(* $Id$ *)
-open Printf
+module C = Cic
exception Meta_not_found of int
exception Subst_not_found of int
| C.Cast (te,ty) -> is_closed k te && is_closed k ty
| C.Prod (name,so,dest) -> is_closed k so && is_closed (k+1) dest
| C.Lambda (_,so,dest) -> is_closed k so && is_closed (k+1) dest
- | C.LetIn (_,so,dest) -> is_closed k so && is_closed (k+1) dest
+ | C.LetIn (_,so,ty,dest) ->
+ is_closed k so && is_closed k ty && is_closed (k+1) dest
| C.Appl l ->
List.fold_right (fun x i -> i && is_closed k x) l true
| C.Var (_,exp_named_subst)
let rec is_meta_closed =
function
- Cic.Rel _ -> true
- | Cic.Meta _ -> false
- | Cic.Sort _ -> true
- | Cic.Implicit _ -> assert false
- | Cic.Cast (te,ty) -> is_meta_closed te && is_meta_closed ty
- | Cic.Prod (name,so,dest) -> is_meta_closed so && is_meta_closed dest
- | Cic.Lambda (_,so,dest) -> is_meta_closed so && is_meta_closed dest
- | Cic.LetIn (_,so,dest) -> is_meta_closed so && is_meta_closed dest
- | Cic.Appl l ->
+ C.Rel _ -> true
+ | C.Meta _ -> false
+ | C.Sort _ -> true
+ | C.Implicit _ -> assert false
+ | C.Cast (te,ty) -> is_meta_closed te && is_meta_closed ty
+ | C.Prod (name,so,dest) -> is_meta_closed so && is_meta_closed dest
+ | C.Lambda (_,so,dest) -> is_meta_closed so && is_meta_closed dest
+ | C.LetIn (_,so,ty,dest) ->
+ is_meta_closed so &&
+ is_meta_closed ty &&
+ is_meta_closed dest
+ | C.Appl l ->
not (List.exists (fun x -> not (is_meta_closed x)) l)
- | Cic.Var (_,exp_named_subst)
- | Cic.Const (_,exp_named_subst)
- | Cic.MutInd (_,_,exp_named_subst)
- | Cic.MutConstruct (_,_,_,exp_named_subst) ->
+ | C.Var (_,exp_named_subst)
+ | C.Const (_,exp_named_subst)
+ | C.MutInd (_,_,exp_named_subst)
+ | C.MutConstruct (_,_,_,exp_named_subst) ->
not (List.exists (fun (_,x) -> not (is_meta_closed x)) exp_named_subst)
- | Cic.MutCase (_,_,out,te,pl) ->
+ | C.MutCase (_,_,out,te,pl) ->
is_meta_closed out && is_meta_closed te &&
not (List.exists (fun x -> not (is_meta_closed x)) pl)
- | Cic.Fix (_,fl) ->
+ | C.Fix (_,fl) ->
not (List.exists
(fun (_,_,ty,bo) ->
not (is_meta_closed ty) || not (is_meta_closed bo))
fl)
- | Cic.CoFix (_,fl) ->
+ | C.CoFix (_,fl) ->
not (List.exists
(fun (_,ty,bo) ->
not (is_meta_closed ty) || not (is_meta_closed bo))
let s = UriManager.string_of_uri uri in
try
(if UriManager.uri_is_con uri then
- Cic.Const (uri, [])
+ C.Const (uri, [])
else if UriManager.uri_is_var uri then
- Cic.Var (uri, [])
+ C.Var (uri, [])
else if not (Str.string_match xpointer_RE s 0) then
raise (UriManager.IllFormedUri s)
else
let (baseuri,xpointer) = (Str.matched_group 1 s, Str.matched_group 2 s) in
let baseuri = UriManager.uri_of_string baseuri in
(match Str.split slash_RE xpointer with
- | [_; tyno] -> Cic.MutInd (baseuri, int_of_string tyno - 1, [])
+ | [_; tyno] -> C.MutInd (baseuri, int_of_string tyno - 1, [])
