs then pr_evar_universe_context uvs else mt ()
and cstrs =
if List.is_empty conv_pbs then mt ()
else
str "CONSTRAINTS:" ++ brk (0, 1) ++
pr_evar_constraints sigma conv_pbs ++ fnl ()
and typeclasses =
let evars = Evd.get_typeclass_evars sigma in
if Evar.Set.is_empty evars then mt ()
else
str "TYPECLASSES:" ++ brk (0, 1) ++
prlist_with_sep spc Evar.print (Evar.Set.elements evars) ++ fnl ()
and obligations =
let evars = Evd.get_obligation_evars sigma in
if Evar.Set.is_empty evars then mt ()
else
str "OBLIGATIONS:" ++ brk (0, 1) ++
prlist_with_sep spc Evar.print (Evar.Set.elements evars) ++ fnl ()
and metas =
if List.is_empty (Evd.meta_list sigma) then mt ()
else
str "METAS:" ++ brk (0, 1) ++ pr_meta_map env sigma
in
evs ++ svs ++ cstrs ++ typeclasses ++ obligations ++ metas
let pr_evar_list env sigma l =
let open Evd in
let pr (ev, evi) =
h 0 (Evar.print ev ++
str "==" ++ pr_evar_info env sigma evi ++
(if evi.evar_body == Evar_empty
then str " {" ++ pr_existential_key sigma ev ++ str "}"
else mt ()))
in
h 0 (prlist_with_sep fnl pr l)
let to_list d =
let open Evd in
(* Workaround for change in Map.fold behavior in ocaml 3.08.4 *)
let l = ref [] in
let fold_def evk evi () = match evi.evar_body with
| Evar_defined _ -> l := (evk, evi) :: !l
| Evar_empty -> ()
in
let fold_undef evk evi () = match evi.evar_body with
| Evar_empty -> l := (evk, evi) :: !l
| Evar_defined _ -> ()
in
Evd.fold fold_def d ();
Evd.fold fold_undef d ();
!l
let pr_evar_by_depth depth env sigma = match depth with
| None ->
(* Print all evars *)
str"EVARS:" ++ brk(0,1) ++ pr_evar_list env sigma (to_list sigma) ++ fnl()
| Some n ->
(* Print closure of undefined evars *)
str"UNDEFINED EVARS:"++
(if Int.equal n 0 then mt() else str" (+level "++int n++str" closure):")++
brk(0,1)++
pr_evar_list env sigma (evar_dependency_closure n sigma) ++ fnl()
let pr_evar_by_filter filter env sigma =
let open Evd in
let elts = Evd.fold (fun evk evi accu -> (evk, evi) :: accu) sigma [] in
let elts = List.rev elts in
let is_def (_, evi) = match evi.evar_body with
| Evar_defined _ -> true
| Evar_empty -> false
in
let (defined, undefined) = List.partition is_def elts in
let filter (evk, evi) = filter evk evi in
let defined = List.filter filter defined in
let undefined = List.filter filter undefined in
let prdef =
if List.is_empty defined then mt ()
else str "DEFINED EVARS:" ++ brk (0, 1) ++
pr_evar_list env sigma defined
in
let prundef =
if List.is_empty undefined then mt ()
else str "UNDEFINED EVARS:" ++ brk (0, 1) ++
pr_evar_list env sigma undefined
in
prdef ++ prundef
let pr_evar_map ?(with_univs=true) depth env sigma =
pr_evar_map_gen with_univs (fun sigma -> pr_evar_by_depth depth env sigma) env sigma
let pr_evar_map_filter ?(with_univs=true) filter env sigma =
pr_evar_map_gen with_univs (fun sigma -> pr_evar_by_filter filter env sigma) env sigma
let pr_metaset metas =
str "[" ++ pr_sequence pr_meta (Evd.Metaset.elements metas) ++ str "]"
let pr_var_decl env decl =
let open NamedDecl in
let sigma = Evd.from_env env in
let pbody = match decl with
| LocalAssum _ -> mt ()
| LocalDef (_,c,_) ->
(* Force evaluation *)
let c = EConstr.of_constr c in
let pb = print_constr_env env sigma c in
(str" := " ++ pb ++ cut () ) in
let pt = print_constr_env env sigma (EConstr.of_constr (get_type decl)) in
let ptyp = (str" : " ++ pt) in
(Id.print (get_id decl) ++ hov 0 (pbody ++ ptyp))
let pr_rel_decl env decl =
let open RelDecl in
let sigma = Evd.from_env env in
let pbody = match decl with
| LocalAssum _ -> mt ()
| LocalDef (_,c,_) ->
(* Force evaluation *)
let c = EConstr.of_constr c in
let pb = print_constr_env env sigma c in
(str":=" ++ spc () ++ pb ++ spc ()) in
let ptyp = print_constr_env env sigma (EConstr.of_constr (get_type decl)) in
match get_name decl with
| Anonymous -> hov 0 (str"<>" ++ spc () ++ pbody ++ str":" ++ spc () ++ ptyp)
| Name id -> hov 0 (Id.print id ++ spc () ++ pbody ++ str":" ++ spc () ++ ptyp)
let print_named_context env =
