(*  Title:      Pure/Isar/proof_context.ML

     Author:     Markus Wenzel, TU Muenchen

 The key concept of Isar proof contexts: elevates primitive local

 reasoning Gamma |- phi to a structured concept, with generic context

 elements.  See also structure Variable and Assumption.

 *)

 signature PROOF_CONTEXT =

 sig

   val theory_of: Proof.context -> theory

   val init_global: theory -> Proof.context

   type mode

   val mode_default: mode

   val mode_stmt: mode

   val mode_pattern: mode

   val mode_schematic: mode

   val mode_abbrev: mode

   val set_mode: mode -> Proof.context -> Proof.context

   val get_mode: Proof.context -> mode

   val restore_mode: Proof.context -> Proof.context -> Proof.context

   val abbrev_mode: Proof.context -> bool

   val set_stmt: bool -> Proof.context -> Proof.context

   val local_naming: Name_Space.naming

   val map_naming: (Name_Space.naming -> Name_Space.naming) -> Proof.context -> Proof.context

   val naming_of: Proof.context -> Name_Space.naming

   val restore_naming: Proof.context -> Proof.context -> Proof.context

   val full_name: Proof.context -> binding -> string

   val syn_of: Proof.context -> Syntax.syntax

   val tsig_of: Proof.context -> Type.tsig

   val set_defsort: sort -> Proof.context -> Proof.context

   val default_sort: Proof.context -> indexname -> sort

   val consts_of: Proof.context -> Consts.T

   val the_const_constraint: Proof.context -> string -> typ

   val set_syntax_mode: Syntax.mode -> Proof.context -> Proof.context

   val restore_syntax_mode: Proof.context -> Proof.context -> Proof.context

   val facts_of: Proof.context -> Facts.T

   val cases_of: Proof.context -> (string * (Rule_Cases.T * bool)) list

   val transfer_syntax: theory -> Proof.context -> Proof.context

   val transfer: theory -> Proof.context -> Proof.context

   val background_theory: (theory -> theory) -> Proof.context -> Proof.context

   val background_theory_result: (theory -> 'a * theory) -> Proof.context -> 'a * Proof.context

   val extern_fact: Proof.context -> string -> xstring

   val pretty_term_abbrev: Proof.context -> term -> Pretty.T

   val pretty_fact_aux: Proof.context -> bool -> string * thm list -> Pretty.T

   val pretty_fact: Proof.context -> string * thm list -> Pretty.T

   val read_class: Proof.context -> xstring -> class

   val read_arity: Proof.context -> xstring * string list * string -> arity

   val cert_arity: Proof.context -> arity -> arity

   val read_typ: Proof.context -> string -> typ

   val read_typ_syntax: Proof.context -> string -> typ

   val read_typ_abbrev: Proof.context -> string -> typ

   val cert_typ: Proof.context -> typ -> typ

   val cert_typ_syntax: Proof.context -> typ -> typ

   val cert_typ_abbrev: Proof.context -> typ -> typ

   val get_skolem: Proof.context -> string -> string

   val revert_skolem: Proof.context -> string -> string

   val infer_type: Proof.context -> string * typ -> typ

   val inferred_param: string -> Proof.context -> typ * Proof.context

   val inferred_fixes: Proof.context -> (string * typ) list * Proof.context

   val read_type_name: Proof.context -> bool -> string -> typ

   val read_type_name_proper: Proof.context -> bool -> string -> typ

   val read_const_proper: Proof.context -> bool -> string -> term

   val read_const: Proof.context -> bool -> typ -> string -> term

   val allow_dummies: Proof.context -> Proof.context

   val check_tvar: Proof.context -> indexname * sort -> indexname * sort

   val check_tfree: Proof.context -> string * sort -> string * sort

   val decode_term: Proof.context -> term -> (Position.T * Markup.T) list * term

   val standard_infer_types: Proof.context -> term list -> term list

   val read_term_pattern: Proof.context -> string -> term

   val read_term_schematic: Proof.context -> string -> term

   val read_term_abbrev: Proof.context -> string -> term

   val show_abbrevs_raw: Config.raw

   val show_abbrevs: bool Config.T

   val expand_abbrevs: Proof.context -> term -> term

   val cert_term: Proof.context -> term -> term

   val cert_prop: Proof.context -> term -> term

   val def_type: Proof.context -> indexname -> typ option

   val goal_export: Proof.context -> Proof.context -> thm list -> thm list

   val export: Proof.context -> Proof.context -> thm list -> thm list

   val export_morphism: Proof.context -> Proof.context -> morphism

   val norm_export_morphism: Proof.context -> Proof.context -> morphism

   val bind_terms: (indexname * term option) list -> Proof.context -> Proof.context

   val auto_bind_goal: term list -> Proof.context -> Proof.context

   val auto_bind_facts: term list -> Proof.context -> Proof.context

   val match_bind: bool -> (string list * string) list -> Proof.context -> term list * Proof.context

   val match_bind_i: bool -> (term list * term) list -> Proof.context -> term list * Proof.context

   val read_propp: Proof.context * (string * string list) list list

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

   val cert_propp: Proof.context * (term * term list) list list

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

   val read_propp_schematic: Proof.context * (string * string list) list list

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

   val cert_propp_schematic: Proof.context * (term * term list) list list

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

   val bind_propp: Proof.context * (string * string list) list list

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

   val bind_propp_i: Proof.context * (term * term list) list list

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

   val bind_propp_schematic: Proof.context * (string * string list) list list

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

   val bind_propp_schematic_i: Proof.context * (term * term list) list list

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

   val fact_tac: thm list -> int -> tactic

   val some_fact_tac: Proof.context -> int -> tactic

   val get_fact: Proof.context -> Facts.ref -> thm list

   val get_fact_single: Proof.context -> Facts.ref -> thm

   val get_thms: Proof.context -> xstring -> thm list

   val get_thm: Proof.context -> xstring -> thm

   val note_thmss: string -> (Thm.binding * (thm list * attribute list) list) list ->

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

   val put_thms: bool -> string * thm list option -> Proof.context -> Proof.context

   val read_vars: (binding * string option * mixfix) list -> Proof.context ->

     (binding * typ option * mixfix) list * Proof.context

   val cert_vars: (binding * typ option * mixfix) list -> Proof.context ->

     (binding * typ option * mixfix) list * Proof.context

   val add_fixes: (binding * typ option * mixfix) list -> Proof.context ->

     string list * Proof.context

   val auto_fixes: Proof.context * (term list list * 'a) -> Proof.context * (term list list * 'a)

   val bind_fixes: string list -> Proof.context -> (term -> term) * Proof.context

   val add_assms: Assumption.export ->

     (Thm.binding * (string * string list) list) list ->

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

   val add_assms_i: Assumption.export ->

     (Thm.binding * (term * term list) list) list ->

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

   val add_cases: bool -> (string * Rule_Cases.T option) list -> Proof.context -> Proof.context

   val apply_case: Rule_Cases.T -> Proof.context -> (string * term list) list * Proof.context

   val get_case: Proof.context -> string -> string option list -> Rule_Cases.T

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

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

   val target_type_notation: bool -> Syntax.mode -> (typ * mixfix) list -> morphism ->

