(*  Title:      Pure/sign.ML

    ID:         $Id$

    Author:     Lawrence C Paulson and Markus Wenzel

The abstract type "sg" of signatures.

TODO:

  pure sign: elim Syntax.constrainC

*)

signature SIGN =

sig

  structure Symtab: SYMTAB

  structure Syntax: SYNTAX

  structure Type: TYPE

  sharing Symtab = Type.Symtab

  local open Type Syntax Syntax.Mixfix in

    type sg

    val rep_sg: sg ->

      {tsig: type_sig,

       const_tab: typ Symtab.table,

       syn: syntax,

       stamps: string ref list}

    val subsig: sg * sg -> bool

    val eq_sg: sg * sg -> bool

    val is_draft: sg -> bool

    val const_type: sg -> string -> typ option

    val print_sg: sg -> unit

    val pprint_sg: sg -> pprint_args -> unit

    val pretty_term: sg -> term -> Pretty.T

    val pretty_typ: sg -> typ -> Pretty.T

    val string_of_term: sg -> term -> string

    val string_of_typ: sg -> typ -> string

    val pprint_term: sg -> term -> pprint_args -> unit

    val pprint_typ: sg -> typ -> pprint_args -> unit

    val certify_typ: sg -> typ -> typ

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

    val read_typ: sg * (indexname -> sort option) -> string -> typ

    val add_classes: (class list * class * class list) list -> sg -> sg

    val add_defsort: sort -> sg -> sg

    val add_types: (string * int * mixfix) list -> sg -> sg

    val add_tyabbrs: (string * string list * string * mixfix) list -> sg -> sg

    val add_tyabbrs_i: (string * string list * typ * mixfix) list -> sg -> sg

    val add_arities: (string * sort list * sort) list -> sg -> sg

    val add_consts: (string * string * mixfix) list -> sg -> sg

    val add_consts_i: (string * typ * mixfix) list -> sg -> sg

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

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

    val add_trfuns:

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

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

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

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

    val add_trrules: xrule list -> sg -> sg

    val add_name: string -> sg -> sg

    val make_draft: sg -> sg

    val extend: sg -> string ->

      (class * class list) list * class list *

      (string list * int) list *

      (string * string list * string) list *

      (string list * (sort list * class)) list *

      (string list * string) list * sext option -> sg

    val merge: sg * sg -> sg

    val pure: sg

    val const_of_class: class -> string

    val class_of_const: string -> class

  end

end;

functor SignFun(structure Syntax: SYNTAX and Type: TYPE): SIGN =

struct

structure Symtab = Type.Symtab;

structure Syntax = Syntax;

structure BasicSyntax: BASIC_SYNTAX = Syntax;

structure Pretty = Syntax.Pretty;

structure Type = Type;

open BasicSyntax Type;

open Syntax.Mixfix;   (* FIXME *)

(** datatype sg **)

(*the "ref" in stamps ensures that no two signatures are identical -- it is

  impossible to forge a signature*)

datatype sg =

  Sg of {

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

    const_tab: typ Symtab.table,    (*types of constants*)

    syn: Syntax.syntax,             (*syntax for parsing and printing*)

    stamps: string ref list};       (*unique theory indentifier*)

fun rep_sg (Sg args) = args;

fun is_draft (Sg {stamps = ref "#" :: _, ...}) = true

  | is_draft _ = false;

fun subsig (Sg {stamps = s1, ...}, Sg {stamps = s2, ...}) = s1 subset s2;

fun eq_sg (Sg {stamps = s1, ...}, Sg {stamps = s2, ...}) = eq_set (s1, s2);

fun const_type (Sg {const_tab, ...}) c =

  Symtab.lookup (const_tab, c);