hv 0 (fold_named_context
(fun env d pps ->
pps ++ ws 2 ++ pr_var_decl env d)
env ~init:(mt ()))
let print_rel_context env =
hv 0 (fold_rel_context
(fun env d pps -> pps ++ ws 2 ++ pr_rel_decl env d)
env ~init:(mt ()))
let print_env env =
let sign_env =
fold_named_context
(fun env d pps ->
let pidt = pr_var_decl env d in
(pps ++ fnl () ++ pidt))
env ~init:(mt ())
in
let db_env =
fold_rel_context
(fun env d pps ->
let pnat = pr_rel_decl env d in (pps ++ fnl () ++ pnat))
env ~init:(mt ())
in
(sign_env ++ db_env)
(* [Rel (n+m);...;Rel(n+1)] *)
let rel_vect n m = Array.init m (fun i -> mkRel(n+m-i))
let rel_list n m =
let open EConstr in
let rec reln l p =
if p>m then l else reln (mkRel(n+p)::l) (p+1)
in
reln [] 1
let push_rel_assum (x,t) env =
let open RelDecl in
let open EConstr in
push_rel (LocalAssum (x,t)) env
let push_rels_assum assums =
let open RelDecl in
push_rel_context (List.map (fun (x,t) -> LocalAssum (x,t)) assums)
let push_named_rec_types (lna,typarray,_) env =
let open NamedDecl in
let ctxt =
Array.map2_i
(fun i na t ->
let id = map_annot (function
| Name id -> id
| Anonymous -> anomaly (Pp.str "Fix declarations must be named.")) na
in LocalAssum (id, lift i t))
lna typarray in
Array.fold_left
(fun e assum -> push_named assum e) env ctxt
let lookup_rel_id id sign =
let open RelDecl in
let rec lookrec n = function
| [] -> raise Not_found
| decl :: l ->
if Names.Name.equal (Name id) (get_name decl)
then (n, get_value decl, get_type decl)
else lookrec (n+1) l
in
lookrec 1 sign
(* Constructs either [forall x:t, c] or [let x:=b:t in c] *)
let mkProd_or_LetIn = EConstr.mkProd_or_LetIn
(* Constructs either [forall x:t, c] or [c] in which [x] is replaced by [b] *)
let mkProd_wo_LetIn decl c =
let open EConstr in
let open RelDecl in
match decl with
| LocalAssum (na,t) -> mkProd (na, t, c)
| LocalDef (_,b,_) -> Vars.subst1 b c
let it_mkProd init = List.fold_left (fun c (n,t) -> EConstr.mkProd (n, t, c)) init
let it_mkLambda init = List.fold_left (fun c (n,t) -> EConstr.mkLambda (n, t, c)) init
let it_named_context_quantifier f ~init =
List.fold_left (fun c d -> f d c) init
let it_mkProd_or_LetIn init = it_named_context_quantifier mkProd_or_LetIn ~init
let it_mkProd_wo_LetIn init = it_named_context_quantifier mkProd_wo_LetIn ~init
let it_mkLambda_or_LetIn init = it_named_context_quantifier mkLambda_or_LetIn ~init
let it_mkNamedProd_or_LetIn init = it_named_context_quantifier EConstr.mkNamedProd_or_LetIn ~init
let it_mkNamedProd_wo_LetIn init = it_named_context_quantifier mkNamedProd_wo_LetIn ~init
let it_mkNamedLambda_or_LetIn init = it_named_context_quantifier EConstr.mkNamedLambda_or_LetIn ~init
let it_mkLambda_or_LetIn_from_no_LetIn c decls =
let open RelDecl in
let rec aux k decls c = match decls with
| [] -> c
| LocalDef (na,b,t) :: decls -> mkLetIn (na,b,t,aux (k-1) decls (liftn 1 k c))
| LocalAssum (na,t) :: decls -> mkLambda (na,t,aux (k-1) decls c)
in aux (List.length decls) (List.rev decls) c
(* *)
(* strips head casts and flattens head applications *)
let rec strip_head_cast sigma c = match EConstr.kind sigma c with
| App (f,cl) ->
let rec collapse_rec f cl2 = match EConstr.kind sigma f with
| App (g,cl1) -> collapse_rec g (Array.append cl1 cl2)
| Cast (c,_,_) -> collapse_rec c cl2
| _ -> if Int.equal (Array.length cl2) 0 then f else EConstr.mkApp (f,cl2)
in
collapse_rec f cl
| Cast (c,_,_) -> strip_head_cast sigma c
| _ -> c
let rec drop_extra_implicit_args sigma c = match EConstr.kind sigma c with
(* Removed trailing extra implicit arguments, what improves compatibility
for constants with recently added maximal implicit arguments *)
| App (f,args) when EConstr.isEvar sigma (Array.last args) ->
let open EConstr in
drop_extra_implicit_args sigma
(mkApp (f,fst (Array.chop (Array.length args - 1) args)))
| _ -> c
(* Get the last arg of an application *)
let last_arg sigma c = match EConstr.kind sigma c with
| App (f,cl) -> Array.last cl
| _ -> anomaly (Pp.str "last_arg.")
