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open Names
module RelDecl = Context.Rel.Declaration
(*********************)(* Occurring *)(*********************)
exception LocalOccur
(* (closedn n M) is true iff M is a (de Brujin) closed term under n binders *)
let closedn n c = let rec closed_rec n c = match Constr.kind c with | Constr.Rel m -> if m>n then raise_notrace 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_notrace 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_notrace 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_notrace 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.exliftnlet liftn = Constr.liftnlet lift = Constr.lift
let liftn_rel_context n k = Context.Rel.map_with_binders (fun i -> liftn n (i+k-1))
let lift_rel_context n = Context.Rel.map_with_binders (liftn n)
(*********************)(* 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 *)
module IntTbl = Hashtbl.Make(Int)
type info = Closed | Open of Constr.t IntTbl.t | Unknowntype substituend = { mutable sinfo: info; sit: Constr.t }
let lift_substituend depth s = match s.sinfo with | Closed -> s.sit | Open cache -> begin match IntTbl.find_opt cache depth with | Some v -> v | None -> let v = lift depth s.sit in let () = IntTbl.add cache depth v in v end | Unknown -> let sit = s.sit in if closed0 sit then let () = s.sinfo <- Closed in sit else let v = lift depth sit in let cache = IntTbl.create 13 in let () = IntTbl.add cache depth v in let () = s.sinfo <- Open cache in v
let lift_substituend depth s = if Int.equal depth 0 then s.sit else lift_substituend depth s
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 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 clet substl laml c = substn_many (make_subst laml) 0 clet 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) rlet substl_decl laml r = RelDecl.map_constr (fun c -> substnl laml 0 c) rlet subst1_decl lam r = RelDecl.map_constr (fun c -> subst1 lam c) r
let substnl_rel_context laml k r = Context.Rel.map_with_binders (fun i -> substnl laml (i+k-1)) r
let substl_rel_context laml r = substnl_rel_context laml 0 rlet subst1_rel_context lam r = substnl_rel_context [lam] 0 r
let esubst mk subst c = let rec esubst subst c = match Constr.kind c with | Constr.Rel i -> let open Esubst in begin match expand_rel i subst with | Util.Inl (k, v) -> mk k v | Util.Inr (m, _) -> Constr.mkRel m end | _ -> Constr.map_with_binders Esubst.subs_lift esubst subst c in if Esubst.is_subs_id subst then c else esubst subst c
(* Instance of contexts *)
type instance = Constr.t arraytype instance_list = Constr.t list
(* Build a substitution from an instance, inserting missing let-ins *)
let subst_of_rel_context_instance_list 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 subst_of_rel_context_instance sign v = subst_of_rel_context_instance_list sign (Array.to_list v)
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'<n then p+1 else p) | [] -> (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 find_var id vars = CList.assoc_f Id.equal id vars
(* (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 -> begin match find_var x var_alist with | var -> lift_substituend n var | exception Not_found -> c end | Constr.Evar _ -> CErrors.anomaly (Pp.str "Substituting an evar in the kernel") | _ -> 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
let smash_rel_context sign = let open Context.Rel.Declaration in let open Esubst in snd (List.fold_right (fun decl (subst, sign) -> match get_value decl with | Some b -> (subs_cons (make_substituend (esubst lift_substituend subst b)) subst, sign) | None -> (subs_lift subst, map_constr (esubst lift_substituend subst) decl :: sign)) sign (subs_id 0, []))