(** print signature **)

val stamp_names = rev o map !;

fun print_sg sg =

  let

    fun prt_typ syn ty = Pretty.quote (Syntax.pretty_typ syn ty);

    fun pretty_sort [cl] = Pretty.str cl

      | pretty_sort cls = Pretty.str_list "{" "}" cls;

    fun pretty_subclass (cl, cls) = Pretty.block

      [Pretty.str (cl ^ " <"), Pretty.brk 1, pretty_sort cls];

    fun pretty_default cls = Pretty.block

      [Pretty.str "default:", Pretty.brk 1, pretty_sort cls];

    fun pretty_arg (ty, n) = Pretty.str (ty ^ " " ^ string_of_int n);

    fun pretty_abbr syn (ty, (vs, rhs)) = Pretty.block

      [prt_typ syn (Type (ty, map (fn v => TVar (v, [])) vs)),

        Pretty.str " =", Pretty.brk 1, prt_typ syn rhs];

    fun pretty_arity ty (cl, []) = Pretty.block

          [Pretty.str (ty ^ " ::"), Pretty.brk 1, Pretty.str cl]

      | pretty_arity ty (cl, srts) = Pretty.block

          [Pretty.str (ty ^ " ::"), Pretty.brk 1,

            Pretty.list "(" ")" (map pretty_sort srts),

            Pretty.brk 1, Pretty.str cl];

    fun pretty_coreg (ty, ars) = map (pretty_arity ty) ars;

    fun pretty_const syn (c, ty) = Pretty.block

      [Pretty.str (quote c ^ " ::"), Pretty.brk 1, prt_typ syn ty];

    val Sg {tsig, const_tab, syn, stamps} = sg;

    val {classes, subclass, default, args, abbrs, coreg} = rep_tsig tsig;

  in

    Pretty.writeln (Pretty.strs ("stamps:" :: stamp_names stamps));

    Pretty.writeln (Pretty.strs ("classes:" :: classes));

    Pretty.writeln (Pretty.big_list "subclass:" (map pretty_subclass subclass));

    Pretty.writeln (pretty_default default);

    Pretty.writeln (Pretty.big_list "types:" (map pretty_arg args));

    Pretty.writeln (Pretty.big_list "abbrs:" (map (pretty_abbr syn) abbrs));

    Pretty.writeln (Pretty.big_list "coreg:" (flat (map pretty_coreg coreg)));

    Pretty.writeln (Pretty.big_list "consts:"

      (map (pretty_const syn) (Symtab.dest const_tab)))

  end;

fun pprint_sg (Sg {stamps, ...}) =

  Pretty.pprint (Pretty.str_list "{" "}" (stamp_names stamps));

(** pretty printing of terms and types **)

fun pretty_term (Sg {syn, ...}) = Syntax.pretty_term syn;

fun pretty_typ (Sg {syn, ...}) = Syntax.pretty_typ syn;

fun string_of_term (Sg {syn, ...}) = Syntax.string_of_term syn;

fun string_of_typ (Sg {syn, ...}) = Syntax.string_of_typ syn;

fun pprint_term sg = Pretty.pprint o Pretty.quote o (pretty_term sg);

fun pprint_typ sg = Pretty.pprint o Pretty.quote o (pretty_typ sg);

(** certify types and terms **)   (*exception TYPE*)

fun certify_typ (Sg {tsig, ...}) ty = cert_typ tsig ty;

fun mapfilt_atoms f (Abs (_, _, t)) = mapfilt_atoms f t

  | mapfilt_atoms f (t $ u) = mapfilt_atoms f t @ mapfilt_atoms f u

  | mapfilt_atoms f a = (case f a of Some y => [y] | None => []);

fun certify_term (sg as Sg {tsig, ...}) tm =

  let

    fun valid_const a T =

      (case const_type sg a of

        Some U => typ_instance (tsig, T, U)

      | _ => false);

    fun atom_err (Const (a, T)) =

          if valid_const a T then None

          else Some ("Illegal type for constant " ^ quote a ^ " :: " ^

            quote (string_of_typ sg T))

      | atom_err (Var ((x, i), _)) =

          if i < 0 then Some ("Negative index for Var " ^ quote x) else None

      | atom_err _ = None;

    val norm_tm =

      (case it_term_types (typ_errors tsig) (tm, []) of

        [] => map_term_types (norm_typ tsig) tm

      | errs => raise_type (cat_lines errs) [] [tm]);

  in

    (case mapfilt_atoms atom_err norm_tm of

      [] => (norm_tm, type_of norm_tm, maxidx_of_term norm_tm)

    | errs => raise_type (cat_lines errs) [] [norm_tm])

  end;

(** read types **)    (*exception ERROR*)

(* FIXME rd_typ vs. read_raw_typ (?) *)

fun rd_typ tsig syn sort_of s =

  let

    val def_sort = defaultS tsig;

    val raw_ty =        (*this may raise ERROR, too!*)