(* Get the last arg of an application *)
let decompose_app_vect sigma c =
match EConstr.kind sigma c with
| App (f,cl) -> (f, cl)
| _ -> (c,[||])
let adjust_app_list_size f1 l1 f2 l2 =
let open EConstr in
let len1 = List.length l1 and len2 = List.length l2 in
if Int.equal len1 len2 then (f1,l1,f2,l2)
else if len1 < len2 then
let extras,restl2 = List.chop (len2-len1) l2 in
(f1, l1, applist (f2,extras), restl2)
else
let extras,restl1 = List.chop (len1-len2) l1 in
(applist (f1,extras), restl1, f2, l2)
let adjust_app_array_size f1 l1 f2 l2 =
let open EConstr in
let len1 = Array.length l1 and len2 = Array.length l2 in
if Int.equal len1 len2 then (f1,l1,f2,l2)
else if len1 < len2 then
let extras,restl2 = Array.chop (len2-len1) l2 in
(f1, l1, mkApp (f2,extras), restl2)
else
let extras,restl1 = Array.chop (len1-len2) l1 in
(mkApp (f1,extras), restl1, f2, l2)
(* [map_constr_with_binders_left_to_right g f n c] maps [f n] on the
immediate subterms of [c]; it carries an extra data [n] (typically
a lift index) which is processed by [g] (which typically add 1 to
[n]) at each binder traversal; the subterms are processed from left
to right according to the usual representation of the constructions
(this may matter if [f] does a side-effect); it is not recursive;
in fact, the usual representation of the constructions is at the
time being almost those of the ML representation (except for
(co-)fixpoint) *)
let fold_rec_types g (lna,typarray,_) e =
let open EConstr in
let open Vars in
let ctxt = Array.map2_i (fun i na t -> RelDecl.LocalAssum (na, lift i t)) lna typarray in
Array.fold_left (fun e assum -> g assum e) e ctxt
let map_left2 f a g b =
let l = Array.length a in
if Int.equal l 0 then [||], [||] else begin
let r = Array.make l (f a.(0)) in
let s = Array.make l (g b.(0)) in
for i = 1 to l - 1 do
r.(i) <- f a.(i);
s.(i) <- g b.(i)
done;
r, s
end
let map_constr_with_binders_left_to_right sigma g f l c =
let open RelDecl in
let open EConstr in
match EConstr.kind sigma c with
| (Rel _ | Meta _ | Var _ | Sort _ | Const _ | Ind _
| Construct _ | Int _) -> c
| Cast (b,k,t) ->
let b' = f l b in
let t' = f l t in
if b' == b && t' == t then c
else mkCast (b',k,t')
| Prod (na,t,b) ->
let t' = f l t in
let b' = f (g (LocalAssum (na,t)) l) b in
if t' == t && b' == b then c
else mkProd (na, t', b')
| Lambda (na,t,b) ->
let t' = f l t in
let b' = f (g (LocalAssum (na,t)) l) b in
if t' == t && b' == b then c
else mkLambda (na, t', b')
| LetIn (na,bo,t,b) ->
let bo' = f l bo in
let t' = f l t in
let b' = f (g (LocalDef (na,bo,t)) l) b in
if bo' == bo && t' == t && b' == b then c
else mkLetIn (na, bo', t', b')
| App (c,[||]) -> assert false
| App (t,al) ->
(*Special treatment to be able to recognize partially applied subterms*)
let a = al.(Array.length al - 1) in
let app = (mkApp (t, Array.sub al 0 (Array.length al - 1))) in
let app' = f l app in
let a' = f l a in
if app' == app && a' == a then c
else mkApp (app', [| a' |])
| Proj (p,b) ->
let b' = f l b in
if b' == b then c
else mkProj (p, b')
| Evar (e,al) ->
let al' = Array.map_left (f l) al in
if Array.for_all2 (==) al' al then c
else mkEvar (e, al')
| Case (ci,p,b,bl) ->
(* In v8 concrete syntax, predicate is after the term to match! *)
let b' = f l b in
let p' = f l p in
let bl' = Array.map_left (f l) bl in
if b' == b && p' == p && bl' == bl then c
else mkCase (ci, p', b', bl')
| Fix (ln,(lna,tl,bl as fx)) ->
let l' = fold_rec_types g fx l in
let (tl', bl') = map_left2 (f l) tl (f l') bl in
if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
then c
else mkFix (ln,(lna,tl',bl'))
| CoFix(ln,(lna,tl,bl as fx)) ->
let l' = fold_rec_types g fx l in
let (tl', bl') = map_left2 (f l) tl (f l') bl in
if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
then c
else mkCoFix (ln,(lna,tl',bl'))
let map_under_context_with_full_binders sigma g f l n d =
let open EConstr in
let f l c = Unsafe.to_constr (f l (of_constr c)) in
let g d l = g (of_rel_decl d) l in
let d = EConstr.Unsafe.to_constr (EConstr.whd_evar sigma d) in
EConstr.of_constr (Constr.map_under_context_with_full_binders g f l n d)
let map_branches_with_full_binders sigma g f l ci bl =
let tags = Array.map List.length ci.ci_pp_info.cstr_tags in
let bl' = Array.map2 (map_under_context_with_full_binders sigma g f l) tags bl in
if Array.for_all2 (==) bl' bl then bl else bl'
let map_return_predicate_with_full_binders sigma g f l ci p =
let n = List.length ci.ci_pp_info.ind_tags in
let p' = map_under_context_with_full_binders sigma g f l n p in
if p' == p then p else p'
(* strong *)
let map_constr_with_full_binders_gen userview sigma g f l cstr =
let open EConstr in
match EConstr.kind sigma cstr with
| (Rel _ | Meta _ | Var _ | Sort _ | Const _ | Ind _
