(*  Title:      Pure/consts.ML

     Author:     Makarius

 Polymorphic constants: declarations, abbreviations, additional type

 constraints.

 *)

 signature CONSTS =

 sig

   type T

   val eq_consts: T * T -> bool

   val retrieve_abbrevs: T -> string list -> term -> (term * term) list

   val dest: T ->

    {constants: (typ * term option) Name_Space.table,

     constraints: typ Name_Space.table}

   val the_const: T -> string -> string * typ                   (*exception TYPE*)

   val the_abbreviation: T -> string -> typ * term              (*exception TYPE*)

   val type_scheme: T -> string -> typ                          (*exception TYPE*)

   val is_monomorphic: T -> string -> bool                      (*exception TYPE*)

   val the_constraint: T -> string -> typ                       (*exception TYPE*)

   val space_of: T -> Name_Space.T

   val alias: Name_Space.naming -> binding -> string -> T -> T

   val is_concealed: T -> string -> bool

   val intern: T -> xstring -> string

   val extern: Proof.context -> T -> string -> xstring

   val intern_syntax: T -> xstring -> string

   val extern_syntax: Proof.context -> T -> string -> xstring

   val read_const: T -> string * Position.T -> term

   val certify: Context.pretty -> Type.tsig -> bool -> T -> term -> term  (*exception TYPE*)

   val typargs: T -> string * typ -> typ list

   val instance: T -> string * typ list -> typ

   val declare: Context.generic -> binding * typ -> T -> T

   val constrain: string * typ option -> T -> T

   val abbreviate: Context.generic -> Type.tsig -> string -> binding * term -> T -> (term * term) * T

   val revert_abbrev: string -> string -> T -> T

   val hide: bool -> string -> T -> T

   val empty: T

   val merge: T * T -> T

 end;

 structure Consts: CONSTS =

 struct

 (** consts type **)

 (* datatype T *)

 type decl = {T: typ, typargs: int list list};

 type abbrev = {rhs: term, normal_rhs: term, force_expand: bool};

 datatype T = Consts of

  {decls: (decl * abbrev option) Name_Space.table,

   constraints: typ Symtab.table,

   rev_abbrevs: (term * term) Item_Net.T Symtab.table};

 fun eq_consts

    (Consts {decls = decls1, constraints = constraints1, rev_abbrevs = rev_abbrevs1},

     Consts {decls = decls2, constraints = constraints2, rev_abbrevs = rev_abbrevs2}) =

   pointer_eq (decls1, decls2) andalso

   pointer_eq (constraints1, constraints2) andalso

   pointer_eq (rev_abbrevs1, rev_abbrevs2);

 fun make_consts (decls, constraints, rev_abbrevs) =

   Consts {decls = decls, constraints = constraints, rev_abbrevs = rev_abbrevs};

 fun map_consts f (Consts {decls, constraints, rev_abbrevs}) =

   make_consts (f (decls, constraints, rev_abbrevs));

 (* reverted abbrevs *)

 val empty_abbrevs =

   Item_Net.init (fn ((t, u), (t', u')) => t aconv t' andalso u aconv u') (single o #1);

 fun update_abbrevs mode abbrs =

   Symtab.map_default (mode, empty_abbrevs) (Item_Net.update abbrs);

 fun retrieve_abbrevs (Consts {rev_abbrevs, ...}) modes =

   let val nets = map_filter (Symtab.lookup rev_abbrevs) modes

   in fn t => maps (fn net => Item_Net.retrieve net t) nets end;

 (* dest consts *)

 fun dest (Consts {decls = (space, decls), constraints, ...}) =

  {constants = (space,

     Symtab.fold (fn (c, ({T, ...}, abbr)) =>

       Symtab.update (c, (T, Option.map #rhs abbr))) decls Symtab.empty),

   constraints = (space, constraints)};