     Context.generic -> Context.generic

   val target_notation: bool -> Syntax.mode -> (term * mixfix) list -> morphism ->

     Context.generic -> Context.generic

   val class_alias: binding -> class -> Proof.context -> Proof.context

   val type_alias: binding -> string -> Proof.context -> Proof.context

   val const_alias: binding -> string -> Proof.context -> Proof.context

   val add_const_constraint: string * typ option -> Proof.context -> Proof.context

   val add_abbrev: string -> binding * term -> Proof.context -> (term * term) * Proof.context

   val revert_abbrev: string -> string -> Proof.context -> Proof.context

   val print_syntax: Proof.context -> unit

   val print_abbrevs: Proof.context -> unit

   val print_binds: Proof.context -> unit

   val print_lthms: Proof.context -> unit

   val print_cases: Proof.context -> unit

   val debug: bool Unsynchronized.ref

   val verbose: bool Unsynchronized.ref

   val pretty_ctxt: Proof.context -> Pretty.T list

   val pretty_context: Proof.context -> Pretty.T list

 end;

 structure ProofContext: PROOF_CONTEXT =

 struct

 open ProofContext;

 (** inner syntax mode **)

 datatype mode =

   Mode of

    {stmt: bool,                (*inner statement mode*)

     pattern: bool,             (*pattern binding schematic variables*)

     schematic: bool,           (*term referencing loose schematic variables*)

     abbrev: bool};             (*abbrev mode -- no normalization*)

 fun make_mode (stmt, pattern, schematic, abbrev) =

   Mode {stmt = stmt, pattern = pattern, schematic = schematic, abbrev = abbrev};

 val mode_default   = make_mode (false, false, false, false);

 val mode_stmt      = make_mode (true, false, false, false);

 val mode_pattern   = make_mode (false, true, false, false);

 val mode_schematic = make_mode (false, false, true, false);

 val mode_abbrev    = make_mode (false, false, false, true);

 (** Isar proof context information **)

 datatype ctxt =

   Ctxt of

    {mode: mode,                  (*inner syntax mode*)

     naming: Name_Space.naming,   (*local naming conventions*)

     syntax: Local_Syntax.T,      (*local syntax*)

     tsig: Type.tsig * Type.tsig, (*local/global type signature -- local name space / defsort only*)

     consts: Consts.T * Consts.T, (*local/global consts -- local name space / abbrevs only*)

     facts: Facts.T,              (*local facts*)

     cases: (string * (Rule_Cases.T * bool)) list};    (*named case contexts*)

 fun make_ctxt (mode, naming, syntax, tsig, consts, facts, cases) =

   Ctxt {mode = mode, naming = naming, syntax = syntax,

     tsig = tsig, consts = consts, facts = facts, cases = cases};

 val local_naming = Name_Space.default_naming |> Name_Space.add_path "local";

 structure Data = Proof_Data

 (

   type T = ctxt;

   fun init thy =

     make_ctxt (mode_default, local_naming, Local_Syntax.init thy,

       (Sign.tsig_of thy, Sign.tsig_of thy),

       (Sign.consts_of thy, Sign.consts_of thy), Facts.empty, []);

 );

 fun rep_context ctxt = Data.get ctxt |> (fn Ctxt args => args);

 fun map_context f =

   Data.map (fn Ctxt {mode, naming, syntax, tsig, consts, facts, cases} =>

     make_ctxt (f (mode, naming, syntax, tsig, consts, facts, cases)));

 fun set_mode mode = map_context (fn (_, naming, syntax, tsig, consts, facts, cases) =>

   (mode, naming, syntax, tsig, consts, facts, cases));

 fun map_mode f =

   map_context (fn (Mode {stmt, pattern, schematic, abbrev}, naming, syntax, tsig, consts, facts, cases) =>

     (make_mode (f (stmt, pattern, schematic, abbrev)), naming, syntax, tsig, consts, facts, cases));

 fun map_naming f =

   map_context (fn (mode, naming, syntax, tsig, consts, facts, cases) =>

     (mode, f naming, syntax, tsig, consts, facts, cases));

 fun map_syntax f =

   map_context (fn (mode, naming, syntax, tsig, consts, facts, cases) =>

     (mode, naming, f syntax, tsig, consts, facts, cases));

 fun map_tsig f =

   map_context (fn (mode, naming, syntax, tsig, consts, facts, cases) =>

     (mode, naming, syntax, f tsig, consts, facts, cases));

 fun map_consts f =

   map_context (fn (mode, naming, syntax, tsig, consts, facts, cases) =>

     (mode, naming, syntax, tsig, f consts, facts, cases));

 fun map_facts f =

   map_context (fn (mode, naming, syntax, tsig, consts, facts, cases) =>

     (mode, naming, syntax, tsig, consts, f facts, cases));

 fun map_cases f =

   map_context (fn (mode, naming, syntax, tsig, consts, facts, cases) =>

     (mode, naming, syntax, tsig, consts, facts, f cases));

 val get_mode = #mode o rep_context;

 val restore_mode = set_mode o get_mode;

 val abbrev_mode = get_mode #> (fn Mode {abbrev, ...} => abbrev);

 fun set_stmt stmt =

   map_mode (fn (_, pattern, schematic, abbrev) => (stmt, pattern, schematic, abbrev));

 val naming_of = #naming o rep_context;

 val restore_naming = map_naming o K o naming_of

 val full_name = Name_Space.full_name o naming_of;

 val syntax_of = #syntax o rep_context;

 val syn_of = Local_Syntax.syn_of o syntax_of;

 val set_syntax_mode = map_syntax o Local_Syntax.set_mode;

 val restore_syntax_mode = map_syntax o Local_Syntax.restore_mode o syntax_of;

 val tsig_of = #1 o #tsig o rep_context;

 val set_defsort = map_tsig o apfst o Type.set_defsort;

 fun default_sort ctxt = the_default (Type.defaultS (tsig_of ctxt)) o Variable.def_sort ctxt;

 val consts_of = #1 o #consts o rep_context;

 val the_const_constraint = Consts.the_constraint o consts_of;

 val facts_of = #facts o rep_context;

 val cases_of = #cases o rep_context;