| Construct _ | Int _) -> cstr
| Cast (c,k, t) ->
let c' = f l c in
let t' = f l t in
if c==c' && t==t' then cstr else mkCast (c', k, t')
| Prod (na,t,c) ->
let t' = f l t in
let c' = f (g (RelDecl.LocalAssum (na, t)) l) c in
if t==t' && c==c' then cstr else mkProd (na, t', c')
| Lambda (na,t,c) ->
let t' = f l t in
let c' = f (g (RelDecl.LocalAssum (na, t)) l) c in
if t==t' && c==c' then cstr else mkLambda (na, t', c')
| LetIn (na,b,t,c) ->
let b' = f l b in
let t' = f l t in
let c' = f (g (RelDecl.LocalDef (na, b, t)) l) c in
if b==b' && t==t' && c==c' then cstr else mkLetIn (na, b', t', c')
| App (c,al) ->
let c' = f l c in
let al' = Array.map (f l) al in
if c==c' && Array.for_all2 (==) al al' then cstr else mkApp (c', al')
| Proj (p,c) ->
let c' = f l c in
if c' == c then cstr else mkProj (p, c')
| Evar (e,al) ->
let al' = Array.map (f l) al in
if Array.for_all2 (==) al al' then cstr else mkEvar (e, al')
| Case (ci,p,c,bl) when userview ->
let p' = map_return_predicate_with_full_binders sigma g f l ci p in
let c' = f l c in
let bl' = map_branches_with_full_binders sigma g f l ci bl in
if p==p' && c==c' && bl'==bl then cstr else
mkCase (ci, p', c', bl')
| Case (ci,p,c,bl) ->
let p' = f l p in
let c' = f l c in
let bl' = Array.map (f l) bl in
if p==p' && c==c' && Array.for_all2 (==) bl bl' then cstr else
mkCase (ci, p', c', bl')
| Fix (ln,(lna,tl,bl as fx)) ->
let tl' = Array.map (f l) tl in
let l' = fold_rec_types g fx l in
let bl' = Array.map (f l') bl in
if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
then cstr
else mkFix (ln,(lna,tl',bl'))
| CoFix(ln,(lna,tl,bl as fx)) ->
let tl' = Array.map (f l) tl in
let l' = fold_rec_types g fx l in
let bl' = Array.map (f l') bl in
if Array.for_all2 (==) tl tl' && Array.for_all2 (==) bl bl'
then cstr
else mkCoFix (ln,(lna,tl',bl'))
let map_constr_with_full_binders sigma g f =
map_constr_with_full_binders_gen false sigma g f
let map_constr_with_full_binders_user_view sigma g f =
map_constr_with_full_binders_gen true sigma g f
(* [fold_constr_with_binders g f n acc c] folds [f n] on the immediate
subterms of [c] starting from [acc] and proceeding from left to
right according to the usual representation of the constructions as
[fold_constr] but it carries an extra data [n] (typically a lift
index) which is processed by [g] (which typically add 1 to [n]) at
each binder traversal; it is not recursive *)
let fold_constr_with_full_binders sigma g f n acc c =
let open EConstr in
let f l acc c = f l acc (of_constr c) in
let g d l = g (of_rel_decl d) l in
let c = Unsafe.to_constr (whd_evar sigma c) in
Constr.fold_with_full_binders g f n acc c
let fold_constr_with_binders sigma g f n acc c =
let open EConstr in
let f l acc c = f l acc (of_constr c) in
let c = Unsafe.to_constr (whd_evar sigma c) in
Constr.fold_constr_with_binders g f n acc c
(* [iter_constr_with_full_binders g f acc c] iters [f acc] on the immediate
subterms of [c]; it carries an extra data [acc] which is processed by [g] at
each binder traversal; it is not recursive and the order with which
subterms are processed is not specified *)
let iter_constr_with_full_binders = EConstr.iter_with_full_binders
(***************************)
(* occurs check functions *)
(***************************)
exception Occur
let occur_meta sigma c =
let rec occrec c = match EConstr.kind sigma c with
| Meta _ -> raise Occur
| _ -> EConstr.iter sigma occrec c
in try occrec c; false with Occur -> true
let occur_existential sigma c =
let rec occrec c = match EConstr.kind sigma c with
| Evar _ -> raise Occur
| _ -> EConstr.iter sigma occrec c
in try occrec c; false with Occur -> true
let occur_meta_or_existential sigma c =
let rec occrec c = match EConstr.kind sigma c with
| Evar _ -> raise Occur
| Meta _ -> raise Occur
| _ -> EConstr.iter sigma occrec c
in try occrec c; false with Occur -> true
let occur_metavariable sigma m c =
let rec occrec c = match EConstr.kind sigma c with
| Meta m' -> if Int.equal m m' then raise Occur
| _ -> EConstr.iter sigma occrec c
in
try occrec c; false with Occur -> true
let occur_evar sigma n c =
let rec occur_rec c = match EConstr.kind sigma c with
| Evar (sp,_) when Evar.equal sp n -> raise Occur
| _ -> EConstr.iter sigma occur_rec c
in
try occur_rec c; false with Occur -> true
let occur_in_global env id constr =
let vars = vars_of_global env constr in
if Id.Set.mem id vars then raise Occur
let occur_var env sigma id c =
let rec occur_rec c =
match EConstr.destRef sigma c with
| gr, _ -> occur_in_global env id gr
| exception DestKO -> EConstr.iter sigma occur_rec c
in
try occur_rec c; false with Occur -> true
let occur_var_in_decl env sigma hyp decl =
let open NamedDecl in
match decl with