(** Universe substitutions *)open Constr
let map_annot_relevance f na = let open Context in let r = na.binder_relevance in let r' = f r in if r' == r then na else { na with binder_relevance = r' }
let map_case_under_context_relevance f (nas,x as v) = let nas' = CArray.Smart.map (map_annot_relevance f) nas in if nas' == nas then v else (nas',x)
let map_rec_declaration_relevance f (i,(nas,x,y) as v) =let nas' = CArray.Smart.map (map_annot_relevance f) nas in if nas' == nas then v else (i,(nas',x,y))
let map_constr_relevance f c = match kind c with | Rel _ | Var _ | Meta _ | Evar _ | Sort _ | Cast _ | App _ | Const _ | Ind _ | Construct _ | Int _ | Float _ | String _ | Array _ -> c
| Prod (na,x,y) -> let na' = map_annot_relevance f na in if na' == na then c else mkProd (na',x,y)
| Lambda (na,x,y) -> let na' = map_annot_relevance f na in if na' == na then c else mkLambda (na',x,y)
| LetIn (na,x,y,z) -> let na' = map_annot_relevance f na in if na' == na then c else mkLetIn (na',x,y,z)
| Case (ci,u,params,(ret,r),iv,v,brs) -> let r' = f r in let ret' = map_case_under_context_relevance f ret in let brs' = CArray.Smart.map (map_case_under_context_relevance f) brs in if r' == r && ret' == ret && brs' == brs then c else mkCase (ci,u,params,(ret',r'),iv,v,brs')
| Fix data -> let data' = map_rec_declaration_relevance f data in if data' == data then c else mkFix data'
| CoFix data -> let data' = map_rec_declaration_relevance f data in if data' == data then c else mkCoFix data'
| Proj (p, r, v) -> let r' = f r in if r' == r then c else mkProj (p, r', v)
let fold_annot_relevance f acc na = f acc na.Context.binder_relevance
let fold_case_under_context_relevance f acc (nas,_) = Array.fold_left (fold_annot_relevance f) acc nas
let fold_rec_declaration_relevance f acc (nas,_,_) = Array.fold_left (fold_annot_relevance f) acc nas
let fold_kind_relevance f acc c = match c with | Rel _ | Var _ | Meta _ | Evar _ | Sort _ | Cast _ | App _ | Const _ | Ind _ | Construct _ | Int _ | Float _ | String _ | Array _ -> acc
| Prod (na,_,_) | Lambda (na,_,_) | LetIn (na,_,_,_) -> fold_annot_relevance f acc na
| Case (_,_u,_params,(ret,r),_iv,_v,brs) -> let acc = f acc r in let acc = fold_case_under_context_relevance f acc ret in let acc = CArray.fold_left (fold_case_under_context_relevance f) acc brs in acc
| Proj (_, r, _) -> f acc r
| Fix (_,data) | CoFix (_,data) -> fold_rec_declaration_relevance f acc data
let subst_univs_level_constr subst c = if UVars.is_empty_sort_subst subst then c else let f = UVars.subst_sort_level_instance subst in (* XXX shouldn't Constr.map return the pointer equal term when unchanged instead? *) let changed = ref false in let rec aux t = let t' = map_constr_relevance (UVars.subst_sort_level_relevance subst) t in let t = if t' == t then t else (changed := true; t') in match kind t with | Const (c, u) -> if UVars.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 UVars.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 UVars.Instance.is_empty u then t else let u' = f u in if u' == u then t else (changed := true; mkConstructU (c, u')) | Sort s -> let s' = UVars.subst_sort_level_sort subst s in if s' == s then t else (changed := true; mkSort s')
| Case (ci, u, pms, p, iv, c, br) -> if UVars.Instance.is_empty u then Constr.map aux t else let u' = f u in if u' == u then Constr.map aux t else (changed:=true; Constr.map aux (mkCase (ci,u',pms,p,iv,c,br)))
| Array (u,elems,def,ty) -> let u' = f u in let elems' = CArray.Smart.map aux elems in let def' = aux def in let ty' = aux ty in if u == u' && elems == elems' && def == def' && ty == ty' then t else (changed := true; mkArray (u',elems',def',ty'))
