(*  Title:      Pure/sign.ML

     Author:     Lawrence C Paulson and Markus Wenzel

 Logical signature content: naming conventions, concrete syntax, type

 signature, polymorphic constants.

 *)

 signature SIGN =

 sig

   val rep_sg: theory ->

    {naming: Name_Space.naming,

     syn: Syntax.syntax,

     tsig: Type.tsig,

     consts: Consts.T}

   val map_naming: (Name_Space.naming -> Name_Space.naming) -> theory -> theory

   val naming_of: theory -> Name_Space.naming

   val full_name: theory -> binding -> string

   val full_name_path: theory -> string -> binding -> string

   val full_bname: theory -> bstring -> string

   val full_bname_path: theory -> string -> bstring -> string

   val syn_of: theory -> Syntax.syntax

   val tsig_of: theory -> Type.tsig

   val classes_of: theory -> Sorts.algebra

   val all_classes: theory -> class list

   val super_classes: theory -> class -> class list

   val minimize_sort: theory -> sort -> sort

   val complete_sort: theory -> sort -> sort

   val set_defsort: sort -> theory -> theory

   val defaultS: theory -> sort

   val subsort: theory -> sort * sort -> bool

   val of_sort: theory -> typ * sort -> bool

   val witness_sorts: theory -> (typ * sort) list -> sort list -> (typ * sort) list

   val is_logtype: theory -> string -> bool

   val typ_instance: theory -> typ * typ -> bool

   val typ_equiv: theory -> typ * typ -> bool

   val typ_match: theory -> typ * typ -> Type.tyenv -> Type.tyenv

   val typ_unify: theory -> typ * typ -> Type.tyenv * int -> Type.tyenv * int

   val consts_of: theory -> Consts.T

   val the_const_constraint: theory -> string -> typ

   val const_type: theory -> string -> typ option

   val the_const_type: theory -> string -> typ

   val declared_tyname: theory -> string -> bool

   val declared_const: theory -> string -> bool

   val const_monomorphic: theory -> string -> bool

   val const_typargs: theory -> string * typ -> typ list

   val const_instance: theory -> string * typ list -> typ

   val mk_const: theory -> string * typ list -> term

   val class_space: theory -> Name_Space.T

   val type_space: theory -> Name_Space.T

   val const_space: theory -> Name_Space.T

   val class_alias: binding -> class -> theory -> theory

   val type_alias: binding -> string -> theory -> theory

   val const_alias: binding -> string -> theory -> theory

   val intern_class: theory -> xstring -> string

   val extern_class: theory -> string -> xstring

   val intern_type: theory -> xstring -> string

   val extern_type: theory -> string -> xstring

   val intern_const: theory -> xstring -> string

   val extern_const: theory -> string -> xstring

   val arity_number: theory -> string -> int

   val arity_sorts: theory -> string -> sort -> sort list

   val certify_class: theory -> class -> class

   val certify_sort: theory -> sort -> sort

   val certify_typ: theory -> typ -> typ

   val certify_typ_mode: Type.mode -> theory -> typ -> typ

   val certify': bool -> Pretty.pp -> bool -> Consts.T -> theory -> term -> term * typ * int

   val certify_term: theory -> term -> term * typ * int

   val cert_term: theory -> term -> term

   val cert_prop: theory -> term -> term

   val no_frees: Pretty.pp -> term -> term

   val no_vars: Pretty.pp -> term -> term

   val add_types: (binding * int * mixfix) list -> theory -> theory

   val add_nonterminals: binding list -> theory -> theory

   val add_type_abbrev: binding * string list * typ -> theory -> theory

   val add_syntax: (string * string * mixfix) list -> theory -> theory

   val add_syntax_i: (string * typ * mixfix) list -> theory -> theory

   val add_modesyntax: Syntax.mode -> (string * string * mixfix) list -> theory -> theory

   val add_modesyntax_i: Syntax.mode -> (string * typ * mixfix) list -> theory -> theory