 (* theory transfer *)

 fun transfer_syntax thy ctxt = ctxt |>

   map_syntax (Local_Syntax.rebuild thy) |>

   map_tsig (fn tsig as (local_tsig, global_tsig) =>

     let val thy_tsig = Sign.tsig_of thy in

       if Type.eq_tsig (thy_tsig, global_tsig) then tsig

       else (Type.merge_tsig (Syntax.pp ctxt) (local_tsig, thy_tsig), thy_tsig)

     end) |>

   map_consts (fn consts as (local_consts, global_consts) =>

     let val thy_consts = Sign.consts_of thy in

       if Consts.eq_consts (thy_consts, global_consts) then consts

       else (Consts.merge (local_consts, thy_consts), thy_consts)

     end);

 fun transfer thy = Context.raw_transfer thy #> transfer_syntax thy;

 fun background_theory f ctxt = transfer (f (theory_of ctxt)) ctxt;

 fun background_theory_result f ctxt =

   let val (res, thy') = f (theory_of ctxt)

   in (res, ctxt |> transfer thy') end;

 (** pretty printing **)

 (* extern *)

 fun extern_fact ctxt name =

   let

     val local_facts = facts_of ctxt;

     val global_facts = Global_Theory.facts_of (theory_of ctxt);

   in

     if is_some (Facts.lookup (Context.Proof ctxt) local_facts name)

     then Facts.extern local_facts name

     else Facts.extern global_facts name

   end;

 (* pretty *)

 fun pretty_term_abbrev ctxt = Syntax.pretty_term (set_mode mode_abbrev ctxt);

 fun pretty_fact_name ctxt a = Pretty.block

   [Pretty.markup (Markup.fact a) [Pretty.str (extern_fact ctxt a)], Pretty.str ":"];

 fun pretty_fact_aux ctxt flag ("", ths) =

       Display.pretty_thms_aux ctxt flag ths

   | pretty_fact_aux ctxt flag (a, [th]) = Pretty.block

       [pretty_fact_name ctxt a, Pretty.brk 1, Display.pretty_thm_aux ctxt flag th]

   | pretty_fact_aux ctxt flag (a, ths) = Pretty.block

       (Pretty.fbreaks (pretty_fact_name ctxt a :: map (Display.pretty_thm_aux ctxt flag) ths));

 fun pretty_fact ctxt = pretty_fact_aux ctxt true;

 (** prepare types **)

 (* classes *)

 fun read_class ctxt text =

   let

     val tsig = tsig_of ctxt;

     val (syms, pos) = Syntax.read_token text;

     val c = Type.cert_class tsig (Type.intern_class tsig (Symbol_Pos.content syms))

       handle TYPE (msg, _, _) => error (msg ^ Position.str_of pos);

     val _ = Context_Position.report ctxt pos (Markup.tclass c);

   in c end;

 (* type arities *)

 local

 fun prep_arity prep_tycon prep_sort ctxt (t, Ss, S) =

   let val arity = (prep_tycon ctxt t, map (prep_sort ctxt) Ss, prep_sort ctxt S)

   in Type.add_arity (Syntax.pp ctxt) arity (tsig_of ctxt); arity end;

 in

 val read_arity = prep_arity (Type.intern_type o tsig_of) Syntax.read_sort;

 val cert_arity = prep_arity (K I) (Type.cert_sort o tsig_of);

 end;

 (* types *)

 fun read_typ_mode mode ctxt s =

   Syntax.read_typ (Type.set_mode mode ctxt) s;

 val read_typ = read_typ_mode Type.mode_default;

 val read_typ_syntax = read_typ_mode Type.mode_syntax;

 val read_typ_abbrev = read_typ_mode Type.mode_abbrev;

 fun cert_typ_mode mode ctxt T =

   Type.cert_typ_mode mode (tsig_of ctxt) T

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

 val cert_typ = cert_typ_mode Type.mode_default;

 val cert_typ_syntax = cert_typ_mode Type.mode_syntax;

 val cert_typ_abbrev = cert_typ_mode Type.mode_abbrev;

 (** prepare variables **)

 (* internalize Skolem constants *)

 val lookup_skolem = AList.lookup (op =) o Variable.fixes_of;

 fun get_skolem ctxt x = the_default x (lookup_skolem ctxt x);

 fun no_skolem internal x =

   if can Name.dest_skolem x then

     error ("Illegal reference to internal Skolem constant: " ^ quote x)

   else if not internal andalso can Name.dest_internal x then

     error ("Illegal reference to internal variable: " ^ quote x)

   else x;

 (* revert Skolem constants -- if possible *)

 fun revert_skolem ctxt x =

   (case find_first (fn (_, y) => y = x) (Variable.fixes_of ctxt) of

     SOME (x', _) => if lookup_skolem ctxt x' = SOME x then x' else x

   | NONE => x);

 (* default token translations *)

 local

 fun free_or_skolem ctxt x =

   (if can Name.dest_skolem x then Pretty.mark Markup.skolem (Pretty.str (revert_skolem ctxt x))

    else Pretty.mark Markup.free (Pretty.str x))

   |> Pretty.mark

     (if Variable.is_fixed ctxt x orelse Syntax.is_pretty_global ctxt then Markup.fixed x

      else Markup.hilite);

 fun var_or_skolem _ s =

   (case Lexicon.read_variable s of

     SOME (x, i) =>

       (case try Name.dest_skolem x of

         NONE => Pretty.mark Markup.var (Pretty.str s)

       | SOME x' => Pretty.mark Markup.skolem (Pretty.str (Term.string_of_vname (x', i))))

   | NONE => Pretty.mark Markup.var (Pretty.str s));

 fun plain_markup m _ s = Pretty.mark m (Pretty.str s);

 val token_trans =

  Syntax.tokentrans_mode ""

   [("tfree", plain_markup Markup.tfree),

    ("tvar", plain_markup Markup.tvar),

    ("free", free_or_skolem),

    ("bound", plain_markup Markup.bound),

    ("var", var_or_skolem),

    ("numeral", plain_markup Markup.numeral),

    ("inner_string", plain_markup Markup.inner_string)];

 in val _ = Context.>> (Context.map_theory (Sign.add_tokentrfuns token_trans)) end;

 (** prepare terms and propositions **)

 (* inferred types of parameters *)

 fun infer_type ctxt x =

   Term.fastype_of (singleton (Syntax.check_terms (set_mode mode_schematic ctxt)) (Free x));

 fun inferred_param x ctxt =

   let val T = infer_type ctxt (x, dummyT)

   in (T, ctxt |> Variable.declare_term (Free (x, T))) end;

 fun inferred_fixes ctxt =

   let

     val xs = rev (map #2 (Variable.fixes_of ctxt));

     val (Ts, ctxt') = fold_map inferred_param xs ctxt;

   in (xs ~~ Ts, ctxt') end;