| _ -> Constr.map aux t in let c' = aux c in if !changed then c' else c
let subst_univs_level_context s ctx = CList.Smart.map (fun d -> let d = RelDecl.map_relevance (UVars.subst_sort_level_relevance s) d in RelDecl.map_constr (subst_univs_level_constr s) d) ctx
let subst_instance_constr subst c = if UVars.Instance.is_empty subst then c else let f u = UVars.subst_instance_instance subst u in let rec aux t = let t = if CArray.is_empty (fst (UVars.Instance.to_array subst)) then t else map_constr_relevance (UVars.subst_instance_relevance subst) t in match kind t with | Const (c, u) -> if UVars.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 UVars.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 UVars.Instance.is_empty u then t else let u' = f u in if u' == u then t else (mkConstructU (c, u')) | Sort s -> let s' = UVars.subst_instance_sort subst s in if s' == s then t else mkSort s'
| Case (ci, u, pms, p, iv, c, br) -> let u' = f u in if u' == u then Constr.map aux t else Constr.map aux (mkCase (ci,u',pms,p,iv,c,br))
| Array (u,elems,def,ty) -> let u' = f u in let elems' = CArray.Smart.map aux elems in let def' = aux def in let ty' = aux ty in if u == u' && elems == elems' && def == def' && ty == ty' then t else mkArray (u',elems',def',ty')
| _ -> Constr.map aux t in aux c
let univ_instantiate_constr u c = let open UVars in assert (UVars.eq_sizes (Instance.length u) (AbstractContext.size c.univ_abstracted_binder)); subst_instance_constr u c.univ_abstracted_value
let subst_instance_context s ctx = if UVars.Instance.is_empty s then ctx else CList.Smart.map (fun d -> let d = RelDecl.map_relevance (UVars.subst_instance_relevance s) d in RelDecl.map_constr (subst_instance_constr s) d) ctx
type ('a,'s,'u,'r) univ_visitor = { visit_sort : 'a -> 's -> 'a; visit_instance : 'a -> 'u -> 'a; visit_relevance : 'a -> 'r -> 'a;}
let univs_and_qvars_visitor = let open Univ in let visit_sort (qs,us as acc) = function | Sorts.Type u -> qs, Universe.levels ~init:us u | Sorts.GSort (q,u) -> Sorts.Quality.Set.add (QGlobal q) qs, Universe.levels ~init:us u | Sorts.VSort (q,u) -> Sorts.Quality.Set.add (QVar q) qs, Universe.levels ~init:us u | Sorts.(SProp | Prop | Set) -> acc in let visit_instance (qs,us) u = let qs', us' = UVars.Instance.to_array u in let qs = Array.fold_left (fun qs q -> let open Sorts.Quality in match q with | QVar _ | QGlobal _ -> Sorts.Quality.Set.add q qs | QConstant _ -> qs) qs qs' in let us = Array.fold_left (fun acc x -> Univ.Level.Set.add x acc) us us' in qs, us in let visit_relevance (qs,us as acc) = let open Sorts in function | Irrelevant | Relevant -> acc | RelevanceVar q -> Quality.Set.add (QVar q) qs, us in { visit_sort = visit_sort; visit_instance = visit_instance; visit_relevance = visit_relevance; }
let visit_kind_univs visit acc c = let acc = fold_kind_relevance visit.visit_relevance acc c in match c with | Const (_, u) | Ind (_, u) | Construct (_,u) -> visit.visit_instance acc u | Sort s -> visit.visit_sort acc s | Array (u,_,_,_) -> let acc = visit.visit_instance acc u in acc | Case (_, u, _, _, _,_ ,_) -> let acc = visit.visit_instance acc u in acc | _ -> acc
let sort_and_universes_of_constr ?(init=Sorts.Quality.Set.empty,Univ.Level.Set.empty) c = let rec aux s c = let s = visit_kind_univs univs_and_qvars_visitor s (kind c) in Constr.fold aux s c in aux init c
let sort_and_universes_of_constr ?init c = NewProfile.profile "sort_and_universes_of_constr" (fun () -> sort_and_universes_of_constr ?init c) ()
let universes_of_constr ?(init=Univ.Level.Set.empty) c = snd (sort_and_universes_of_constr ~init:(Sorts.Quality.Set.empty,init) c)