| LocalAssum (_,typ) -> occur_var env sigma hyp typ
| LocalDef (_, body, typ) ->
occur_var env sigma hyp typ ||
occur_var env sigma hyp body
let local_occur_var sigma id c =
let rec occur c = match EConstr.kind sigma c with
| Var id' -> if Id.equal id id' then raise Occur
| _ -> EConstr.iter sigma occur c
in
try occur c; false with Occur -> true
(* returns the list of free debruijn indices in a term *)
let free_rels sigma m =
let rec frec depth acc c = match EConstr.kind sigma c with
| Rel n -> if n >= depth then Int.Set.add (n-depth+1) acc else acc
| _ -> fold_constr_with_binders sigma succ frec depth acc c
in
frec 1 Int.Set.empty m
(* collects all metavar occurrences, in left-to-right order, preserving
* repetitions and all. *)
let collect_metas sigma c =
let rec collrec acc c =
match EConstr.kind sigma c with
| Meta mv -> List.add_set Int.equal mv acc
| _ -> EConstr.fold sigma collrec acc c
in
List.rev (collrec [] c)
(* collects all vars; warning: this is only visible vars, not dependencies in
all section variables; for the latter, use global_vars_set *)
let collect_vars sigma c =
let rec aux vars c = match EConstr.kind sigma c with
| Var id -> Id.Set.add id vars
| _ -> EConstr.fold sigma aux vars c in
aux Id.Set.empty c
let vars_of_global_reference = vars_of_global
(* Tests whether [m] is a subterm of [t]:
[m] is appropriately lifted through abstractions of [t] *)
let dependent_main noevar sigma m t =
let open EConstr in
let eqc x y = eq_constr_nounivs sigma x y in
let rec deprec m t =
if eqc m t then
raise Occur
else
match EConstr.kind sigma m, EConstr.kind sigma t with
| App (fm,lm), App (ft,lt) when Array.length lm < Array.length lt ->
deprec m (mkApp (ft,Array.sub lt 0 (Array.length lm)));
Array.Fun1.iter deprec m
(Array.sub lt
(Array.length lm) ((Array.length lt) - (Array.length lm)))
| _, Cast (c,_,_) when noevar && isMeta sigma c -> ()
| _, Evar _ when noevar -> ()
| _ -> EConstr.iter_with_binders sigma (fun c -> Vars.lift 1 c) deprec m t
in
try deprec m t; false with Occur -> true
let dependent sigma c t = dependent_main false sigma c t
let dependent_no_evar sigma c t = dependent_main true sigma c t
let dependent_in_decl sigma a decl =
let open NamedDecl in
match decl with
| LocalAssum (_,t) -> dependent sigma a t
| LocalDef (_, body, t) -> dependent sigma a body || dependent sigma a t
let count_occurrences sigma m t =
let open EConstr in
let n = ref 0 in
let rec countrec m t =
if EConstr.eq_constr sigma m t then
incr n
else
match EConstr.kind sigma m, EConstr.kind sigma t with
| App (fm,lm), App (ft,lt) when Array.length lm < Array.length lt ->
countrec m (mkApp (ft,Array.sub lt 0 (Array.length lm)));
Array.iter (countrec m)
(Array.sub lt
(Array.length lm) ((Array.length lt) - (Array.length lm)))
| _, Cast (c,_,_) when isMeta sigma c -> ()
| _, Evar _ -> ()
| _ -> EConstr.iter_with_binders sigma (Vars.lift 1) countrec m t
in
countrec m t;
!n
let pop t = EConstr.Vars.lift (-1) t
(***************************)
(* bindings functions *)
(***************************)
type meta_type_map = (metavariable * types) list
type meta_value_map = (metavariable * constr) list
let isMetaOf sigma mv c =
match EConstr.kind sigma c with Meta mv' -> Int.equal mv mv' | _ -> false
let rec subst_meta bl c =
match kind c with
| Meta i -> (try Int.List.assoc i bl with Not_found -> c)
| _ -> Constr.map (subst_meta bl) c
let rec strip_outer_cast sigma c = match EConstr.kind sigma c with
| Cast (c,_,_) -> strip_outer_cast sigma c
| _ -> c
(* flattens application lists throwing casts in-between *)
let collapse_appl sigma c = match EConstr.kind sigma c with
| App (f,cl) ->
if EConstr.isCast sigma f then
let rec collapse_rec f cl2 =
match EConstr.kind sigma (strip_outer_cast sigma f) with
| App (g,cl1) -> collapse_rec g (Array.append cl1 cl2)
| _ -> EConstr.mkApp (f,cl2)
in
collapse_rec f cl
else c
| _ -> c
(* First utilities for avoiding telescope computation for subst_term *)
let prefix_application sigma eq_fun (k,c) t =
let open EConstr in
let c' = collapse_appl sigma c and t' = collapse_appl sigma t in
match EConstr.kind sigma c', EConstr.kind sigma t' with
| App (f1,cl1), App (f2,cl2) ->
let l1 = Array.length cl1
and l2 = Array.length cl2 in
if l1 <= l2
&& eq_fun sigma c' (mkApp (f2, Array.sub cl2 0 l1)) then
Some (mkApp (mkRel k, Array.sub cl2 l1 (l2 - l1)))
else
None
| _ -> None
let my_prefix_application sigma eq_fun (k,c) by_c t =
let open EConstr in
let c' = collapse_appl sigma c and t' = collapse_appl sigma t in
match EConstr.kind sigma c', EConstr.kind sigma t' with
| App (f1,cl1), App (f2,cl2) ->
let l1 = Array.length cl1
and l2 = Array.length cl2 in
if l1 <= l2
&& eq_fun sigma c' (mkApp (f2, Array.sub cl2 0 l1)) then