 (* type and constant names *)

 local

 val token_content = Syntax.read_token #>> Symbol_Pos.content;

 fun prep_const_proper ctxt strict (c, pos) =

   let

     fun err msg = error (msg ^ Position.str_of pos);

     val consts = consts_of ctxt;

     val t as Const (d, _) =

       (case Variable.lookup_const ctxt c of

         SOME d =>

           Const (d, Consts.type_scheme (consts_of ctxt) d handle TYPE (msg, _, _) => err msg)

       | NONE => Consts.read_const consts c);

     val _ =

       if strict then ignore (Consts.the_type consts d) handle TYPE (msg, _, _) => err msg

       else ();

     val _ = Context_Position.report ctxt pos (Markup.const d);

   in t end;

 in

 fun read_type_name ctxt strict text =

   let

     val tsig = tsig_of ctxt;

     val (c, pos) = token_content text;

   in

     if Syntax.is_tid c then

      (Context_Position.report ctxt pos Markup.tfree;

       TFree (c, default_sort ctxt (c, ~1)))

     else

       let

         val d = Type.intern_type tsig c;

         val decl = Type.the_decl tsig d;

         val _ = Context_Position.report ctxt pos (Markup.tycon d);

         fun err () = error ("Bad type name: " ^ quote d);

         val args =

           (case decl of

             Type.LogicalType n => n

           | Type.Abbreviation (vs, _, _) => if strict then err () else length vs

           | Type.Nonterminal => if strict then err () else 0);

       in Type (d, replicate args dummyT) end

   end;

 fun read_type_name_proper ctxt strict text =

   (case read_type_name ctxt strict text of

     T as Type _ => T

   | T => error ("Not a type constructor: " ^ Syntax.string_of_typ ctxt T));

 fun read_const_proper ctxt strict = prep_const_proper ctxt strict o token_content;

 fun read_const ctxt strict ty text =

   let

     val (c, pos) = token_content text;

     val _ = no_skolem false c;

   in

     (case (lookup_skolem ctxt c, Variable.is_const ctxt c) of

       (SOME x, false) =>

         (Context_Position.report ctxt pos

             (Markup.name x (if can Name.dest_skolem x then Markup.skolem else Markup.free));

           Free (x, infer_type ctxt (x, ty)))

     | _ => prep_const_proper ctxt strict (c, pos))

   end;

 end;

 (* read_term *)

 fun read_term_mode mode ctxt = Syntax.read_term (set_mode mode ctxt);

 val read_term_pattern   = read_term_mode mode_pattern;

 val read_term_schematic = read_term_mode mode_schematic;

 val read_term_abbrev    = read_term_mode mode_abbrev;

 (* local abbreviations *)

 local

 fun certify_consts ctxt = Consts.certify (Syntax.pp ctxt) (tsig_of ctxt)

   (not (abbrev_mode ctxt)) (consts_of ctxt);

 fun expand_binds ctxt =

   let

     val Mode {pattern, schematic, ...} = get_mode ctxt;

     fun reject_schematic (t as Var _) =

           error ("Unbound schematic variable: " ^ Syntax.string_of_term ctxt t)

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

       | reject_schematic (t $ u) = (reject_schematic t; reject_schematic u)

       | reject_schematic _ = ();

   in

     if pattern then I

     else Variable.expand_binds ctxt #> (if schematic then I else tap reject_schematic)

   end;

 in

 fun expand_abbrevs ctxt = certify_consts ctxt #> expand_binds ctxt;

 end;

 val show_abbrevs_raw = Config.declare "show_abbrevs" (fn _ => Config.Bool true);

 val show_abbrevs = Config.bool show_abbrevs_raw;

 fun contract_abbrevs ctxt t =

   let

     val thy = theory_of ctxt;

     val consts = consts_of ctxt;

     val Mode {abbrev, ...} = get_mode ctxt;

     val retrieve = Consts.retrieve_abbrevs consts (print_mode_value () @ [""]);

     fun match_abbrev u = Option.map #1 (get_first (Pattern.match_rew thy u) (retrieve u));

   in

     if abbrev orelse not (Config.get ctxt show_abbrevs) orelse not (can Term.type_of t) then t

     else Pattern.rewrite_term_top thy [] [match_abbrev] t

   end;

 (* patterns *)

 fun prepare_patternT ctxt T =

   let

     val Mode {pattern, schematic, ...} = get_mode ctxt;

     val _ =

       pattern orelse schematic orelse

         T |> Term.exists_subtype

           (fn T as TVar (xi, _) =>

             not (Type_Infer.is_param xi) andalso

               error ("Illegal schematic type variable: " ^ Syntax.string_of_typ ctxt T)

           | _ => false)

   in T end;

 local

 val dummies = Config.bool (Config.declare "ProofContext.dummies" (K (Config.Bool false)));

 fun check_dummies ctxt t =

   if Config.get ctxt dummies then t

   else Term.no_dummy_patterns t handle TERM _ => error "Illegal dummy pattern(s) in term";

 fun prepare_dummies ts = #1 (fold_map Term.replace_dummy_patterns ts 1);

 in

 val allow_dummies = Config.put dummies true;

 fun prepare_patterns ctxt =

   let val Mode {pattern, ...} = get_mode ctxt in

     Type_Infer.fixate ctxt #>

     pattern ? Variable.polymorphic ctxt #>

     (map o Term.map_types) (prepare_patternT ctxt) #>

     (if pattern then prepare_dummies else map (check_dummies ctxt))

   end;

 end;

 (* decoding raw terms (syntax trees) *)

 (* types *)

 fun get_sort ctxt raw_text =

   let

     val tsig = tsig_of ctxt;

     val text = distinct (op =) (map (apsnd (Type.minimize_sort tsig)) raw_text);

     val _ =

       (case duplicates (eq_fst (op =)) text of

         [] => ()

       | dups => error ("Inconsistent sort constraints for type variable(s) "