   val del_modesyntax: Syntax.mode -> (string * string * mixfix) list -> theory -> theory

   val del_modesyntax_i: Syntax.mode -> (string * typ * mixfix) list -> theory -> theory

   val type_notation: bool -> Syntax.mode -> (typ * mixfix) list -> theory -> theory

   val notation: bool -> Syntax.mode -> (term * mixfix) list -> theory -> theory

   val declare_const: (binding * typ) * mixfix -> theory -> term * theory

   val add_consts: (binding * string * mixfix) list -> theory -> theory

   val add_consts_i: (binding * typ * mixfix) list -> theory -> theory

   val add_abbrev: string -> binding * term -> theory -> (term * term) * theory

   val revert_abbrev: string -> string -> theory -> theory

   val add_const_constraint: string * typ option -> theory -> theory

   val primitive_class: binding * class list -> theory -> theory

   val primitive_classrel: class * class -> theory -> theory

   val primitive_arity: arity -> theory -> theory

   val add_trfuns:

     (string * (ast list -> ast)) list *

     (string * (term list -> term)) list *

     (string * (term list -> term)) list *

     (string * (ast list -> ast)) list -> theory -> theory

   val add_trfunsT:

     (string * (bool -> typ -> term list -> term)) list -> theory -> theory

   val add_advanced_trfuns:

     (string * (Proof.context -> ast list -> ast)) list *

     (string * (Proof.context -> term list -> term)) list *

     (string * (Proof.context -> term list -> term)) list *

     (string * (Proof.context -> ast list -> ast)) list -> theory -> theory

   val add_advanced_trfunsT:

     (string * (Proof.context -> bool -> typ -> term list -> term)) list -> theory -> theory

   val add_tokentrfuns:

     (string * string * (Proof.context -> string -> Pretty.T)) list -> theory -> theory

   val add_mode_tokentrfuns: string -> (string * (Proof.context -> string -> Pretty.T)) list

     -> theory -> theory

   val add_trrules: (xstring * string) Syntax.trrule list -> theory -> theory

   val del_trrules: (xstring * string) Syntax.trrule list -> theory -> theory

   val add_trrules_i: ast Syntax.trrule list -> theory -> theory

   val del_trrules_i: ast Syntax.trrule list -> theory -> theory

   val new_group: theory -> theory

   val reset_group: theory -> theory

   val add_path: string -> theory -> theory

   val root_path: theory -> theory

   val parent_path: theory -> theory

   val mandatory_path: string -> theory -> theory

   val qualified_path: bool -> binding -> theory -> theory

   val local_path: theory -> theory

   val restore_naming: theory -> theory -> theory

   val hide_class: bool -> string -> theory -> theory

   val hide_type: bool -> string -> theory -> theory

   val hide_const: bool -> string -> theory -> theory

 end

 structure Sign: SIGN =

 struct

 (** datatype sign **)

 datatype sign = Sign of

  {naming: Name_Space.naming,    (*common naming conventions*)

   syn: Syntax.syntax,           (*concrete syntax for terms, types, sorts*)

   tsig: Type.tsig,              (*order-sorted signature of types*)

   consts: Consts.T};            (*polymorphic constants*)

 fun make_sign (naming, syn, tsig, consts) =

   Sign {naming = naming, syn = syn, tsig = tsig, consts = consts};

 structure Data = Theory_Data_PP

 (

   type T = sign;

   fun extend (Sign {syn, tsig, consts, ...}) =

     make_sign (Name_Space.default_naming, syn, tsig, consts);

   val empty =

     make_sign (Name_Space.default_naming, Syntax.basic_syntax, Type.empty_tsig, Consts.empty);

   fun merge pp (sign1, sign2) =

     let

       val Sign {naming = _, syn = syn1, tsig = tsig1, consts = consts1} = sign1;

       val Sign {naming = _, syn = syn2, tsig = tsig2, consts = consts2} = sign2;

       val naming = Name_Space.default_naming;

       val syn = Syntax.merge_syntaxes syn1 syn2;

       val tsig = Type.merge_tsig pp (tsig1, tsig2);

       val consts = Consts.merge (consts1, consts2);

     in make_sign (naming, syn, tsig, consts) end;

