package acgtk
Abstract Categorial Grammar development toolkit
Install
Dune Dependency
Authors
Maintainers
Sources
acg-2.1.0-20240219.tar.gz
sha512=5d380a947658fb1201895cb4cb449b1f60f54914c563e85181d628a89f045c1dd7b5b2226bb7865dd090f87caa9187e0ea6c7a4ee3dc3dda340d404c4e76c7c2
doc/src/acgtk.acgData/signature.ml.html
Source file signature.ml
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(**************************************************************************) (* *) (* ACG development toolkit *) (* *) (* Copyright 2008-2023 INRIA *) (* *) (* More information on "https://acg.loria.fr/" *) (* License: CeCILL, see the LICENSE file or "http://www.cecill.info" *) (* Authors: see the AUTHORS file *) (* *) (* *) (* *) (* *) (* *) (**************************************************************************) open UtilsLib open Table open Logic.Lambda open Logic.Abstract_syntax type sig_entry = | Type_declaration of string * int * Lambda.kind | Type_definition of string * int * Lambda.kind * Lambda.stype | Term_declaration of string * int * Abstract_syntax.syntactic_behavior * Lambda.stype | Term_definition of string * int * Abstract_syntax.syntactic_behavior * Lambda.stype * Lambda.term module Log = Xlog.Make (struct let name = "Signature" end) module Make (Symbols : TABLE with type key = String.t) (Id : TABLE with type key = int) = struct exception Duplicate_type_definition exception Duplicate_term_definition exception Not_found exception Not_functional_type (* exception Not_yet_implemented *) type entry = sig_entry type id = int [@@@warning "-69"] type t = { name : string * id ; loc : string * Abstract_syntax.location; (* name of the file where the signature is defined and its location *) size : int; terms : entry Symbols.t; types : entry Symbols.t; precedence : (float * string option) Symbols.t; (* indicates the precedence and a link to the previous one *) max_pred : float * string option; (* indicates the greatest precedence and a link to the previous one *) ids : entry Id.t; is_2nd_order : bool; extension_timestamp : float; definition_timestamp : float; } [@@@warning "+69"] type term = Lambda.term type stype = Lambda.stype type data = Type of stype | Term of (term * stype) let find_term sym { terms = syms; _ } = match Symbols.find sym syms with | Term_declaration (x, id, _, const_type) when sym = x -> (Lambda.Const id, const_type) | Term_declaration _ -> failwith "Bug in find_term" (* x should match the symbol *) | Term_definition (x, id, _, const_type, _) when sym = x -> (Lambda.DConst id, const_type) | Term_definition _ -> failwith "Bug in find_term" (* x should match the symbol *) | _ -> failwith "Bug in find_term" (* x should return a Term, not a type *) | exception Symbols.Not_found -> raise Not_found let id_to_string { ids; _ } i = match Id.find i ids with | Type_declaration (s, _, _) -> (Abstract_syntax.Default, s) | Type_definition (s, _, _, _) -> (Abstract_syntax.Default, s) | Term_declaration (s, _, behavior, _) -> (behavior, s) | Term_definition (s, _, behavior, _, _) -> (behavior, s) let pp_type sg ppf ty = Lambda.pp_type (id_to_string sg) ppf ty let pp_term sg ppf t = Lambda.pp_term (id_to_string sg) ppf t let empty ~filename (n, l) = let timestamp = Unix.time () in { name = (n, Random.