| [_; tyno; consno] ->
- Cic.MutConstruct
+ C.MutConstruct
(baseuri, int_of_string tyno - 1, int_of_string consno, [])
| _ -> raise Exit))
with
| Not_found -> raise (UriManager.IllFormedUri s)
let uri_of_term = function
- | Cic.Const (uri, _)
- | Cic.Var (uri, _) -> uri
- | Cic.MutInd (baseuri, tyno, _) ->
+ | C.Const (uri, _)
+ | C.Var (uri, _) -> uri
+ | C.MutInd (baseuri, tyno, _) ->
UriManager.uri_of_string
- (sprintf "%s#xpointer(1/%d)" (UriManager.string_of_uri baseuri) (tyno+1))
- | Cic.MutConstruct (baseuri, tyno, consno, _) ->
+ (Printf.sprintf "%s#xpointer(1/%d)" (UriManager.string_of_uri baseuri) (tyno+1))
+ | C.MutConstruct (baseuri, tyno, consno, _) ->
UriManager.uri_of_string
- (sprintf "%s#xpointer(1/%d/%d)" (UriManager.string_of_uri baseuri)
+ (Printf.sprintf "%s#xpointer(1/%d/%d)" (UriManager.string_of_uri baseuri)
(tyno + 1) consno)
| _ -> raise (Invalid_argument "uri_of_term")
(*
let pack terms =
List.fold_right
- (fun term acc -> Cic.Prod (Cic.Anonymous, term, acc))
- terms (Cic.Sort (Cic.Type (CicUniv.fresh ())))
+ (fun term acc -> C.Prod (C.Anonymous, term, acc))
+ terms (C.Sort (C.Type (CicUniv.fresh ())))
let rec unpack = function
- | Cic.Prod (Cic.Anonymous, term, Cic.Sort (Cic.Type _)) -> [term]
- | Cic.Prod (Cic.Anonymous, term, tgt) -> term :: unpack tgt
+ | C.Prod (C.Anonymous, term, C.Sort (C.Type _)) -> [term]
+ | C.Prod (C.Anonymous, term, tgt) -> term :: unpack tgt
| _ -> assert false
*)
let rec strip_prods n = function
| t when n = 0 -> t
- | Cic.Prod (_, _, tgt) when n > 0 -> strip_prods (n-1) tgt
+ | C.Prod (_, _, tgt) when n > 0 -> strip_prods (n-1) tgt
| _ -> failwith "not enough prods"
let params_of_obj = function
- | Cic.Constant (_, _, _, params, _)
- | Cic.Variable (_, _, _, params, _)
- | Cic.CurrentProof (_, _, _, _, params, _)
- | Cic.InductiveDefinition (_, params, _, _) ->
+ | C.Constant (_, _, _, params, _)
+ | C.Variable (_, _, _, params, _)
+ | C.CurrentProof (_, _, _, _, params, _)
+ | C.InductiveDefinition (_, params, _, _) ->
params
let attributes_of_obj = function
- | Cic.Constant (_, _, _, _, attributes)
- | Cic.Variable (_, _, _, _, attributes)
- | Cic.CurrentProof (_, _, _, _, _, attributes)
- | Cic.InductiveDefinition (_, _, _, attributes) ->
+ | C.Constant (_, _, _, _, attributes)
+ | C.Variable (_, _, _, _, attributes)
+ | C.CurrentProof (_, _, _, _, _, attributes)
+ | C.InductiveDefinition (_, _, _, attributes) ->
attributes
let is_generated obj = List.exists ((=) `Generated) (attributes_of_obj obj)
let rec mk_rels howmany from =
match howmany with
| 0 -> []
- | _ -> (Cic.Rel (howmany + from)) :: (mk_rels (howmany-1) from)
+ | _ -> (C.Rel (howmany + from)) :: (mk_rels (howmany-1) from)
let id_of_annterm =
function
- | Cic.ARel (id,_,_,_)
- | Cic.AVar (id,_,_)