 );

 fun rep_sg thy = Data.get thy |> (fn Sign args => args);

 fun map_sign f = Data.map (fn Sign {naming, syn, tsig, consts} =>

   make_sign (f (naming, syn, tsig, consts)));

 fun map_naming f = map_sign (fn (naming, syn, tsig, consts) => (f naming, syn, tsig, consts));

 fun map_syn f = map_sign (fn (naming, syn, tsig, consts) => (naming, f syn, tsig, consts));

 fun map_tsig f = map_sign (fn (naming, syn, tsig, consts) => (naming, syn, f tsig, consts));

 fun map_consts f = map_sign (fn (naming, syn, tsig, consts) => (naming, syn, tsig, f consts));

 (* naming *)

 val naming_of = #naming o rep_sg;

 val full_name = Name_Space.full_name o naming_of;

 fun full_name_path thy path = Name_Space.full_name (Name_Space.add_path path (naming_of thy));

 fun full_bname thy = Name_Space.full_name (naming_of thy) o Binding.name;

 fun full_bname_path thy path = full_name_path thy path o Binding.name;

 (* syntax *)

 val syn_of = #syn o rep_sg;

 (* type signature *)

 val tsig_of = #tsig o rep_sg;

 val classes_of = #2 o #classes o Type.rep_tsig o tsig_of;

 val all_classes = Sorts.all_classes o classes_of;

 val super_classes = Sorts.super_classes o classes_of;

 val minimize_sort = Sorts.minimize_sort o classes_of;

 val complete_sort = Sorts.complete_sort o classes_of;

 val set_defsort = map_tsig o Type.set_defsort;

 val defaultS = Type.defaultS o tsig_of;

 val subsort = Type.subsort o tsig_of;

 val of_sort = Type.of_sort o tsig_of;

 val witness_sorts = Type.witness_sorts o tsig_of;

 val is_logtype = member (op =) o Type.logical_types o tsig_of;

 val typ_instance = Type.typ_instance o tsig_of;

 fun typ_equiv thy (T, U) = typ_instance thy (T, U) andalso typ_instance thy (U, T);

 val typ_match = Type.typ_match o tsig_of;

 val typ_unify = Type.unify o tsig_of;

 (* polymorphic constants *)

 val consts_of = #consts o rep_sg;

 val the_const_constraint = Consts.the_constraint o consts_of;

 val the_const_type = Consts.the_type o consts_of;

 val const_type = try o the_const_type;

 val const_monomorphic = Consts.is_monomorphic o consts_of;

 val const_typargs = Consts.typargs o consts_of;

 val const_instance = Consts.instance o consts_of;

 fun mk_const thy (c, Ts) = Const (c, const_instance thy (c, Ts));

 val declared_tyname = Symtab.defined o #2 o #types o Type.rep_tsig o tsig_of;

 val declared_const = can o the_const_constraint;

 (** intern / extern names **)

 val class_space = Type.class_space o tsig_of;

 val type_space = Type.type_space o tsig_of;

 val const_space = Consts.space_of o consts_of;

 fun class_alias b c thy = map_tsig (Type.class_alias (naming_of thy) b c) thy;

 fun type_alias b c thy = map_tsig (Type.type_alias (naming_of thy) b c) thy;

 fun const_alias b c thy = map_consts (Consts.alias (naming_of thy) b c) thy;

 val intern_class = Name_Space.intern o class_space;

 val extern_class = Name_Space.extern o class_space;

 val intern_type = Name_Space.intern o type_space;

 val extern_type = Name_Space.extern o type_space;

 val intern_const = Name_Space.intern o const_space;

 val extern_const = Name_Space.extern o const_space;

 (** certify entities **)    (*exception TYPE*)