Some (mkApp ((Vars.lift k by_c), Array.sub cl2 l1 (l2 - l1)))
else
None
| _ -> None
(* Recognizing occurrences of a given subterm in a term: [subst_term c t]
substitutes [(Rel 1)] for all occurrences of term [c] in a term [t];
works if [c] has rels *)
let subst_term_gen sigma eq_fun c t =
let open EConstr in
let open Vars in
let rec substrec (k,c as kc) t =
match prefix_application sigma eq_fun kc t with
| Some x -> x
| None ->
if eq_fun sigma c t then mkRel k
else
EConstr.map_with_binders sigma (fun (k,c) -> (k+1,lift 1 c)) substrec kc t
in
substrec (1,c) t
let subst_term sigma c t = subst_term_gen sigma EConstr.eq_constr c t
(* Recognizing occurrences of a given subterm in a term :
[replace_term c1 c2 t] substitutes [c2] for all occurrences of
term [c1] in a term [t]; works if [c1] and [c2] have rels *)
let replace_term_gen sigma eq_fun c by_c in_t =
let rec substrec (k,c as kc) t =
match my_prefix_application sigma eq_fun kc by_c t with
| Some x -> x
| None ->
(if eq_fun sigma c t then (EConstr.Vars.lift k by_c) else
EConstr.map_with_binders sigma (fun (k,c) -> (k+1,EConstr.Vars.lift 1 c))
substrec kc t)
in
substrec (0,c) in_t
let replace_term sigma c byc t = replace_term_gen sigma EConstr.eq_constr c byc t
let vars_of_env env =
let s = Environ.ids_of_named_context_val (Environ.named_context_val env) in
if List.is_empty (Environ.rel_context env) then s
else
Context.Rel.fold_outside
(fun decl s -> match RelDecl.get_name decl with Name id -> Id.Set.add id s | _ -> s)
(rel_context env) ~init:s
let add_vname vars = function
Name id -> Id.Set.add id vars
| _ -> vars
(*************************)
(* Names environments *)
(*************************)
type names_context = Name.t list
let add_name n nl = n::nl
let lookup_name_of_rel p names =
try List.nth names (p-1)
with Invalid_argument _ | Failure _ -> raise Not_found
let lookup_rel_of_name id names =
let rec lookrec n = function
| Anonymous :: l -> lookrec (n+1) l
| (Name id') :: l -> if Id.equal id' id then n else lookrec (n+1) l
| [] -> raise Not_found
in
lookrec 1 names
let empty_names_context = []
let ids_of_rel_context sign =
Context.Rel.fold_outside
(fun decl l -> match RelDecl.get_name decl with Name id -> id::l | Anonymous -> l)
sign ~init:[]
let ids_of_named_context sign =
Context.Named.fold_outside (fun decl idl -> NamedDecl.get_id decl :: idl) sign ~init:[]
let ids_of_context env =
(ids_of_rel_context (rel_context env))
@ (ids_of_named_context (named_context env))
let names_of_rel_context env =
List.map RelDecl.get_name (rel_context env)
let is_section_variable id =
try let _ = Global.lookup_named id in true
with Not_found -> false
let global_of_constr sigma c =
let open Globnames in
match EConstr.kind sigma c with
| Const (c, u) -> ConstRef c, u
| Ind (i, u) -> IndRef i, u
| Construct (c, u) -> ConstructRef c, u
| Var id -> VarRef id, EConstr.EInstance.empty
| _ -> raise Not_found
let is_global sigma c t =
let open Globnames in
match c, EConstr.kind sigma t with
| ConstRef c, Const (c', _) -> Constant.equal c c'
| IndRef i, Ind (i', _) -> eq_ind i i'
| ConstructRef i, Construct (i', _) -> eq_constructor i i'
| VarRef id, Var id' -> Id.equal id id'
| _ -> false
let isGlobalRef sigma c =
match EConstr.kind sigma c with
| Const _ | Ind _ | Construct _ | Var _ -> true
| _ -> false
let is_template_polymorphic_ind env sigma f =
match EConstr.kind sigma f with
| Ind (ind, u) ->
if not (EConstr.EInstance.is_empty u) then false
else Environ.template_polymorphic_ind ind env
| _ -> false
let base_sort_cmp pb s0 s1 =
match (s0,s1) with
| SProp, SProp | Prop, Prop | Set, Set | Type _, Type _ -> true
| SProp, _ | _, SProp -> false
| Prop, Set | Prop, Type _ | Set, Type _ -> pb == Reduction.CUMUL
| Set, Prop | Type _, Prop | Type _, Set -> false
let rec is_Prop sigma c = match EConstr.kind sigma c with
| Sort u ->
begin match EConstr.ESorts.kind sigma u with
| Prop -> true
| _ -> false
end
| Cast (c,_,_) -> is_Prop sigma c
| _ -> false
let rec is_Set sigma c = match EConstr.kind sigma c with
| Sort u ->
begin match EConstr.ESorts.kind sigma u with
| Set -> true
| _ -> false
end
| Cast (c,_,_) -> is_Set sigma c
| _ -> false
let rec is_Type sigma c = match EConstr.kind sigma c with
| Sort u ->
begin match EConstr.ESorts.kind sigma u with
| Type _ -> true
| _ -> false
end
| Cast (c,_,_) -> is_Type sigma c
| _ -> false
(* eq_constr extended with universe erasure *)
let compare_constr_univ sigma f cv_pb t1 t2 =
let open EConstr in
match EConstr.kind sigma t1, EConstr.kind sigma t2 with
Sort s1, Sort s2 -> base_sort_cmp cv_pb (ESorts.kind sigma s1) (ESorts.kind sigma s2)
| Prod (_,t1,c1), Prod (_,t2,c2) ->
f Reduction.CONV t1 t2 && f cv_pb c1 c2
| Const (c, u), Const (c', u') -> Constant.equal c c'