- | Cic.AMeta (id,_,_)
- | Cic.ASort (id,_)
- | Cic.AImplicit (id,_)
- | Cic.ACast (id,_,_)
- | Cic.AProd (id,_,_,_)
- | Cic.ALambda (id,_,_,_)
- | Cic.ALetIn (id,_,_,_)
- | Cic.AAppl (id,_)
- | Cic.AConst (id,_,_)
- | Cic.AMutInd (id,_,_,_)
- | Cic.AMutConstruct (id,_,_,_,_)
- | Cic.AMutCase (id,_,_,_,_,_)
- | Cic.AFix (id,_,_)
- | Cic.ACoFix (id,_,_) -> id
+ | C.ARel (id,_,_,_)
+ | C.AVar (id,_,_)
+ | C.AMeta (id,_,_)
+ | C.ASort (id,_)
+ | C.AImplicit (id,_)
+ | C.ACast (id,_,_)
+ | C.AProd (id,_,_,_)
+ | C.ALambda (id,_,_,_)
+ | C.ALetIn (id,_,_,_,_)
+ | C.AAppl (id,_)
+ | C.AConst (id,_,_)
+ | C.AMutInd (id,_,_,_)
+ | C.AMutConstruct (id,_,_,_,_)
+ | C.AMutCase (id,_,_,_,_,_)
+ | C.AFix (id,_,_)
+ | C.ACoFix (id,_,_) -> id
let rec rehash_term =
| C.Cast (te,ty) -> C.Cast (rehash_term te, rehash_term ty)
| C.Prod (n,s,t) -> C.Prod (n, rehash_term s, rehash_term t)
| C.Lambda (n,s,t) -> C.Lambda (n, rehash_term s, rehash_term t)
- | C.LetIn (n,s,t) -> C.LetIn (n, rehash_term s, rehash_term t)
+ | C.LetIn (n,s,ty,t) ->
+ C.LetIn (n, rehash_term s, rehash_term ty, rehash_term t)
| C.Appl l -> C.Appl (List.map rehash_term l)
| C.Const (uri,exp_named_subst) ->
let uri' = recons uri in
| Some (name,C.Decl t) ->
Some (name,C.Decl (rehash_term t))
| Some (name,C.Def (bo,ty)) ->
- let ty' =
- match ty with
- None -> None
- | Some ty'' -> Some (rehash_term ty'')
- in
- Some (name,C.Def (rehash_term bo, ty'))) hyps,
+ Some (name,C.Def (rehash_term bo, rehash_term ty))) hyps,
rehash_term ty))
conjs
in
C.InductiveDefinition (tl', params', paramsno, attrs)
let rec metas_of_term = function
- | Cic.Meta (i, c) -> [i,c]
- | Cic.Var (_, ens)
- | Cic.Const (_, ens)
- | Cic.MutInd (_, _, ens)
- | Cic.MutConstruct (_, _, _, ens) ->
+ | C.Meta (i, c) -> [i,c]
+ | C.Var (_, ens)
+ | C.Const (_, ens)
+ | C.MutInd (_, _, ens)
+ | C.MutConstruct (_, _, _, ens) ->
List.flatten (List.map (fun (u, t) -> metas_of_term t) ens)
- | Cic.Cast (s, t)
- | Cic.Prod (_, s, t)
- | Cic.Lambda (_, s, t)
- | Cic.LetIn (_, s, t) -> (metas_of_term s) @ (metas_of_term t)
- | Cic.Appl l -> List.flatten (List.map metas_of_term l)
- | Cic.MutCase (uri, i, s, t, l) ->
+ | C.Cast (s, t)
+ | C.Prod (_, s, t)
+ | C.Lambda (_, s, t) -> (metas_of_term s) @ (metas_of_term t)
+ | C.LetIn (_, s, ty, t) ->
+ (metas_of_term s) @ (metas_of_term ty) @ (metas_of_term t)
+ | C.Appl l -> List.flatten (List.map metas_of_term l)
+ | C.MutCase (uri, i, s, t, l) ->
(metas_of_term s) @ (metas_of_term t) @
(List.flatten (List.map metas_of_term l))
- | Cic.Fix (i, il) ->
+ | C.Fix (i, il) ->
List.flatten
(List.map (fun (s, i, t1, t2) ->
(metas_of_term t1) @ (metas_of_term t2)) il)
- | Cic.CoFix (i, il) ->
+ | C.CoFix (i, il) ->
List.flatten
(List.map (fun (s, t1, t2) ->
(metas_of_term t1) @ (metas_of_term t2)) il)