 (* certify wrt. type signature *)

 val arity_number = Type.arity_number o tsig_of;

 fun arity_sorts thy = Type.arity_sorts (Syntax.pp_global thy) (tsig_of thy);

 val certify_class         = Type.cert_class o tsig_of;

 val certify_sort          = Type.cert_sort o tsig_of;

 val certify_typ           = Type.cert_typ o tsig_of;

 fun certify_typ_mode mode = Type.cert_typ_mode mode o tsig_of;

 (* certify term/prop *)

 local

 fun type_check pp tm =

   let

     fun err_appl why bs t T u U =

       let

         val xs = map Free bs;           (*we do not rename here*)

         val t' = subst_bounds (xs, t);

         val u' = subst_bounds (xs, u);

         val msg = cat_lines

           (Type_Infer.appl_error (Syntax.pp_show_brackets pp) why t' T u' U);

       in raise TYPE (msg, [T, U], [t', u']) end;

     fun typ_of (_, Const (_, T)) = T

       | typ_of (_, Free  (_, T)) = T

       | typ_of (_, Var (_, T)) = T

       | typ_of (bs, Bound i) = snd (nth bs i handle Subscript =>

           raise TYPE ("Loose bound variable: B." ^ string_of_int i, [], [Bound i]))

       | typ_of (bs, Abs (x, T, body)) = T --> typ_of ((x, T) :: bs, body)

       | typ_of (bs, t $ u) =

           let val T = typ_of (bs, t) and U = typ_of (bs, u) in

             (case T of

               Type ("fun", [T1, T2]) =>

                 if T1 = U then T2 else err_appl "Incompatible operand type" bs t T u U

             | _ => err_appl "Operator not of function type" bs t T u U)

           end;

   in typ_of ([], tm) end;

 fun err msg = raise TYPE (msg, [], []);

 fun check_vars (t $ u) = (check_vars t; check_vars u)

   | check_vars (Abs (_, _, t)) = check_vars t

   | check_vars (Free (x, _)) =

       if Long_Name.is_qualified x then err ("Malformed variable: " ^ quote x) else ()

   | check_vars (Var (xi as (_, i), _)) =

       if i < 0 then err ("Malformed variable: " ^ quote (Term.string_of_vname xi)) else ()

   | check_vars _ = ();

 in

 fun certify' prop pp do_expand consts thy tm =

   let

     val _ = check_vars tm;

     val tm' = Term.map_types (certify_typ thy) tm;

     val T = type_check pp tm';

     val _ = if prop andalso T <> propT then err "Term not of type prop" else ();

     val tm'' = Consts.certify pp (tsig_of thy) do_expand consts tm';

   in (if tm = tm'' then tm else tm'', T, Term.maxidx_of_term tm'') end;

 fun certify_term thy = certify' false (Syntax.pp_global thy) true (consts_of thy) thy;

 fun cert_term_abbrev thy = #1 o certify' false (Syntax.pp_global thy) false (consts_of thy) thy;

 val cert_term = #1 oo certify_term;

 fun cert_prop thy = #1 o certify' true (Syntax.pp_global thy) true (consts_of thy) thy;

 end;

 (* specifications *)

 fun no_variables kind add addT mk mkT pp tm =

   (case (add tm [], addT tm []) of

     ([], []) => tm

   | (frees, tfrees) => error (Pretty.string_of (Pretty.block

       (Pretty.str ("Illegal " ^ kind ^ " variable(s) in term:") :: Pretty.brk 1 ::

        Pretty.commas (map (Pretty.term pp o mk) frees @ map (Pretty.typ pp o mkT) tfrees)))));

 val no_frees = no_variables "free" Term.add_frees Term.add_tfrees Free TFree;

 val no_vars = no_variables "schematic" Term.add_vars Term.add_tvars Var TVar;

 (** signature extension functions **)  (*exception ERROR/TYPE*)