(let () = self_init () in bits ())) ; loc = filename , l ; size = 0; terms = Symbols.empty; types = Symbols.empty; ids = Id.empty; is_2nd_order = true; precedence = Symbols.empty; max_pred = (0., None); definition_timestamp = timestamp; extension_timestamp = timestamp; } let name { name = n, _ ; loc = _, l; _ } = n, l let full_name { name = n ; loc = filename, _; _ } = n, filename let find_atomic_type s { types = syms; _ } = (* TODO : Replace by an assert within IFDEFDEBUG *) match Symbols.find s syms with | Type_declaration (x, id, _) when x = s -> Lambda.Atom id | Type_declaration _ -> failwith "Bug in find_atomic_type" (* x and s should match if something is returned *) | Type_definition (x, id, _, _) when x = s -> Lambda.DAtom id | Type_definition _ -> failwith "Bug in find_atomic_type" (* x and s should match if something is returned *) | _ -> failwith "Bug in find_atomic_type" (* A type, not a term should be returned *) | exception Symbols.Not_found -> failwith "Bug in find_atomic_type" let find_type s sg = (* TODO : Replace by an assert within IFDEFDEBUG *) match Symbols.find s sg.types with | Type_declaration (x, id, _) when x = s -> Lambda.Atom id | Type_definition (x, id, _, _) when x = s -> Lambda.DAtom id | _ -> failwith "Bug in find_type" (* A type, not a term should be returned and x and s should match *) | exception Symbols.Not_found -> raise Not_found [@@warning "-32"] let rec convert_type ty sg = match ty with | Abstract_syntax.Type_atom (s, _, _) -> find_atomic_type s sg | Abstract_syntax.Linear_arrow (ty1, ty2, _) -> Lambda.LFun (convert_type ty1 sg, convert_type ty2 sg) | Abstract_syntax.Arrow (ty1, ty2, _) -> Lambda.Fun (convert_type ty1 sg, convert_type ty2 sg) let abstract_on_dependent_types lst sg = List.fold_right (fun x acc -> Lambda.Depend (convert_type x sg, acc)) lst Lambda.Type let add_sig_type t e ({ size = s; types = syms; ids; _ } as sg) = try (* First perform addition on the functional data structure *) let new_symbols = Symbols.add t e syms in (* timestamps modified at add_entry function *) { sg with size = s + 1; types = new_symbols; ids = Id.add s e ids } with | Symbols.Conflict -> raise Duplicate_type_definition | Id.Conflict -> raise Duplicate_type_definition let add_sig_term t e ({ size = s; terms = syms; ids; _ } as sg) = try (* First perform addition on the functional data structure *) let new_symbols = Symbols.add t e syms in (* timestamps modified at add_entry function *) { sg with size = s + 1; terms = new_symbols; ids = Id.add s e ids } with | Symbols.Conflict -> raise Duplicate_term_definition | Id.Conflict -> raise Duplicate_term_definition let rec expand_type ty ({ ids; _ } as sg) = match ty with | Lambda.Atom _ -> ty | Lambda.DAtom i -> ( match Id.find i ids with | Type_definition (_, _, _, ty1) -> expand_type ty1 sg | _ -> failwith "Bug in expand type") | Lambda.LFun (ty1, ty2) -> Lambda.LFun (expand_type ty1 sg, expand_type ty2 sg) | Lambda.Fun (ty1, ty2) -> Lambda.Fun (expand_type ty1 sg, expand_type ty2 sg) | _ -> failwith "Not yet implemented" let rec expand_term t ({ ids; _ } as sg) = match t with | Lambda.Var _ | Lambda.LVar _ | Lambda.Const _ -> t | Lambda.DConst i -> ( match Id.find i ids with | Term_definition (_, _, _, _, u) -> expand_term u sg | _ -> failwith "Bug in expand term") | Lambda.Abs (x, u) -> Lambda.Abs (x, expand_term u sg) | Lambda.LAbs (x, u) -> Lambda.LAbs (x, expand_term u sg) | Lambda.App (u, v) -> Lambda.App (expand_term u sg, expand_term v sg) | _ -> failwith "Not yet implemented" let unfold_type_definition i ({ ids; _ } as sg) = match Id.find i ids with | Type_definition (_, _, _, ty1) -> expand_type