(*  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 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_defsort: string -> theory -> theory

  val add_defsort_i: sort -> theory -> theory

  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_tsigs 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 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

          (TypeInfer.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 default sort *)

fun gen_add_defsort prep_sort s thy =

  thy |> map_tsig (Type.set_defsort (prep_sort thy s));

val add_defsort = gen_add_defsort Syntax.read_sort_global;

val add_defsort_i = gen_add_defsort certify_sort;

(* 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 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 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 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;