| Ind (i, _), Ind (i', _) -> eq_ind i i'
| Construct (i, _), Construct (i', _) -> eq_constructor i i'
| _ -> EConstr.compare_constr sigma (fun t1 t2 -> f Reduction.CONV t1 t2) t1 t2
let constr_cmp sigma cv_pb t1 t2 =
let rec compare cv_pb t1 t2 = compare_constr_univ sigma compare cv_pb t1 t2 in
compare cv_pb t1 t2
let eq_constr sigma t1 t2 = constr_cmp sigma Reduction.CONV t1 t2
(* App(c,[t1,...tn]) -> ([c,t1,...,tn-1],tn)
App(c,[||]) -> ([],c) *)
let split_app sigma c = match EConstr.kind sigma c with
App(c,l) ->
let len = Array.length l in
if Int.equal len 0 then ([],c) else
let last = Array.get l (len-1) in
let prev = Array.sub l 0 (len-1) in
c::(Array.to_list prev), last
| _ -> assert false
type subst = (EConstr.rel_context * EConstr.constr) Evar.Map.t
exception CannotFilter
let filtering sigma env cv_pb c1 c2 =
let open EConstr in
let open Vars in
let evm = ref Evar.Map.empty in
let define cv_pb e1 ev c1 =
try let (e2,c2) = Evar.Map.find ev !evm in
let shift = List.length e1 - List.length e2 in
if constr_cmp sigma cv_pb c1 (lift shift c2) then () else raise CannotFilter
with Not_found ->
evm := Evar.Map.add ev (e1,c1) !evm
in
let rec aux env cv_pb c1 c2 =
match EConstr.kind sigma c1, EConstr.kind sigma c2 with
| App _, App _ ->
let ((p1,l1),(p2,l2)) = (split_app sigma c1),(split_app sigma c2) in
let () = aux env cv_pb l1 l2 in
begin match p1, p2 with
| [], [] -> ()
| (h1 :: p1), (h2 :: p2) ->
aux env cv_pb (applist (h1, p1)) (applist (h2, p2))
| _ -> assert false
end
| Prod (n,t1,c1), Prod (_,t2,c2) ->
aux env cv_pb t1 t2;
aux (RelDecl.LocalAssum (n,t1) :: env) cv_pb c1 c2
| _, Evar (ev,_) -> define cv_pb env ev c1
| Evar (ev,_), _ -> define cv_pb env ev c2
| _ ->
if compare_constr_univ sigma
(fun pb c1 c2 -> aux env pb c1 c2; true) cv_pb c1 c2 then ()
else raise CannotFilter
(* TODO: le reste des binders *)
in
aux env cv_pb c1 c2; !evm
let decompose_prod_letin sigma c =
let rec prodec_rec i l c = match EConstr.kind sigma c with
| Prod (n,t,c) -> prodec_rec (succ i) (RelDecl.LocalAssum (n,t)::l) c
| LetIn (n,d,t,c) -> prodec_rec (succ i) (RelDecl.LocalDef (n,d,t)::l) c
| Cast (c,_,_) -> prodec_rec i l c
| _ -> i,l,c in
prodec_rec 0 [] c
(* (nb_lam [na1:T1]...[nan:Tan]c) where c is not an abstraction
* gives n (casts are ignored) *)
let nb_lam sigma c =
let rec nbrec n c = match EConstr.kind sigma c with
| Lambda (_,_,c) -> nbrec (n+1) c
| Cast (c,_,_) -> nbrec n c
| _ -> n
in
nbrec 0 c
(* similar to nb_lam, but gives the number of products instead *)
let nb_prod sigma c =
let rec nbrec n c = match EConstr.kind sigma c with
| Prod (_,_,c) -> nbrec (n+1) c
| Cast (c,_,_) -> nbrec n c
| _ -> n
in
nbrec 0 c
let nb_prod_modulo_zeta sigma x =
let rec count n c =
match EConstr.kind sigma c with
Prod(_,_,t) -> count (n+1) t
| LetIn(_,a,_,t) -> count n (EConstr.Vars.subst1 a t)
| Cast(c,_,_) -> count n c
| _ -> n
in count 0 x
let align_prod_letin sigma c a =
let (lc,_,_) = decompose_prod_letin sigma c in
let (la,l,a) = decompose_prod_letin sigma a in
if not (la >= lc) then invalid_arg "align_prod_letin";
let (l1,l2) = Util.List.chop lc l in
l2,it_mkProd_or_LetIn a l1
(* We reduce a series of head eta-redex or nothing at all *)
(* [x1:c1;...;xn:cn]@(f;a1...an;x1;...;xn) --> @(f;a1...an) *)
(* Remplace 2 earlier buggish versions *)
let rec eta_reduce_head sigma c =
let open EConstr in
let open Vars in
match EConstr.kind sigma c with
| Lambda (_,c1,c') ->
(match EConstr.kind sigma (eta_reduce_head sigma c') with
| App (f,cl) ->
let lastn = (Array.length cl) - 1 in
if lastn < 0 then anomaly (Pp.str "application without arguments.")
else
(match EConstr.kind sigma cl.(lastn) with
| Rel 1 ->
let c' =
if Int.equal lastn 0 then f
else mkApp (f, Array.sub cl 0 lastn)
in
if noccurn sigma 1 c'
then lift (-1) c'
else c
| _ -> c)
| _ -> c)
| _ -> c
(* iterator on rel context *)
let process_rel_context f env =
let sign = named_context_val env in
let rels = EConstr.rel_context env in
let env0 = reset_with_named_context sign env in
Context.Rel.fold_outside f rels ~init:env0
let assums_of_rel_context sign =
Context.Rel.fold_outside
(fun decl l ->
match decl with
| RelDecl.LocalDef _ -> l
| RelDecl.LocalAssum (na,t) -> (na, t)::l)
sign ~init:[]
let map_rel_context_in_env f env sign =
let rec aux env acc = function
| d::sign ->
aux (push_rel d env) (RelDecl.map_constr (f env) d :: acc) sign
| [] ->
acc
in
aux env [] (List.rev sign)
let map_rel_context_with_binders f sign =
let rec aux k = function
| d::sign -> RelDecl.map_constr (f k) d :: aux (k-1) sign
| [] -> []
in
aux (Context.Rel.length sign) sign
let substl_rel_context l =
map_rel_context_with_binders (fun k -> substnl l (k-1))
let lift_rel_context n =
map_rel_context_with_binders (liftn n)