ty1 sg | _ -> failwith "Bug in unfold_type_definition" let unfold_term_definition i ({ ids; _ } as sg) = match Id.find i ids with | Term_definition (_, _, _, _, t) -> expand_term t sg | _ -> failwith "Bug in unfold_term_definition" let get_type_of_const_id i ({ ids; _ } as sg) = match Id.find i ids with | Term_declaration (_, _, _, ty) -> expand_type ty sg | Term_definition (_, _, _, ty, _) -> expand_type ty sg | _ -> failwith "Should be applied only on constants" | exception Id.Not_found -> failwith "Bug in get_type_of_const_id" let rec decompose_functional_type ty ({ ids; _ } as sg) = match ty with | Lambda.LFun (ty1, ty2) -> (ty1, ty2, Abstract_syntax.Linear) | Lambda.Fun (ty1, ty2) -> (ty1, ty2, Abstract_syntax.Non_linear) | Lambda.DAtom i -> ( match Id.find i ids with | Type_definition (_, _, _, ty1) -> decompose_functional_type ty1 sg | _ -> failwith "Bug in decompose_functional_type") | _ -> raise Not_functional_type let get_binder_argument_functional_type x ({ terms; _ } as sg) = let ty = match Symbols.find x terms with | Term_declaration (_, _, _, ty) -> ty | Term_definition (_, _, _, ty, _) -> ty | _ -> failwith (Printf.sprintf "Bug: Request of the type of the non constant \"%s\"" x) in try let ty1, _, _ = decompose_functional_type ty sg in let _, _, lin = decompose_functional_type ty1 sg in Some lin with Not_functional_type -> None (* We assume here that [term] is well typed and in beta-normal form and that types and terms definitions have been unfolded*) let eta_long_form term stype sg = let expanded_type = expand_type stype sg in let expanded_term = expand_term term sg in let res = Lambda.eta_long_form expanded_term expanded_type (fun id -> get_type_of_const_id id sg) in let f1 = pp_term sg in let f2 = pp_type sg in Log.debug (fun m -> m "term: %a:%a" f1 term f2 stype); Log.debug (fun m -> m "eta_long_form: %a:%a" f1 res f2 expanded_type); res let unfold t sg = Lambda.normalize (expand_term t sg) let is_atomic t sg = Lambda.is_atomic t (fun i -> unfold_type_definition i sg) type temp_t = t (* type temp_entry=entry *) module Type_System = Type_system.Type_System.Make (struct exception Not_found type t = temp_t let unfold_type_definition = unfold_type_definition let expand_type = expand_type let find_term = find_term let pp_type = pp_type let pp_term = pp_term end) let typecheck = Type_System.typecheck let stamp_declaration sg = { sg with extension_timestamp = Unix.time () } let stamp_definition sg = { sg with definition_timestamp = Unix.time () } let add_entry e ({ size = s; _ } as sg) = match e with | Abstract_syntax.Type_decl (t, _, Abstract_syntax.K k) -> stamp_declaration (add_sig_type t (Type_declaration (t, s, abstract_on_dependent_types k sg)) sg) | Abstract_syntax.Type_def (t, _, ty, Abstract_syntax.K k) -> stamp_definition (add_sig_type t (Type_definition (t, s, abstract_on_dependent_types k sg, convert_type ty sg)) sg) | Abstract_syntax.Term_decl (t, behavior, _, ty) -> let t_type = convert_type ty sg in let sg_is_2nd_order = sg.is_2nd_order && Lambda.is_2nd_order t_type (fun i -> unfold_type_definition i sg) in stamp_declaration (add_sig_term t (Term_declaration (t, s, behavior, convert_type ty sg)) { sg with is_2nd_order = sg_is_2nd_order }) | Abstract_syntax.Term_def (t, behavior, _, term, ty) -> let t_type = convert_type ty sg in let t_term, _ = typecheck term t_type sg in stamp_definition (add_sig_term t (Term_definition (t, s, behavior, t_type, t_term)) sg) let is_type ?