           ^ commas_quote (map (Term.string_of_vname' o fst) dups)));

     fun lookup xi =

       (case AList.lookup (op =) text xi of

         NONE => NONE

       | SOME S => if S = dummyS then NONE else SOME S);

     fun get xi =

       (case (lookup xi, Variable.def_sort ctxt xi) of

         (NONE, NONE) => Type.defaultS tsig

       | (NONE, SOME S) => S

       | (SOME S, NONE) => S

       | (SOME S, SOME S') =>

           if Type.eq_sort tsig (S, S') then S'

           else error ("Sort constraint " ^ Syntax.string_of_sort ctxt S ^

             " inconsistent with default " ^ Syntax.string_of_sort ctxt S' ^

             " for type variable " ^ quote (Term.string_of_vname' xi)));

   in get end;

 fun check_tvar ctxt (xi, S) = (xi, get_sort ctxt [(xi, S)] xi);

 fun check_tfree ctxt (x, S) = apfst fst (check_tvar ctxt ((x, ~1), S));

 local

 fun intern_skolem ctxt def_type x =

   let

     val _ = no_skolem false x;

     val sko = lookup_skolem ctxt x;

     val is_const = can (read_const_proper ctxt false) x orelse Long_Name.is_qualified x;

     val is_declared = is_some (def_type (x, ~1));

   in

     if Variable.is_const ctxt x then NONE

     else if is_some sko then sko

     else if not is_const orelse is_declared then SOME x

     else NONE

   end;

 in

 fun term_context ctxt =

   {get_sort = get_sort ctxt,

    map_const = fn a => ((true, #1 (Term.dest_Const (read_const_proper ctxt false a)))

      handle ERROR _ => (false, Consts.intern (consts_of ctxt) a)),

    map_free = intern_skolem ctxt (Variable.def_type ctxt false)};

 fun decode_term ctxt =

   let val {get_sort, map_const, map_free} = term_context ctxt

   in Syntax.decode_term get_sort map_const map_free end;

 end;

 (* certify terms *)

 local

 fun gen_cert prop ctxt t =

   t

   |> expand_abbrevs ctxt

   |> (fn t' => #1 (Sign.certify' prop (Syntax.pp ctxt) false (consts_of ctxt) (theory_of ctxt) t')

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

       | TERM (msg, _) => error msg);

 in

 val cert_term = gen_cert false;

 val cert_prop = gen_cert true;

 end;

 (* type checking/inference *)

 fun def_type ctxt =

   let val Mode {pattern, ...} = get_mode ctxt

   in Variable.def_type ctxt pattern end;

 fun standard_infer_types ctxt =

   Type_Infer.infer_types ctxt (try (Consts.the_constraint (consts_of ctxt))) (def_type ctxt);

 local

 fun standard_typ_check ctxt =

   map (cert_typ_mode (Type.get_mode ctxt) ctxt) #>

   map (prepare_patternT ctxt);

 fun standard_term_check ctxt =

   standard_infer_types ctxt #>

   map (expand_abbrevs ctxt);

 fun standard_term_uncheck ctxt =

   map (contract_abbrevs ctxt);

 fun add eq what f = Context.>> (what (fn xs => fn ctxt =>

   let val xs' = f ctxt xs in if eq_list eq (xs, xs') then NONE else SOME (xs', ctxt) end));

 in

 val _ = add (op =) (Syntax.add_typ_check 0 "standard") standard_typ_check;

 val _ = add (op aconv) (Syntax.add_term_check 0 "standard") standard_term_check;

 val _ = add (op aconv) (Syntax.add_term_check 100 "fixate") prepare_patterns;

 val _ = add (op aconv) (Syntax.add_term_uncheck 0 "standard") standard_term_uncheck;

 end;

 (** inner syntax operations **)

 local

 fun parse_failed ctxt pos msg kind =

   cat_error msg ("Failed to parse " ^ kind ^

     Markup.markup Markup.report (Context_Position.reported_text ctxt pos Markup.bad ""));

 fun parse_sort ctxt text =

   let

     val (syms, pos) = Syntax.parse_token ctxt Markup.sort text;

     val S = Syntax.standard_parse_sort ctxt (syn_of ctxt) (syms, pos)

       handle ERROR msg => parse_failed ctxt pos msg "sort";

   in Type.minimize_sort (tsig_of ctxt) S end;

 fun parse_typ ctxt text =

   let

     val (syms, pos) = Syntax.parse_token ctxt Markup.typ text;

     val T = Syntax.standard_parse_typ ctxt (syn_of ctxt) (get_sort ctxt) (syms, pos)

       handle ERROR msg => parse_failed ctxt pos msg "type";

   in T end;

 fun parse_term T ctxt text =

   let

     val {get_sort, map_const, map_free} = term_context ctxt;

     val (T', _) = Type_Infer.paramify_dummies T 0;

     val (markup, kind) =

       if T' = propT then (Markup.prop, "proposition") else (Markup.term, "term");

     val (syms, pos) = Syntax.parse_token ctxt markup text;

     val default_root = Config.get ctxt Syntax.default_root;

     val root =

       (case T' of

         Type (c, _) =>

           if c <> "prop" andalso Type.is_logtype (tsig_of ctxt) c

           then default_root else c

       | _ => default_root);

     fun check t = (Syntax.check_term ctxt (Type.constraint T' t); NONE)

       handle ERROR msg => SOME msg;

     val t =

       Syntax.standard_parse_term check get_sort map_const map_free

         ctxt (syn_of ctxt) root (syms, pos)

       handle ERROR msg => parse_failed ctxt pos msg kind;

   in t end;

 fun unparse_sort ctxt =

   Syntax.standard_unparse_sort {extern_class = Type.extern_class (tsig_of ctxt)}

     ctxt (syn_of ctxt);

 fun unparse_typ ctxt =

   let

     val tsig = tsig_of ctxt;

     val extern = {extern_class = Type.extern_class tsig, extern_type = Type.extern_type tsig};

   in Syntax.standard_unparse_typ extern ctxt (syn_of ctxt) end;

 fun unparse_term ctxt =

   let

     val tsig = tsig_of ctxt;

     val syntax = syntax_of ctxt;

     val consts = consts_of ctxt;

     val extern =

      {extern_class = Type.extern_class tsig,

       extern_type = Type.extern_type tsig,

       extern_const = Consts.extern consts};

   in

     Syntax.standard_unparse_term (Local_Syntax.idents_of syntax) extern ctxt

       (Local_Syntax.syn_of syntax) (not (Pure_Thy.old_appl_syntax (theory_of ctxt)))

   end;

 in

 val _ = Syntax.install_operations

   {parse_sort = parse_sort,

    parse_typ = parse_typ,

    parse_term = parse_term dummyT,

    parse_prop = parse_term propT,

    unparse_sort = unparse_sort,

    unparse_typ = unparse_typ,

    unparse_term = unparse_term};

 end;

 (** export results **)

 fun common_export is_goal inner outer =

   map (Assumption.export is_goal inner outer) #>

   Variable.export inner outer;

 val goal_export = common_export true;

 val export = common_export false;

 fun export_morphism inner outer =

   Assumption.export_morphism inner outer $>

   Variable.export_morphism inner outer;

 fun norm_export_morphism inner outer =

   export_morphism inner outer $>

   Morphism.thm_morphism Goal.norm_result;

 (** term bindings **)

 (* simult_matches *)

 fun simult_matches ctxt (t, pats) =

   (case Seq.pull (Unify.matchers (theory_of ctxt) (map (rpair t) pats)) of

     NONE => error "Pattern match failed!"