 (* add type constructors *)

 fun add_types types thy = thy |> map_sign (fn (naming, syn, tsig, consts) =>

   let

     fun type_syntax (b, n, mx) =

       (Syntax.mark_type (Name_Space.full_name naming b), Syntax.make_type n, mx);

     val syn' = Syntax.update_type_gram true Syntax.mode_default (map type_syntax types) syn;

     val tsig' = fold (fn (a, n, _) => Type.add_type naming (a, n)) types tsig;

   in (naming, syn', tsig', consts) end);

 (* add nonterminals *)

 fun add_nonterminals ns = map_sign (fn (naming, syn, tsig, consts) =>

   (naming, syn, fold (Type.add_nonterminal naming) ns tsig, consts));

 (* add type abbreviations *)

 fun add_type_abbrev abbr = map_sign (fn (naming, syn, tsig, consts) =>

   (naming, syn, Type.add_abbrev naming abbr tsig, consts));

 (* modify syntax *)

 fun gen_syntax change_gram parse_typ mode args thy =

   let

     val ctxt = ProofContext.init_global thy;

     fun prep (c, T, mx) = (c, certify_typ_mode Type.mode_syntax thy (parse_typ ctxt T), mx)

       handle ERROR msg => cat_error msg ("in syntax declaration " ^ quote c);

   in thy |> map_syn (change_gram (is_logtype thy) mode (map prep args)) end;

 fun gen_add_syntax x = gen_syntax (Syntax.update_const_gram true) x;

 val add_modesyntax = gen_add_syntax Syntax.parse_typ;

 val add_modesyntax_i = gen_add_syntax (K I);

 val add_syntax = add_modesyntax Syntax.mode_default;

 val add_syntax_i = add_modesyntax_i Syntax.mode_default;

 val del_modesyntax = gen_syntax (Syntax.update_const_gram false) Syntax.parse_typ;

 val del_modesyntax_i = gen_syntax (Syntax.update_const_gram false) (K I);

 fun type_notation add mode args =

   let

     fun type_syntax (Type (c, args), mx) =

           SOME (Syntax.mark_type c, Syntax.make_type (length args), mx)

       | type_syntax _ = NONE;

   in map_syn (Syntax.update_type_gram add mode (map_filter type_syntax args)) end;

 fun notation add mode args thy =

   let

     fun const_syntax (Const (c, _), mx) =

           (case try (Consts.type_scheme (consts_of thy)) c of

             SOME T => SOME (Syntax.mark_const c, T, mx)

           | NONE => NONE)

       | const_syntax _ = NONE;

   in gen_syntax (Syntax.update_const_gram add) (K I) mode (map_filter const_syntax args) thy end;

 (* add constants *)

 local

 fun gen_add_consts parse_typ raw_args thy =

   let

     val ctxt = ProofContext.init_global thy;

     val prepT = Type.no_tvars o Term.no_dummyT o certify_typ thy o parse_typ ctxt;

     fun prep (b, raw_T, mx) =

       let

         val c = full_name thy b;

         val T = (prepT raw_T handle TYPE (msg, _, _) => error msg) handle ERROR msg =>

           cat_error msg ("in declaration of constant " ^ quote (Binding.str_of b));

         val T' = Logic.varifyT_global T;

       in ((b, T'), (Syntax.mark_const c, T', mx), Const (c, T)) end;

     val args = map prep raw_args;

   in

     thy

     |> map_consts (fold (Consts.declare (naming_of thy) o #1) args)

     |> add_syntax_i (map #2 args)

     |> pair (map #3 args)

   end;

 in

 fun add_consts args = snd o gen_add_consts Syntax.parse_typ args;

 fun add_consts_i args = snd o gen_add_consts (K I) args;

 fun declare_const ((b, T), mx) thy =

   let

     val pos = Binding.pos_of b;

     val ([const as Const (c, _)], thy') = gen_add_consts (K I) [(b, T, mx)] thy;

     val _ = Position.report (Markup.const_decl c) pos;

   in (const, thy') end;

 end;