      Syntax.read_typ syn (fn x => if_none (sort_of x) def_sort) s;

  in

    cert_typ tsig raw_ty

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

  end

  handle ERROR => error ("The error(s) above occurred in type " ^ quote s);

fun read_typ (Sg {tsig, syn, ...}, sort_of) s = rd_typ tsig syn sort_of s;

(** extend signature **)    (*exception ERROR*)

(* FIXME -> type.ML *)

(* FIXME replace? *)

fun varify_typ (Type (t, tys)) = Type (t, map varify_typ tys)

  | varify_typ (TFree (a, s)) = TVar ((a, 0), s)

  | varify_typ (ty as TVar _) =

      raise_type "Illegal schematic type variable" [ty] [];

(* fake newstyle interfaces *) (* FIXME -> type.ML *)

fun ext_tsig_classes tsig classes =

  if exists (fn ([], _, _) => false | _ => true) classes then

    sys_error "FIXME ext_tsig_classes"

  else

    extend_tsig tsig (map (fn (_, c, cs) => (c, cs)) classes, [], [], []);

fun ext_tsig_defsort tsig defsort =

  extend_tsig tsig ([], defsort, [], []);

fun ext_tsig_types tsig types =

  extend_tsig tsig ([], [], map (fn (t, n) => ([t], n)) types, []);

(* FIXME varify_typ, rem_sorts; norm_typ (?) *)

fun ext_tsig_abbrs tsig abbrs = Type.ext_tsig_abbrs tsig

  (map (fn (t, vs, rhs) => (t, (map (rpair 0) vs, varifyT rhs))) abbrs);

fun ext_tsig_arities tsig arities = extend_tsig tsig

  ([], [], [], flat (map (fn (t, ss, cs) => map (fn c => ([t], (ss, c))) cs) arities));

(** read types **)  (*exception ERROR*)

fun err_in_type s =

  error ("The error(s) above occurred in type " ^ quote s);

fun read_raw_typ syn tsig sort_of str =

  Syntax.read_typ syn (fn x => if_none (sort_of x) (defaultS tsig)) str

    handle ERROR => err_in_type str;

(*read and certify typ wrt a signature*)

fun read_typ (Sg {tsig, syn, ...}, sort_of) str =

  cert_typ tsig (read_raw_typ syn tsig sort_of str)

    handle TYPE (msg, _, _) => (writeln msg; err_in_type str);

(** extension functions **)  (*exception ERROR*)

fun decls_of name_of mfixs =

  map (fn (x, y, mx) => (name_of x mx, y)) mfixs;

(* add default sort *)

fun ext_defsort (syn, tsig, ctab) defsort =

  (syn, ext_tsig_defsort tsig defsort, ctab);

(* add type constructors *)

fun ext_types (syn, tsig, ctab) types =

  (Syntax.extend_type_gram syn types,

    ext_tsig_types tsig (decls_of type_name types),

    ctab);

(* add type abbreviations *)

fun read_abbr syn tsig (t, vs, rhs_src) =

  (t, vs, read_raw_typ syn tsig (K None) rhs_src)

    handle ERROR => error ("in type abbreviation " ^ t);

fun ext_abbrs rd_abbr (syn, tsig, ctab) abbrs =

  let

    fun mfix_of (t, vs, _, mx) = (t, length vs, mx);

    val syn1 = Syntax.extend_type_gram syn (map mfix_of abbrs);

    fun decl_of (t, vs, rhs, mx) =

      rd_abbr syn1 tsig (type_name t mx, vs, rhs);

  in

    (syn1, ext_tsig_abbrs tsig (map decl_of abbrs), ctab)

  end;

val ext_tyabbrs_i = ext_abbrs (K (K I));

val ext_tyabbrs = ext_abbrs read_abbr;

(* add type arities *)

fun ext_arities (syn, tsig, ctab) arities =

  let

    val tsig1 = ext_tsig_arities tsig arities;

    val log_types = logical_types tsig1;

  in

    (Syntax.extend_log_types syn log_types, tsig1, ctab)

  end;