   | SOME (env, _) => Vartab.fold (fn (v, (_, t)) => cons (v, t)) (Envir.term_env env) []);

 (* bind_terms *)

 val bind_terms = fold (fn (xi, t) => fn ctxt =>

   ctxt

   |> Variable.bind_term (xi, Option.map (cert_term (set_mode mode_default ctxt)) t));

 (* auto_bind *)

 fun drop_schematic (b as (xi, SOME t)) = if Term.exists_subterm is_Var t then (xi, NONE) else b

   | drop_schematic b = b;

 fun auto_bind f ts ctxt = ctxt |> bind_terms (map drop_schematic (f (theory_of ctxt) ts));

 val auto_bind_goal = auto_bind Auto_Bind.goal;

 val auto_bind_facts = auto_bind Auto_Bind.facts;

 (* match_bind(_i) *)

 local

 fun gen_bind prep_terms gen raw_binds ctxt =

   let

     fun prep_bind (raw_pats, t) ctxt1 =

       let

         val T = Term.fastype_of t;

         val ctxt2 = Variable.declare_term t ctxt1;

         val pats = prep_terms (set_mode mode_pattern ctxt2) T raw_pats;

         val binds = simult_matches ctxt2 (t, pats);

       in (binds, ctxt2) end;

     val ts = prep_terms ctxt dummyT (map snd raw_binds);

     val (binds, ctxt') = apfst flat (fold_map prep_bind (map fst raw_binds ~~ ts) ctxt);

     val binds' =

       if gen then map #1 binds ~~ Variable.exportT_terms ctxt' ctxt (map #2 binds)

       else binds;

     val binds'' = map (apsnd SOME) binds';

     val ctxt'' =

       tap (Variable.warn_extra_tfrees ctxt)

        (if gen then

           ctxt (*sic!*) |> fold Variable.declare_term (map #2 binds') |> bind_terms binds''

         else ctxt' |> bind_terms binds'');

   in (ts, ctxt'') end;

 in

 fun read_terms ctxt T =

   map (Syntax.parse_term ctxt #> Type.constraint T) #> Syntax.check_terms ctxt;

 val match_bind = gen_bind read_terms;

 val match_bind_i = gen_bind (fn ctxt => fn _ => map (cert_term ctxt));

 end;

 (* propositions with patterns *)

 local

 fun prep_propp mode prep_props (context, args) =

   let

     fun prep (_, raw_pats) (ctxt, prop :: props) =

       let val ctxt' = Variable.declare_term prop ctxt

       in ((prop, prep_props (set_mode mode_pattern ctxt') raw_pats), (ctxt', props)) end;

     val (propp, (context', _)) = (fold_map o fold_map) prep args

       (context, prep_props (set_mode mode context) (maps (map fst) args));

   in (context', propp) end;

 fun gen_bind_propp mode parse_prop (ctxt, raw_args) =

   let

     val (ctxt', args) = prep_propp mode parse_prop (ctxt, raw_args);

     val binds = flat (flat (map (map (simult_matches ctxt')) args));

     val propss = map (map #1) args;

     (*generalize result: context evaluated now, binds added later*)

     val gen = Variable.exportT_terms ctxt' ctxt;

     fun gen_binds c = c |> bind_terms (map #1 binds ~~ map SOME (gen (map #2 binds)));

   in (ctxt' |> bind_terms (map (apsnd SOME) binds), (propss, gen_binds)) end;

 in

 val read_propp           = prep_propp mode_default Syntax.read_props;

 val cert_propp           = prep_propp mode_default (map o cert_prop);

 val read_propp_schematic = prep_propp mode_schematic Syntax.read_props;

 val cert_propp_schematic = prep_propp mode_schematic (map o cert_prop);

 val bind_propp             = gen_bind_propp mode_default Syntax.read_props;

 val bind_propp_i           = gen_bind_propp mode_default (map o cert_prop);

 val bind_propp_schematic   = gen_bind_propp mode_schematic Syntax.read_props;

 val bind_propp_schematic_i = gen_bind_propp mode_schematic (map o cert_prop);

 end;

 (** theorems **)

 (* fact_tac *)

 fun comp_incr_tac [] _ = no_tac

   | comp_incr_tac (th :: ths) i =

       (fn st => Goal.compose_hhf_tac (Drule.incr_indexes st th) i st) APPEND comp_incr_tac ths i;

 fun fact_tac facts = Goal.norm_hhf_tac THEN' comp_incr_tac facts;

 fun potential_facts ctxt prop =

   Facts.could_unify (facts_of ctxt) (Term.strip_all_body prop);

 fun some_fact_tac ctxt = SUBGOAL (fn (goal, i) => fact_tac (potential_facts ctxt goal) i);

 (* get_thm(s) *)

 local

 fun retrieve_thms pick ctxt (Facts.Fact s) =

       let

         val (_, pos) = Syntax.read_token s;

         val prop = Syntax.read_prop (set_mode mode_default ctxt) s

           |> singleton (Variable.polymorphic ctxt);

         fun prove_fact th =

           Goal.prove ctxt [] [] prop (K (ALLGOALS (fact_tac [th])));

         val res =

           (case get_first (try prove_fact) (potential_facts ctxt prop) of

             SOME res => res

           | NONE => error ("Failed to retrieve literal fact" ^ Position.str_of pos ^ ":\n" ^

               Syntax.string_of_term ctxt prop))

       in pick "" [res] end

   | retrieve_thms pick ctxt xthmref =

       let

         val thy = theory_of ctxt;

         val local_facts = facts_of ctxt;

         val thmref = Facts.map_name_of_ref (Facts.intern local_facts) xthmref;

         val name = Facts.name_of_ref thmref;

         val pos = Facts.pos_of_ref xthmref;

         val thms =

           if name = "" then [Thm.transfer thy Drule.dummy_thm]

           else

             (case Facts.lookup (Context.Proof ctxt) local_facts name of

               SOME (_, ths) =>

                (Context_Position.report ctxt pos (Markup.local_fact name);

                 map (Thm.transfer thy) (Facts.select thmref ths))

             | NONE => Global_Theory.get_fact (Context.Proof ctxt) thy xthmref);

       in pick name thms end;

 in

 val get_fact = retrieve_thms (K I);

 val get_fact_single = retrieve_thms Facts.the_single;

 fun get_thms ctxt = get_fact ctxt o Facts.named;

 fun get_thm ctxt = get_fact_single ctxt o Facts.named;

 end;