;;
module MetaOT = struct
- type t = int * Cic.term option list
+ type t = int * C.term option list
let compare = Pervasives.compare
end
module S = Set.Make(MetaOT)
let rec metas_of_term_set = function
- | Cic.Meta (i, c) -> S.singleton (i,c)
- | Cic.Var (_, ens)
- | Cic.Const (_, ens)
- | Cic.MutInd (_, _, ens)
- | Cic.MutConstruct (_, _, _, ens) ->
+ | C.Meta (i, c) -> S.singleton (i,c)
+ | C.Var (_, ens)
+ | C.Const (_, ens)
+ | C.MutInd (_, _, ens)
+ | C.MutConstruct (_, _, _, ens) ->
List.fold_left
(fun s (_,t) -> S.union s (metas_of_term_set t))
S.empty ens
- | Cic.Cast (s, t)
- | Cic.Prod (_, s, t)
- | Cic.Lambda (_, s, t)
- | Cic.LetIn (_, s, t) -> S.union (metas_of_term_set s) (metas_of_term_set t)
- | Cic.Appl l ->
+ | C.Cast (s, t)
+ | C.Prod (_, s, t)
+ | C.Lambda (_, s, t) -> S.union (metas_of_term_set s) (metas_of_term_set t)
+ | C.LetIn (_, s, ty, t) ->
+ S.union (metas_of_term_set s)
+ (S.union (metas_of_term_set ty) (metas_of_term_set t))
+ | C.Appl l ->
List.fold_left
(fun s t -> S.union s (metas_of_term_set t))
S.empty l
- | Cic.MutCase (uri, i, s, t, l) ->
+ | C.MutCase (uri, i, s, t, l) ->
S.union
(S.union (metas_of_term_set s) (metas_of_term_set t))
(List.fold_left
(fun s t -> S.union s (metas_of_term_set t))
S.empty l)
- | Cic.Fix (_, il) ->
+ | C.Fix (_, il) ->
(List.fold_left
(fun s (_,_,t1,t2) ->
S.union s (S.union (metas_of_term_set t1) (metas_of_term_set t2))))
S.empty il
- | Cic.CoFix (i, il) ->
+ | C.CoFix (i, il) ->
(List.fold_left
(fun s (_,t1,t2) ->
S.union s (S.union (metas_of_term_set t1) (metas_of_term_set t2))))
S.elements s
;;
+(* syntactic_equality up to the *)
+(* distinction between fake dependent products *)
+(* and non-dependent products, alfa-conversion *)
+let alpha_equivalence =
+ let rec aux t t' =
+ if t = t' then true
+ else
+ match t,t' with
+ C.Var (uri1,exp_named_subst1), C.Var (uri2,exp_named_subst2) ->
+ UriManager.eq uri1 uri2 &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.Cast (te,ty), C.Cast (te',ty') ->
+ aux te te' && aux ty ty'
+ | C.Prod (_,s,t), C.Prod (_,s',t') ->
+ aux s s' && aux t t'
+ | C.Lambda (_,s,t), C.Lambda (_,s',t') ->
+ aux s s' && aux t t'
+ | C.LetIn (_,s,ty,t), C.LetIn(_,s',ty',t') ->
+ aux s s' && aux ty ty' && aux t t'
+ | C.Appl l, C.Appl l' when List.length l = List.length l' ->
+ (try
+ List.fold_left2
+ (fun b t1 t2 -> b && aux t1 t2) true l l'
+ with
+ Invalid_argument _ -> false)
+ | C.Const (uri,exp_named_subst1), C.Const (uri',exp_named_subst2) ->
+ UriManager.eq uri uri' &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.MutInd (uri,i,exp_named_subst1), C.MutInd (uri',i',exp_named_subst2) ->
+ UriManager.eq uri uri' && i = i' &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.MutConstruct (uri,i,j,exp_named_subst1),