(* add term constants and syntax *)

fun err_in_const c =

  error ("in declaration of constant " ^ quote c);

fun err_dup_consts cs =

  error ("Duplicate declaration of constant(s) " ^ commas_quote cs);

fun read_const syn tsig (c, ty_src, mx) =

  (c, read_raw_typ syn tsig (K None) ty_src, mx)

    handle ERROR => err_in_const (const_name c mx);

fun ext_cnsts rd_const syn_only (syn, tsig, ctab) raw_consts =

  let

    fun prep_const (c, ty, mx) = (c, cert_typ tsig (varify_typ ty), mx)

      handle TYPE (msg, _, _) => (writeln msg; err_in_const (const_name c mx));

    val consts = map (prep_const o rd_const syn tsig) raw_consts;

    val decls =

      if syn_only then []

      else filter_out (equal "" o fst) (decls_of const_name consts);

  in

    (Syntax.extend_const_gram syn consts, tsig,

      Symtab.extend_new (ctab, decls)

        handle Symtab.DUPS cs => err_dup_consts cs)

  end;

val ext_consts_i = ext_cnsts (K (K I)) false;

val ext_consts = ext_cnsts read_const false;

val ext_syntax_i = ext_cnsts (K (K I)) true;

val ext_syntax = ext_cnsts read_const true;

(* add type classes *)

fun const_of_class c = c ^ "_class";

fun class_of_const c_class =

  let

    val c = implode (take (size c_class - 6, explode c_class));

  in

    if const_of_class c = c_class then c

    else raise_term ("class_of_const: bad name " ^ quote c_class) []

  end;

fun ext_classes (syn, tsig, ctab) classes =

  let

    val names = map (fn (_, c, _) => c) classes;

    val consts =

      map (fn c => (const_of_class c, a_itselfT --> propT, NoSyn)) names;

  in

    ext_consts_i

      (Syntax.extend_consts syn names, ext_tsig_classes tsig classes, ctab)

      consts

  end;

(* add syntactic translations *)

fun ext_trfuns (syn, tsig, ctab) trfuns =

  (Syntax.extend_trfuns syn trfuns, tsig, ctab);

fun ext_trrules (syn, tsig, ctab) xrules =

  (Syntax.extend_trrules syn xrules, tsig, ctab);

(* build signature *)

(* FIXME debug *)

fun assert_stamps_ok stamps =

  let val names = map ! stamps;

  in

    if not (null (duplicates stamps)) then

      error "DEBUG dup stamps"

    else if not (null (duplicates names)) then

      error "DEBUG dup stamp names"

    else if not (null names) andalso exists (equal "#") (tl names) then

      error "DEBUG misplaced draft stamp name"

    else stamps

  end;

fun ext_stamps stamps name =

  let

    val stmps = (case stamps of ref "#" :: ss => ss | ss => ss);

  in

    if exists (equal name o !) stmps then

      error ("Theory already contains a " ^ quote name ^ " component")

    else assert_stamps_ok (ref name :: stmps)

  end;

fun make_sign (syn, tsig, ctab) stamps name =

  Sg {tsig = tsig, const_tab = ctab, syn = syn,

    stamps = ext_stamps stamps name};

fun extend_sign extfun name decls (Sg {tsig, const_tab, syn, stamps}) =

  make_sign (extfun (syn, tsig, const_tab) decls) stamps name;

(* the external interfaces *)

val add_classes   = extend_sign ext_classes "#";

val add_defsort   = extend_sign ext_defsort "#";

val add_types     = extend_sign ext_types "#";

val add_tyabbrs   = extend_sign ext_tyabbrs "#";

val add_tyabbrs_i = extend_sign ext_tyabbrs_i "#";

val add_arities   = extend_sign ext_arities "#";

val add_consts    = extend_sign ext_consts "#";

val add_consts_i  = extend_sign ext_consts_i "#";

val add_syntax    = extend_sign ext_syntax "#";

val add_syntax_i  = extend_sign ext_syntax_i "#";

val add_trfuns    = extend_sign ext_trfuns "#";

val add_trrules   = extend_sign ext_trrules "#";

fun add_name name sg = extend_sign K name () sg;

val make_draft = add_name "#";

(** extend signature (old) **)      (* FIXME remove *)

fun extend sg name (classes, default, types, abbrs, arities, consts, opt_sext) =

  let

    fun read_abbr syn (c, vs, rhs_src) =

      (c, (map (rpair 0) vs, varifyT (Syntax.read_typ syn (K []) rhs_src)))

        handle ERROR => error ("The error(s) above occurred in the rhs " ^

          quote rhs_src ^ "\nof type abbreviation " ^ quote c);