 (* facts *)

 local

 fun update_thms _ (b, NONE) ctxt = ctxt |> map_facts (Facts.del (full_name ctxt b))

   | update_thms do_props (b, SOME ths) ctxt = ctxt |> map_facts

       (Facts.add_local do_props (naming_of ctxt) (b, ths) #> snd);

 in

 fun note_thmss kind = fold_map (fn ((b, more_attrs), raw_facts) => fn ctxt =>

   let

     val pos = Binding.pos_of b;

     val name = full_name ctxt b;

     val _ = Context_Position.report ctxt pos (Markup.local_fact_decl name);

     val facts = Global_Theory.name_thmss false name raw_facts;

     fun app (th, attrs) x =

       swap (Library.foldl_map

         (Thm.proof_attributes (surround (Thm.kind kind) (attrs @ more_attrs))) (x, th));

     val (res, ctxt') = fold_map app facts ctxt;

     val thms = Global_Theory.name_thms false false name (flat res);

     val Mode {stmt, ...} = get_mode ctxt;

   in ((name, thms), ctxt' |> update_thms stmt (b, SOME thms)) end);

 fun put_thms do_props thms ctxt = ctxt

   |> map_naming (K local_naming)

   |> Context_Position.set_visible false

   |> update_thms do_props (apfst Binding.name thms)

   |> Context_Position.restore_visible ctxt

   |> restore_naming ctxt;

 end;

 (** basic logical entities **)

 (* variables *)

 fun declare_var (x, opt_T, mx) ctxt =

   let val T = (case opt_T of SOME T => T | NONE => Syntax.mixfixT mx)

   in ((x, T, mx), ctxt |> Variable.declare_constraints (Free (x, T))) end;

 local

 fun prep_vars prep_typ internal =

   fold_map (fn (b, raw_T, mx) => fn ctxt =>

     let

       val x = Name.of_binding b;

       val _ = Syntax.is_identifier (no_skolem internal x) orelse

         error ("Illegal variable name: " ^ quote (Binding.str_of b));

       fun cond_tvars T =

         if internal then T

         else Type.no_tvars T handle TYPE (msg, _, _) => error msg;

       val opt_T = Option.map (cond_tvars o cert_typ ctxt o prep_typ ctxt) raw_T;

       val (_, ctxt') = ctxt |> declare_var (x, opt_T, mx);

     in ((b, opt_T, mx), ctxt') end);

 in

 val read_vars = prep_vars Syntax.parse_typ false;

 val cert_vars = prep_vars (K I) true;

 end;

 (* authentic syntax *)

 val _ = Context.>>

   (Context.map_theory

     (Sign.add_advanced_trfuns

       (Syntax.type_ast_trs

         {read_class = read_class,

           read_type = fn ctxt => #1 o dest_Type o read_type_name_proper ctxt false}, [], [], [])));

 local

 fun const_ast_tr intern ctxt [Syntax.Variable c] =

       let

         val Const (c', _) = read_const_proper ctxt false c;

         val d = if intern then Syntax.mark_const c' else c;

       in Syntax.Constant d end

   | const_ast_tr _ _ asts = raise Syntax.AST ("const_ast_tr", asts);

 val typ = Simple_Syntax.read_typ;

 in

 val _ = Context.>> (Context.map_theory

  (Sign.add_syntax_i

    [("_context_const", typ "id => logic", Delimfix "CONST _"),

     ("_context_const", typ "id => aprop", Delimfix "CONST _"),

     ("_context_const", typ "longid => logic", Delimfix "CONST _"),

     ("_context_const", typ "longid => aprop", Delimfix "CONST _"),

     ("_context_xconst", typ "id => logic", Delimfix "XCONST _"),

     ("_context_xconst", typ "id => aprop", Delimfix "XCONST _"),

     ("_context_xconst", typ "longid => logic", Delimfix "XCONST _"),

     ("_context_xconst", typ "longid => aprop", Delimfix "XCONST _")] #>

   Sign.add_advanced_trfuns

     ([("_context_const", const_ast_tr true), ("_context_xconst", const_ast_tr false)], [], [], [])));

 end;

 (* notation *)

 local

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

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

   | type_syntax _ = NONE;

 fun const_syntax _ (Free (x, T), mx) = SOME (Local_Syntax.Fixed, (x, T, mx))

   | const_syntax ctxt (Const (c, _), mx) =

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

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

       | NONE => NONE)

   | const_syntax _ _ = NONE;

 fun gen_notation syntax add mode args ctxt =

   ctxt |> map_syntax

     (Local_Syntax.update_modesyntax (theory_of ctxt) add mode (map_filter (syntax ctxt) args));

 in

 val type_notation = gen_notation (K type_syntax);

 val notation = gen_notation const_syntax;

 fun target_type_notation add mode args phi =

   let

     val args' = args |> map_filter (fn (T, mx) =>

       let

         val T' = Morphism.typ phi T;

         val similar = (case (T, T') of (Type (c, _), Type (c', _)) => c = c' | _ => false);

       in if similar then SOME (T', mx) else NONE end);

   in Context.mapping (Sign.type_notation add mode args') (type_notation add mode args') end;

 fun target_notation add mode args phi =

   let

     val args' = args |> map_filter (fn (t, mx) =>

       let val t' = Morphism.term phi t

       in if Term.aconv_untyped (t, t') then SOME (t', mx) else NONE end);

   in Context.mapping (Sign.notation add mode args') (notation add mode args') end;

 end;

 (* aliases *)

 fun class_alias b c ctxt = (map_tsig o apfst) (Type.class_alias (naming_of ctxt) b c) ctxt;

 fun type_alias b c ctxt = (map_tsig o apfst) (Type.type_alias (naming_of ctxt) b c) ctxt;

 fun const_alias b c ctxt = (map_consts o apfst) (Consts.alias (naming_of ctxt) b c) ctxt;

 (* local constants *)

 fun add_const_constraint (c, opt_T) ctxt =

   let

     fun prepT raw_T =

       let val T = cert_typ ctxt raw_T

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

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

 fun add_abbrev mode (b, raw_t) ctxt =

   let

     val t0 = cert_term (ctxt |> set_mode mode_abbrev) raw_t

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

     val [t] = Variable.exportT_terms (Variable.declare_term t0 ctxt) ctxt [t0];

     val ((lhs, rhs), consts') = consts_of ctxt

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

   in

     ctxt

     |> (map_consts o apfst) (K consts')

     |> Variable.declare_term rhs

     |> pair (lhs, rhs)

   end;

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

 (* fixes *)

 fun add_fixes raw_vars ctxt =

   let

     val (vars, _) = cert_vars raw_vars ctxt;

     val (xs', ctxt') = Variable.add_fixes (map (Name.of_binding o #1) vars) ctxt;

     val ctxt'' =

       ctxt'

       |> fold_map declare_var (map2 (fn x' => fn (_, T, mx) => (x', T, mx)) xs' vars)

       |-> (map_syntax o Local_Syntax.add_syntax (theory_of ctxt) o map (pair Local_Syntax.Fixed));

     val _ = (vars ~~ xs') |> List.app (fn ((b, _, _), x') =>

       Context_Position.report ctxt (Binding.pos_of b) (Markup.fixed_decl x'));

   in (xs', ctxt'') end;