 (* lookup consts *)

 fun the_entry (Consts {decls = (_, tab), ...}) c =

   (case Symtab.lookup_key tab c of

     SOME entry => entry

   | NONE => raise TYPE ("Unknown constant: " ^ quote c, [], []));

 fun the_const consts c =

   (case the_entry consts c of

     (c', ({T, ...}, NONE)) => (c', T)

   | _ => raise TYPE ("Not a logical constant: " ^ quote c, [], []));

 fun the_abbreviation consts c =

   (case the_entry consts c of

     (_, ({T, ...}, SOME {rhs, ...})) => (T, rhs)

   | _ => raise TYPE ("Not an abbreviated constant: " ^ quote c, [], []));

 fun the_decl consts = #1 o #2 o the_entry consts;

 val type_scheme = #T oo the_decl;

 val type_arguments = #typargs oo the_decl;

 val is_monomorphic = null oo type_arguments;

 fun the_constraint (consts as Consts {constraints, ...}) c =

   (case Symtab.lookup constraints c of

     SOME T => T

   | NONE => type_scheme consts c);

 (* name space and syntax *)

 fun space_of (Consts {decls = (space, _), ...}) = space;

 fun alias naming binding name = map_consts (fn ((space, decls), constraints, rev_abbrevs) =>

   ((Name_Space.alias naming binding name space, decls), constraints, rev_abbrevs));

 val is_concealed = Name_Space.is_concealed o space_of;

 val intern = Name_Space.intern o space_of;

 fun extern ctxt = Name_Space.extern ctxt o space_of;

 fun intern_syntax consts s =

   (case try Lexicon.unmark_const s of

     SOME c => c

   | NONE => intern consts s);

 fun extern_syntax ctxt consts s =

   (case try Lexicon.unmark_const s of

     SOME c => extern ctxt consts c

   | NONE => s);

 (* read_const *)

 fun read_const consts (raw_c, pos) =

   let

     val c = intern consts raw_c;

     val T = type_scheme consts c handle TYPE (msg, _, _) => error (msg ^ Position.str_of pos);

   in Const (c, T) end;

 (* certify *)

 fun certify pp tsig do_expand consts =

   let

     fun err msg (c, T) =

       raise TYPE (msg ^ " " ^ quote c ^ " :: " ^

         Syntax.string_of_typ (Syntax.init_pretty pp) T, [], []);

     val certT = Type.cert_typ tsig;

     fun cert tm =

       let

         val (head, args) = Term.strip_comb tm;

         val args' = map cert args;

         fun comb head' = Term.list_comb (head', args');

       in

         (case head of

           Abs (x, T, t) => comb (Abs (x, certT T, cert t))

         | Const (c, T) =>

             let

               val T' = certT T;

               val (_, ({T = U, ...}, abbr)) = the_entry consts c;

               fun expand u =

                 Term.betapplys (Envir.expand_atom T' (U, u) handle TYPE _ =>

                   err "Illegal type for abbreviation" (c, T), args');

             in

               if not (Type.raw_instance (T', U)) then

                 err "Illegal type for constant" (c, T)

               else

                 (case abbr of

                   SOME {rhs, normal_rhs, force_expand} =>

                     if do_expand then expand normal_rhs

                     else if force_expand then expand rhs

                     else comb head

                 | _ => comb head)

             end

         | _ => comb head)

       end;

   in cert end;

 (* typargs -- view actual const type as instance of declaration *)

 local

 fun args_of (Type (_, Ts)) pos = args_of_list Ts 0 pos

   | args_of (TVar v) pos = insert (eq_fst op =) (v, rev pos)

   | args_of (TFree _) _ = I

 and args_of_list (T :: Ts) i is = args_of T (i :: is) #> args_of_list Ts (i + 1) is

   | args_of_list [] _ _ = I;

 fun subscript (Type (_, Ts)) (i :: is) = subscript (nth Ts i) is

   | subscript T [] = T

   | subscript _ _ = raise Subscript;

 in

 fun typargs_of T = map #2 (rev (args_of T [] []));

 fun typargs consts (c, T) = map (subscript T) (type_arguments consts c);

 end;

 fun instance consts (c, Ts) =

   let

     val declT = type_scheme consts c;

     val vars = map Term.dest_TVar (typargs consts (c, declT));

     val inst = vars ~~ Ts handle ListPair.UnequalLengths =>

       raise TYPE ("Consts.instance", Ts, [Const (c, dummyT)]);

   in declT |> Term_Subst.instantiateT inst end;