+ C.MutConstruct (uri',i',j',exp_named_subst2) ->
+ UriManager.eq uri uri' && i = i' && j = j' &&
+ aux_exp_named_subst exp_named_subst1 exp_named_subst2
+ | C.MutCase (sp,i,outt,t,pl), C.MutCase (sp',i',outt',t',pl') ->
+ UriManager.eq sp sp' && i = i' &&
+ aux outt outt' && aux t t' &&
+ (try
+ List.fold_left2
+ (fun b t1 t2 -> b && aux t1 t2) true pl pl'
+ with
+ Invalid_argument _ -> false)
+ | C.Fix (i,fl), C.Fix (i',fl') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b (_,i,ty,bo) (_,i',ty',bo') ->
+ b && i = i' && aux ty ty' && aux bo bo'
+ ) true fl fl'
+ with
+ Invalid_argument _ -> false)
+ | C.CoFix (i,fl), C.CoFix (i',fl') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b (_,ty,bo) (_,ty',bo') ->
+ b && aux ty ty' && aux bo bo'
+ ) true fl fl'
+ with
+ Invalid_argument _ -> false)
+ | C.Meta (i, subst), C.Meta (i', subst') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b xt xt' -> match xt,xt' with
+ | Some t, Some t' -> b && aux t t'
+ | _ -> b
+ ) true subst subst'
+ with
+ Invalid_argument _ -> false)
+ | C.Appl [t], t' | t, C.Appl [t'] -> assert false
+(* FG: are we _really_ sure of these?
+ | C.Sort (C.Type u), C.Sort (C.Type u') -> u = u'
+ | C.Implicit a, C.Implicit a' -> a = a'
+ we insert an unused variable below to genarate a warning at compile time
+*)
+ | _,_ -> false (* we already know that t != t' *)
+ and aux_exp_named_subst exp_named_subst1 exp_named_subst2 =
+ try
+ List.fold_left2
+ (fun b (uri1,t1) (uri2,t2) ->
+ b && UriManager.eq uri1 uri2 && aux t1 t2
+ ) true exp_named_subst1 exp_named_subst2
+ with
+ Invalid_argument _ -> false
+ in
+ aux
+
+let is_sober t =
+ let rec sober_term g = function
+ | C.Rel _
+ | C.Sort _
+ | C.Implicit _ -> g
+ | C.Const (_, xnss)
+ | C.Var (_, xnss)
+ | C.MutConstruct (_, _, _, xnss)
+ | C.MutInd (_, _, xnss) -> sober_xnss g xnss
+ | C.Meta (_, xss) -> sober_xss g xss
+ | C.Lambda (_, v, t)
+ | C.Prod (_, v, t)
+ | C.Cast (t, v) -> sober_term (sober_term g t) v
+ | C.LetIn (_, v, ty, t) -> sober_term
+ (sober_term (sober_term g t) ty) v
+ | C.Appl []
+ | C.Appl [_] -> fun b -> false
+ | C.Appl ts -> sober_terms g ts
+ | C.MutCase (_, _, t, v, ts) ->
+ sober_terms (sober_term (sober_term g t) v) ts
+ | C.Fix (_, ifs) -> sober_ifs g ifs
+ | C.CoFix (_, cifs) -> sober_cifs g cifs
+ and sober_terms g = List.fold_left sober_term g
+ and sober_xnss g =
+ let map g (_, t) = sober_term g t in
+ List.fold_left map g
+ and sober_xss g =
+ let map g = function
+ | None -> g
+ | Some t -> sober_term g t
+ in
+ List.fold_left map g
+ and sober_ifs g =
+ let map g (_, _, t, v) = sober_term (sober_term g t) v in
+ List.fold_left map g
+ and sober_cifs g =
+ let map g (_, t, v) = sober_term (sober_term g t) v in
+ List.fold_left map g
+ in
+ sober_term (fun b -> b) t true