    (*reset TVar indices to 0, renaming to preserve distinctness*)

    fun zero_tvar_idxs T =

      let

        val inxSs = typ_tvars T;

        val nms' = variantlist (map (#1 o #1) inxSs, []);

        val tye = map2 (fn ((v, S), a) => (v, TVar ((a, 0), S))) (inxSs, nms');

      in

        typ_subst_TVars tye T

      end;

    (*read and check the type mentioned in a const declaration; zero type var

      indices because type inference requires it*)

    fun read_const tsig syn (c, s) =

      (c, zero_tvar_idxs (varifyT (rd_typ tsig syn (K None) s)))

        handle ERROR => error ("in declaration of constant " ^ quote c);

    val Sg {tsig, const_tab, syn, stamps} = sg;

    val xconsts = map #1 classes @ flat (map #1 types) @ map #1 abbrs @

      flat (map #1 consts);

    val sext = if_none opt_sext Syntax.empty_sext;

    val tsig' = extend_tsig tsig (classes, default, types, arities);

    val tsig1 = Type.ext_tsig_abbrs tsig' (map (read_abbr syn) abbrs);

    val syn1 = Syntax.extend syn (rd_typ tsig1 syn (K None))

      (logical_types tsig1, xconsts, sext);

    val all_consts = flat (map (fn (cs, s) => map (rpair s) cs)

      (Syntax.constants sext @ consts));

    val const_tab1 =

      Symtab.extend_new (const_tab, map (read_const tsig1 syn) all_consts)

        handle Symtab.DUPS cs => err_dup_consts cs;

    val stamps1 = ext_stamps stamps name;

  in

    Sg {tsig = tsig1, const_tab = const_tab1, syn = syn1, stamps = stamps1}

  end;

(** merge signatures **)    (*exception TERM*)

fun merge (sg1, sg2) =

  if subsig (sg2, sg1) then sg1

  else if subsig (sg1, sg2) then sg2

  else if is_draft sg1 orelse is_draft sg2 then

    raise_term "Illegal merge of draft signatures" []

  else

    (*neither is union already; must form union*)

    let

      val Sg {tsig = tsig1, const_tab = const_tab1, syn = syn1,

        stamps = stamps1} = sg1;

      val Sg {tsig = tsig2, const_tab = const_tab2, syn = syn2,

        stamps = stamps2} = sg2;

      val tsig = merge_tsigs (tsig1, tsig2);

      val const_tab = Symtab.merge (op =) (const_tab1, const_tab2)

        handle Symtab.DUPS cs =>

          raise_term ("Incompatible types for constant(s) " ^ commas_quote cs) [];

      val syn = Syntax.merge_syntaxes syn1 syn2;

      val stamps = merge_rev_lists stamps1 stamps2;

      val dups = duplicates (stamp_names stamps);

    in

      if null dups then assert_stamps_ok stamps    (* FIXME debug *)

      else raise_term ("Attempt to merge different versions of theories " ^

        commas_quote dups) [];

      Sg {tsig = tsig, const_tab = const_tab, syn = syn, stamps = stamps}

    end;

(** the Pure signature **)

val pure =

  make_sign (Syntax.type_syn, tsig0, Symtab.null) [] "#"

  also add_types

   (("fun", 2, NoSyn) ::

    ("prop", 0, NoSyn) ::

    ("itself", 1, NoSyn) ::

    Syntax.Mixfix.pure_types)

  also add_classes [([], logicC, [])]

  also add_defsort logicS

  also add_arities

   [("fun", [logicS, logicS], logicS),

    ("prop", [], logicS),

    ("itself", [logicS], logicS)]

  also add_syntax Syntax.Mixfix.pure_syntax

  also add_trfuns Syntax.pure_trfuns

  also add_consts

   [("==", "['a::{}, 'a] => prop", Mixfix ("(_ ==/ _)", [3, 2], 2)),

    ("=?=", "['a::{}, 'a] => prop", Mixfix ("(_ =?=/ _)", [3, 2], 2)),

    ("==>", "[prop, prop] => prop", Mixfix ("(_ ==>/ _)", [2, 1], 1)),

    ("all", "('a => prop) => prop", Binder ("!!", 0)),

    ("TYPE", "'a itself", NoSyn),

    (Syntax.constrainC, "'a::{} => 'a", NoSyn)]

  also add_name "Pure";

end;