 (** build consts **)

 (* name space *)

 fun hide fully c = map_consts (fn (decls, constraints, rev_abbrevs) =>

   (apfst (Name_Space.hide fully c) decls, constraints, rev_abbrevs));

 (* declarations *)

 fun declare context (b, declT) =

   map_consts (fn (decls, constraints, rev_abbrevs) =>

     let

       val decl = {T = declT, typargs = typargs_of declT};

       val _ = Binding.check b;

       val (_, decls') = decls |> Name_Space.define context true (b, (decl, NONE));

     in (decls', constraints, rev_abbrevs) end);

 (* constraints *)

 fun constrain (c, C) consts =

   consts |> map_consts (fn (decls, constraints, rev_abbrevs) =>

     (#2 (the_entry consts c) handle TYPE (msg, _, _) => error msg;

       (decls,

         constraints |> (case C of SOME T => Symtab.update (c, T) | NONE => Symtab.delete_safe c),

         rev_abbrevs)));

 (* abbreviations *)

 local

 fun strip_abss (t as Abs (x, T, b)) =

       if Term.is_dependent b then strip_abss b |>> cons (x, T)  (* FIXME decr!? *)

       else ([], t)

   | strip_abss t = ([], t);

 fun rev_abbrev lhs rhs =

   let

     val (xs, body) = strip_abss (Envir.beta_eta_contract rhs);

     val vars = fold (fn (x, T) => cons (Var ((x, 0), T))) (Term.rename_wrt_term body xs) [];

   in (Term.subst_bounds (rev vars, body), Term.list_comb (lhs, vars)) end;

 in

 fun abbreviate context tsig mode (b, raw_rhs) consts =

   let

     val pp = Context.pretty_generic context;

     val cert_term = certify pp tsig false consts;

     val expand_term = certify pp tsig true consts;

     val force_expand = mode = Print_Mode.internal;

     val _ = Term.exists_subterm Term.is_Var raw_rhs andalso

       error ("Illegal schematic variables on rhs of abbreviation " ^ Binding.print b);

     val rhs = raw_rhs

       |> Term.map_types (Type.cert_typ tsig)

       |> cert_term

       |> Term.close_schematic_term;

     val normal_rhs = expand_term rhs;

     val T = Term.fastype_of rhs;

     val lhs = Const (Name_Space.full_name (Name_Space.naming_of context) b, T);

   in

     consts |> map_consts (fn (decls, constraints, rev_abbrevs) =>

       let

         val decl = {T = T, typargs = typargs_of T};

         val abbr = {rhs = rhs, normal_rhs = normal_rhs, force_expand = force_expand};

         val _ = Binding.check b;

         val (_, decls') = decls

           |> Name_Space.define context true (b, (decl, SOME abbr));

         val rev_abbrevs' = rev_abbrevs

           |> update_abbrevs mode (rev_abbrev lhs rhs);

       in (decls', constraints, rev_abbrevs') end)

     |> pair (lhs, rhs)

   end;

 fun revert_abbrev mode c consts = consts |> map_consts (fn (decls, constraints, rev_abbrevs) =>

   let

     val (T, rhs) = the_abbreviation consts c;

     val rev_abbrevs' = rev_abbrevs

       |> update_abbrevs mode (rev_abbrev (Const (c, T)) rhs);

   in (decls, constraints, rev_abbrevs') end);

 end;

 (* empty and merge *)

 val empty =

   make_consts (Name_Space.empty_table Isabelle_Markup.constantN, Symtab.empty, Symtab.empty);

 fun merge

    (Consts {decls = decls1, constraints = constraints1, rev_abbrevs = rev_abbrevs1},

     Consts {decls = decls2, constraints = constraints2, rev_abbrevs = rev_abbrevs2}) =

   let

     val decls' = Name_Space.merge_tables (decls1, decls2);

     val constraints' = Symtab.join (K fst) (constraints1, constraints2);

     val rev_abbrevs' = Symtab.join (K Item_Net.merge) (rev_abbrevs1, rev_abbrevs2);

   in make_consts (decls', constraints', rev_abbrevs') end;

 end;