let smash_rel_context sign =
let rec aux acc = function
| [] -> acc
| (RelDecl.LocalAssum _ as d) :: l -> aux (d::acc) l
| RelDecl.LocalDef (_,b,_) :: l ->
(* Quadratic in the number of let but there are probably a few of them *)
aux (List.rev (substl_rel_context [b] (List.rev acc))) l
in List.rev (aux [] sign)
let fold_named_context_both_sides f l ~init = List.fold_right_and_left f l init
let mem_named_context_val id ctxt =
try ignore(Environ.lookup_named_ctxt id ctxt); true with Not_found -> false
let map_rel_decl f = function
| RelDecl.LocalAssum (id, t) -> RelDecl.LocalAssum (id, f t)
| RelDecl.LocalDef (id, b, t) -> RelDecl.LocalDef (id, f b, f t)
let map_named_decl f = function
| NamedDecl.LocalAssum (id, t) -> NamedDecl.LocalAssum (id, f t)
| NamedDecl.LocalDef (id, b, t) -> NamedDecl.LocalDef (id, f b, f t)
let compact_named_context sign =
let compact l decl =
match decl, l with
| NamedDecl.LocalAssum (i,t), [] ->
[CompactedDecl.LocalAssum ([i],t)]
| NamedDecl.LocalDef (i,c,t), [] ->
[CompactedDecl.LocalDef ([i],c,t)]
| NamedDecl.LocalAssum (i1,t1), CompactedDecl.LocalAssum (li,t2) :: q ->
if Constr.equal t1 t2
then CompactedDecl.LocalAssum (i1::li, t2) :: q
else CompactedDecl.LocalAssum ([i1],t1) :: CompactedDecl.LocalAssum (li,t2) :: q
| NamedDecl.LocalDef (i1,c1,t1), CompactedDecl.LocalDef (li,c2,t2) :: q ->
if Constr.equal c1 c2 && Constr.equal t1 t2
then CompactedDecl.LocalDef (i1::li, c2, t2) :: q
else CompactedDecl.LocalDef ([i1],c1,t1) :: CompactedDecl.LocalDef (li,c2,t2) :: q
| NamedDecl.LocalAssum (i,t), q ->
CompactedDecl.LocalAssum ([i],t) :: q
| NamedDecl.LocalDef (i,c,t), q ->
CompactedDecl.LocalDef ([i],c,t) :: q
in
sign |> Context.Named.fold_inside compact ~init:[] |> List.rev
let clear_named_body id env =
let open NamedDecl in
let aux _ = function
| LocalDef (id',c,t) when Id.equal id id'.binder_name -> push_named (LocalAssum (id',t))
| d -> push_named d in
fold_named_context aux env ~init:(reset_context env)
let global_vars_set env sigma constr =
let rec filtrec acc c =
match EConstr.destRef sigma c with
| gr, _ -> Id.Set.union (vars_of_global env gr) acc
| exception DestKO -> EConstr.fold sigma filtrec acc c
in
filtrec Id.Set.empty constr
let global_vars env sigma ids = Id.Set.elements (global_vars_set env sigma ids)
let global_vars_set_of_decl env sigma = function
| NamedDecl.LocalAssum (_,t) -> global_vars_set env sigma t
| NamedDecl.LocalDef (_,c,t) ->
Id.Set.union (global_vars_set env sigma t)
(global_vars_set env sigma c)
let dependency_closure env sigma sign hyps =
if Id.Set.is_empty hyps then [] else
let (_,lh) =
Context.Named.fold_inside
(fun (hs,hl) d ->
let x = NamedDecl.get_id d in
if Id.Set.mem x hs then
(Id.Set.union (global_vars_set_of_decl env sigma d) (Id.Set.remove x hs),
x::hl)
else (hs,hl))
~init:(hyps,[])
sign in
List.rev lh
let global_app_of_constr sigma c =
let open Globnames in
match EConstr.kind sigma c with
| Const (c, u) -> (ConstRef c, u), None
| Ind (i, u) -> (IndRef i, u), None
| Construct (c, u) -> (ConstructRef c, u), None
| Var id -> (VarRef id, EConstr.EInstance.empty), None
| Proj (p, c) -> (ConstRef (Projection.constant p), EConstr.EInstance.empty), Some c
| _ -> raise Not_found
let prod_applist sigma c l =
let open EConstr in
let rec app subst c l =
match EConstr.kind sigma c, l with
| Prod(_,_,c), arg::l -> app (arg::subst) c l
| _, [] -> Vars.substl subst c
| _ -> anomaly (Pp.str "Not enough prod's.") in
app [] c l
let prod_applist_assum sigma n c l =
let open EConstr in
let rec app n subst c l =
if Int.equal n 0 then
if l == [] then Vars.substl subst c
else anomaly (Pp.str "Not enough arguments.")
else match EConstr.kind sigma c, l with
| Prod(_,_,c), arg::l -> app (n-1) (arg::subst) c l
| LetIn(_,b,_,c), _ -> app (n-1) (Vars.substl subst b::subst) c l
| _ -> anomaly (Pp.str "Not enough prod/let's.") in
app n [] c l
let on_judgment = Environ.on_judgment
let on_judgment_value = Environ.on_judgment_value
let on_judgment_type = Environ.on_judgment_type
(* Cut a context ctx in 2 parts (ctx1,ctx2) with ctx1 containing k non let-in
variables skips let-in's; let-in's in the middle are put in ctx2 *)
let context_chop k ctx =
let rec chop_aux acc = function
| (0, l2) -> (List.rev acc, l2)
| (n, (RelDecl.LocalDef _ as h)::t) -> chop_aux (h::acc) (n, t)
| (n, (h::t)) -> chop_aux (h::acc) (pred n, t)
| (_, []) -> anomaly (Pp.str "context_chop.")
in chop_aux [] (k,ctx)
(* Do not skip let-in's *)
let env_rel_context_chop k env =
let open EConstr in
let rels = rel_context env in
let ctx1,ctx2 = List.chop k rels in
push_rel_context ctx2 (reset_with_named_context (named_context_val env) env),
ctx1
end
include Internal
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