(atomic = false) s { types = syms; _ } = match Symbols.find s syms with | Type_declaration _ -> true | Type_definition _ when not atomic -> true | _ -> false | exception Symbols.Not_found -> false let is_constant s ({ terms = syms; _ } as sg) = match Symbols.find s syms with | Term_declaration (_, _, behavior, ty) -> (true, Some (behavior, false, is_atomic (expand_type ty sg) sg)) | Term_definition (_, _, behavior, ty, _) -> (true, Some (behavior, true, is_atomic (expand_type ty sg) sg)) | _ -> (false, None) | exception Symbols.Not_found -> (false, None) (* let precedence s {precedence;_} = match Symbols.find s precedence with | f,_ -> Some f | exception Symbols.Not_found -> None *) let new_precedence ?before id sg = match (before, sg.max_pred) with | None, (f, None) -> let p = f +. 1. in ( p, { sg with max_pred = (p, Some id); precedence = Symbols.add id (p, None) sg.precedence; } ) | None, (f, (Some _ as max)) -> let p = f +. 1. in ( p, { sg with max_pred = (p, Some id); precedence = Symbols.add id (p, max) sg.precedence; } ) | Some _, (f, None) -> (* Strange to give an upper bound when there is no max. Behaves like introducing the first element *) let p = f +. 1. in ( p, { sg with max_pred = (p, Some id); precedence = Symbols.add id (p, None) sg.precedence; } ) | Some upper_bound, _ -> ( match Symbols.find upper_bound sg.precedence with | f_up, None -> let f_down = 0. in let p = (f_up +. f_down) /. 2. in let new_pred = Symbols.add ~overwrite:true upper_bound (f_up, Some id) (Symbols.add id (p, None) sg.precedence) in (p, { sg with precedence = new_pred }) | f_up, Some lower_bound -> let f_down, _ = Symbols.find lower_bound sg.precedence in let p = (f_up +. f_down) /. 2. in let new_pred = Symbols.add upper_bound (f_up, Some id) (Symbols.add id (p, Some lower_bound) sg.precedence) in (p, { sg with precedence = new_pred }) | exception Not_found -> failwith "Bug: Shouldn't happen") let raw_to_string t = Lambda.raw_to_string t [@@warning "-32"] let behavior_to_string = function | Abstract_syntax.Default -> "" | Abstract_syntax.Prefix -> "prefix " | Abstract_syntax.Infix _ -> "infix " | Abstract_syntax.Binder -> "binder " let pp_entry f fmt decl = let pp_kind = Lambda.pp_kind f in let pp_type = Lambda.pp_type f in let pp_term = Lambda.pp_term f in match decl with | Type_declaration (s, _, k) -> Format.fprintf fmt "@[<hov 4>%s :@ @[%a@];@]" s pp_kind k | Type_definition (s, _, k, ty) -> Format.fprintf fmt "@[<hov 4>%s =@ @[%a :@ @[%a@];@]@]" s pp_type ty pp_kind k | Term_declaration (s, _, behavior, ty) -> Format.fprintf fmt "@[<hov 4>%s%s :@ @[%a@];@]" (behavior_to_string behavior) s pp_type ty | Term_definition (s, _, behavior, ty, t) -> Format.fprintf fmt "@[<hov 4>%s%s =@ @[%a :@ @[%a@];@]@]" (behavior_to_string behavior) s pp_term t pp_type ty let pp fmt ({ name = n, _ ; ids; _ } as sg) = Format.fprintf fmt "signature %s =@,@[<v 2>@[%a@]@]@,end@." n (Id.pp (fun fmt _ entry -> pp_entry (id_to_string sg) fmt entry)) ids let convert_term t ty sg = let t_type = convert_type ty sg in let t, _ = typecheck t t_type sg in (t, t_type) let type_of_constant x { terms = syms; _ } = match Symbols.find x syms with | Term_declaration (s, _, _, ty) when x = s -> ty | Term_definition (s, _, _, ty, _) when x = s -> ty | _ -> failwith "Bug in type_of_constant" | exception Symbols.Not_found -> failwith "Bug in type_of_constant" let fold f a { ids; _ } = Id.fold (fun _ att acc -> f att acc) a