 (* abbreviations *)

 fun add_abbrev mode (b, raw_t) thy =

   let

     val pp = Syntax.pp_global thy;

     val prep_tm = no_frees pp o Term.no_dummy_patterns o cert_term_abbrev thy;

     val t = (prep_tm raw_t handle TYPE (msg, _, _) => error msg | TERM (msg, _) => error msg)

       handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote (Binding.str_of b));

     val (res, consts') = consts_of thy

       |> Consts.abbreviate pp (tsig_of thy) (naming_of thy) mode (b, t);

   in (res, thy |> map_consts (K consts')) end;

 fun revert_abbrev mode c = map_consts (Consts.revert_abbrev mode c);

 (* add constraints *)

 fun add_const_constraint (c, opt_T) thy =

   let

     fun prepT raw_T =

       let val T = Logic.varifyT_global (Type.no_tvars (Term.no_dummyT (certify_typ thy raw_T)))

       in cert_term thy (Const (c, T)); T end

       handle TYPE (msg, _, _) => error msg;

   in thy |> map_consts (Consts.constrain (c, Option.map prepT opt_T)) end;

 (* primitive classes and arities *)

 fun primitive_class (bclass, classes) thy =

   thy |> map_sign (fn (naming, syn, tsig, consts) =>

     let

       val tsig' = Type.add_class (Syntax.pp_global thy) naming (bclass, classes) tsig;

     in (naming, syn, tsig', consts) end)

   |> add_consts_i [(Binding.map_name Logic.const_of_class bclass, Term.a_itselfT --> propT, NoSyn)];

 fun primitive_classrel arg thy = thy |> map_tsig (Type.add_classrel (Syntax.pp_global thy) arg);

 fun primitive_arity arg thy = thy |> map_tsig (Type.add_arity (Syntax.pp_global thy) arg);

 (* add translation functions *)

 local

 fun mk trs = map Syntax.mk_trfun trs;

 fun gen_add_trfuns ext non_typed (atrs, trs, tr's, atr's) =

   map_syn (ext (mk atrs, mk trs, mk (map (apsnd non_typed) tr's), mk atr's));

 fun gen_add_trfunsT ext tr's = map_syn (ext ([], [], mk tr's, []));

 in

 val add_trfuns = gen_add_trfuns Syntax.update_trfuns Syntax.non_typed_tr';

 val add_trfunsT = gen_add_trfunsT Syntax.update_trfuns;

 val add_advanced_trfuns = gen_add_trfuns Syntax.update_advanced_trfuns Syntax.non_typed_tr'';

 val add_advanced_trfunsT = gen_add_trfunsT Syntax.update_advanced_trfuns;

 end;

 val add_tokentrfuns = map_syn o Syntax.extend_tokentrfuns;

 fun add_mode_tokentrfuns m = add_tokentrfuns o map (fn (s, f) => (m, s, f));

 (* translation rules *)

 fun gen_trrules f args thy = thy |> map_syn (fn syn =>

   let val rules = map (Syntax.map_trrule (apfst (intern_type thy))) args

   in f (ProofContext.init_global thy) (is_logtype thy) syn rules syn end);

 val add_trrules = gen_trrules Syntax.update_trrules;

 val del_trrules = gen_trrules Syntax.remove_trrules;

 val add_trrules_i = map_syn o Syntax.update_trrules_i;

 val del_trrules_i = map_syn o Syntax.remove_trrules_i;

 (* naming *)

 val new_group = map_naming Name_Space.new_group;

 val reset_group = map_naming Name_Space.reset_group;

 val add_path = map_naming o Name_Space.add_path;

 val root_path = map_naming Name_Space.root_path;

 val parent_path = map_naming Name_Space.parent_path;

 val mandatory_path = map_naming o Name_Space.mandatory_path;

 val qualified_path = map_naming oo Name_Space.qualified_path;

 fun local_path thy = thy |> root_path |> add_path (Context.theory_name thy);

 val restore_naming = map_naming o K o naming_of;

 (* hide names *)

 val hide_class = map_tsig oo Type.hide_class;

 val hide_type = map_tsig oo Type.hide_type;

 val hide_const = map_consts oo Consts.hide;

 end;