ids let is_declared e _ = match e with | Type_declaration (s, _, _) -> Some s | Term_declaration (s, _, _, _) -> Some s | _ -> None let is_2nd_order { is_2nd_order; _ } = is_2nd_order let entry_to_data e = match e with | Type_declaration (_,id,_) -> Type(Lambda.Atom id) | Type_definition (_,_,_,stype) -> Type stype | Term_declaration (_,id,_,stype) -> Term(Lambda.Const id,stype) | Term_definition (_,_,_,stype,term) -> Term (term,stype) let gen_term_list sg ty min_depth max_depth shuffle = let incr_vars vars = List.map (fun e -> let (args, t, tc) = e in match tc with | Lambda.Var n -> (args, t, Lambda.Var (n + 1)) | Lambda.LVar n -> (args, t, Lambda.LVar (n + 1)) | _ -> e) vars in (* This function decrements the indexes of all linear variables in the list "vars". We use it when the term of a linear abstraction has been built, because we need to return the linear variables list (which contains those which don't appear in the term) to the caller. At the same time, we check that we don't have a linear variable with an index of 0 in the list, because this would mean that it has not been used in the term, so it is invalid. *) let rec decr_vars vars = match vars with | (args, t, tc)::t_vars -> (match tc with | Lambda.LVar n -> if n = 0 then None else Option.map (fun vars -> (args, t, Lambda.LVar (n - 1))::vars) (decr_vars t_vars) | _ -> Option.map (fun vars -> (args, t, tc)::vars) (decr_vars t_vars)) | [] -> Some [] in let shuffle_rules rules = let pairs = List.map (fun r -> (Random.bits (), r)) rules in let sorted_pairs = List.sort (fun p1 p2 -> compare (fst p1) (fst p2)) pairs in List.map snd sorted_pairs in let get_letter i = String.make 1 (Char.chr (97 + (i mod 26))) in let type_to_rule ty term = let ty = expand_type ty sg in let rec gen_arg_list ty acc = match ty with | Lambda.Atom _ -> (acc, ty) | Lambda.Fun (ty1, ty2) -> gen_arg_list ty2 ((ty1, false)::acc) | Lambda.LFun (ty1, ty2) -> gen_arg_list ty2 ((ty1, true)::acc) | _ -> failwith "Not implemented" in let (arg_list, ty_f) = gen_arg_list ty [] in (arg_list, ty_f, term) in (* This builds a rule list from all term declarations in the signature. A rule is of type "((stype, bool) list, stype, term)" and if "(arg_list, ty, te)" is a rule, it says "to build a term of type "ty"", one needs to compute a term of each type in the list "arg_list", add apply all theses terms to "te". The type "ty" is always an atom. The boolean associated to each type in the list "arg_list" is true iff free linear variables are allowed in the corresponding term to build. In other words, the rule "([(A, true), (B, true), (A, false)], C, build_c)" corresponds to this signature entry : "build_c : A -> B -> A => C". *) let env = fold (fun e l -> match e with | Term_declaration (_, i, _, t) -> (type_to_rule t (Lambda.Const i))::l | _ -> l) [] sg in let term_depth t = let rec term_depth_rec t add = match t with | Lambda.Abs (_, t) -> term_depth_rec t 1 | Lambda.LAbs (_, t) -> term_depth_rec t 1 | Lambda.App (t1, t2) -> add + max (term_depth_rec t1 0) (term_depth_rec t2 1) | _ -> 1 in term_depth_rec t 1 in let rec compute_arg (ty, lin) vars lvars_l letter fuel = LazyList.join_mix (LazyList.map (fun lvars_b -> (LazyList.map (fun (lvars_a, term) -> ((if lin then lvars_a else lvars_b), term)) (gen_term_rec ty vars (if lin then lvars_b else []) letter (fuel - 1)))) lvars_l) and apply_rule args term vars lvars letter fuel = match args with | arg::args -> LazyList.bind_mix (fun (lvars, arg_term) -> LazyList.map (fun (lvars, term) -> (lvars, Lambda.App (term, arg_term))) (apply_rule args term vars lvars letter fuel)) (compute_arg arg vars (LazyList.one lvars) letter fuel) | [] -> LazyList.one (lvars, term) (* This function builds all possible terms using the rules in the list "rules". The rules are tried one by one (by calling the function "apply_rule"). When a rule corresponds to a linear variable (when it is of the form "(_, _, Lvar _)"), we need to remove its corresponding rule from the current context. *) and apply_rules rules vars lvars letter fuel = match rules with | (args, _, tc)::rules -> let lvars_f = (match tc with | Lambda.LVar i -> List.filter (fun (_, _, term) -> match term with | Lambda.LVar j -> not (i = j) | _ -> false) lvars | _ -> lvars) in LazyList.append_mix (apply_rule args tc vars lvars_f letter fuel) (fun () -> apply_rules rules vars lvars letter fuel) | [] -> LazyList.Nil (* To generate the terms of type "t" with the rules in the list "env", the variables in the list "vars" and the linear variables in the list "l_vars", we have three cases : - The type "t" is an atom, so we select all the rules which give a term of type "t" from the environment "env" and the list of linear variables "l_vars", shuffle them in a random order, and try all of them to build all possible terms. - The type is a normal arrow, "A -> B", so we add a new rule corresponding to A in the variables list, and try to build all possible terms of type B with this new environment. We apply an abstraction to all generated terms. - The type is a linear arrow, "A => B", so we add a new rule corresponding to A in the linear variables list, and try to build all possible terms of type B. We then return all generated terms in which this linear variable has been used, with a linear abstraction. *) and gen_term_rec ty vars lvars letter fuel = let ty = expand_type ty sg in if fuel = 0 then LazyList.Nil else match ty with | Lambda.Atom _ -> let rules = List.filter (fun (_, ty_rule, _) -> ty = ty_rule) (env @ vars @ lvars) in let res = if shuffle then apply_rules (shuffle_rules rules) vars lvars letter fuel else apply_rules rules vars lvars letter fuel in res | Lambda.Fun (ty1, ty2) -> LazyList.map (fun (lvars, term) -> (lvars, Lambda.Abs (get_letter letter, term))) (gen_term_rec ty2 ((type_to_rule ty1 (Lambda.Var 0))::(incr_vars vars)) lvars (letter + 1) fuel) | Lambda.LFun (ty1, ty2) -> LazyList.filter_map (fun (lvars, term) -> Option.map (fun lvars -> (lvars, Lambda.LAbs (get_letter letter, term))) (decr_vars lvars)) (gen_term_rec ty2 vars ((type_to_rule ty1 (Lambda.LVar 0))::(incr_vars lvars)) (letter + 1) fuel) | _ -> LazyList.Nil in LazyList.filter_map (fun (_, t) -> if term_depth t >= min_depth then Some t else None) (gen_term_rec ty [] [] 0 max_depth) end module Table = Table.Make_table (struct let b = 10 end) (*module Table = struct module IntMap = Map.Make(struct type t=int let compare i j = i-j end) type 'a t = 'a IntMap.t type key = int exception Conflict let empty = IntMap.empty let add ?(overwrite=false) k v t = try let _ = IntMap.find k t in if overwrite then IntMap.add k v t else raise Conflict with | Not_found -> IntMap.add k v t exception Not_found let find k t = try IntMap.find k t with | Not_found -> raise Not_found let fold f acc t = IntMap.fold f t acc end *) module Data_Signature = Make (Tries.Tries) (Table)
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