 (* fixes vs. frees *)

 fun auto_fixes (ctxt, (propss, x)) =

   ((fold o fold) Variable.auto_fixes propss ctxt, (propss, x));

 fun bind_fixes xs ctxt =

   let

     val (_, ctxt') = ctxt |> add_fixes (map (fn x => (Binding.name x, NONE, NoSyn)) xs);

     fun bind (t as Free (x, T)) =

           if member (op =) xs x then

             (case lookup_skolem ctxt' x of SOME x' => Free (x', T) | NONE => t)

           else t

       | bind (t $ u) = bind t $ bind u

       | bind (Abs (x, T, t)) = Abs (x, T, bind t)

       | bind a = a;

   in (bind, ctxt') end;

 (** assumptions **)

 local

 fun gen_assms prepp exp args ctxt =

   let

     val cert = Thm.cterm_of (theory_of ctxt);

     val (propss, ctxt1) = swap (prepp (ctxt, map snd args));

     val _ = Variable.warn_extra_tfrees ctxt ctxt1;

     val (premss, ctxt2) = fold_burrow (Assumption.add_assms exp o map cert) propss ctxt1;

   in

     ctxt2

     |> auto_bind_facts (flat propss)

     |> note_thmss "" (map fst args ~~ map (map (fn th => ([th], []))) premss)

   end;

 in

 val add_assms = gen_assms (apsnd #1 o bind_propp);

 val add_assms_i = gen_assms (apsnd #1 o bind_propp_i);

 end;

 (** cases **)

 local

 fun rem_case name = remove (fn (x: string, (y, _)) => x = y) name;

 fun add_case _ ("", _) cases = cases

   | add_case _ (name, NONE) cases = rem_case name cases

   | add_case is_proper (name, SOME c) cases = (name, (c, is_proper)) :: rem_case name cases;

 fun prep_case name fxs c =

   let

     fun replace (opt_x :: xs) ((y, T) :: ys) = (the_default y opt_x, T) :: replace xs ys

       | replace [] ys = ys

       | replace (_ :: _) [] = error ("Too many parameters for case " ^ quote name);

     val Rule_Cases.Case {fixes, assumes, binds, cases} = c;

     val fixes' = replace fxs fixes;

     val binds' = map drop_schematic binds;

   in

     if null (fold (Term.add_tvarsT o snd) fixes []) andalso

       null (fold (fold Term.add_vars o snd) assumes []) then

         Rule_Cases.Case {fixes = fixes', assumes = assumes, binds = binds', cases = cases}

     else error ("Illegal schematic variable(s) in case " ^ quote name)

   end;

 fun fix (x, T) ctxt =

   let

     val (bind, ctxt') = bind_fixes [x] ctxt;

     val t = bind (Free (x, T));

   in (t, ctxt' |> Variable.declare_constraints t) end;

 in

 fun add_cases is_proper = map_cases o fold (add_case is_proper);

 fun case_result c ctxt =

   let

     val Rule_Cases.Case {fixes, ...} = c;

     val (ts, ctxt') = ctxt |> fold_map fix fixes;

     val Rule_Cases.Case {assumes, binds, cases, ...} = Rule_Cases.apply ts c;

   in

     ctxt'

     |> bind_terms (map drop_schematic binds)

     |> add_cases true (map (apsnd SOME) cases)

     |> pair (assumes, (binds, cases))

   end;

 val apply_case = apfst fst oo case_result;

 fun get_case ctxt name xs =

   (case AList.lookup (op =) (cases_of ctxt) name of

     NONE => error ("Unknown case: " ^ quote name)

   | SOME (c, _) => prep_case name xs c);

 end;

 (** print context information **)

 (* local syntax *)

 val print_syntax = Syntax.print_syntax o syn_of;

 (* abbreviations *)

 fun pretty_abbrevs show_globals ctxt =

   let

     val ((space, consts), (_, globals)) =

       pairself (#constants o Consts.dest) (#consts (rep_context ctxt));

     fun add_abbr (_, (_, NONE)) = I

       | add_abbr (c, (T, SOME t)) =

           if not show_globals andalso Symtab.defined globals c then I

           else cons (c, Logic.mk_equals (Const (c, T), t));

     val abbrevs = Name_Space.extern_table (space, Symtab.make (Symtab.fold add_abbr consts []));

   in

     if null abbrevs then []

     else [Pretty.big_list "abbreviations:" (map (pretty_term_abbrev ctxt o #2) abbrevs)]

   end;

 val print_abbrevs = Pretty.writeln o Pretty.chunks o pretty_abbrevs true;

 (* term bindings *)

 fun pretty_binds ctxt =

   let

     val binds = Variable.binds_of ctxt;

     fun prt_bind (xi, (T, t)) = pretty_term_abbrev ctxt (Logic.mk_equals (Var (xi, T), t));

   in

     if Vartab.is_empty binds then []

     else [Pretty.big_list "term bindings:" (map prt_bind (Vartab.dest binds))]

   end;

 val print_binds = Pretty.writeln o Pretty.chunks o pretty_binds;

 (* local theorems *)

 fun pretty_lthms ctxt =

   let

     val local_facts = facts_of ctxt;

     val props = Facts.props local_facts;

     val facts =

       (if null props then [] else [("<unnamed>", props)]) @

       Facts.dest_static [] local_facts;

   in

     if null facts then []

     else [Pretty.big_list "facts:" (map #1 (sort_wrt (#1 o #2) (map (`(pretty_fact ctxt)) facts)))]

   end;

 val print_lthms = Pretty.writeln o Pretty.chunks o pretty_lthms;

 (* local contexts *)

 local

 fun pretty_case (name, (fixes, ((asms, (lets, cs)), ctxt))) =

   let

     val prt_term = Syntax.pretty_term ctxt;

     fun prt_let (xi, t) = Pretty.block

       [Pretty.quote (prt_term (Var (xi, Term.fastype_of t))), Pretty.str " =", Pretty.brk 1,

         Pretty.quote (prt_term t)];

     fun prt_asm (a, ts) = Pretty.block (Pretty.breaks

       ((if a = "" then [] else [Pretty.str (a ^ ":")]) @ map (Pretty.quote o prt_term) ts));

     fun prt_sect _ _ _ [] = []

       | prt_sect s sep prt xs =

           [Pretty.block (Pretty.breaks (Pretty.str s ::

             flat (separate sep (map (single o prt) xs))))];

   in

     Pretty.block (Pretty.fbreaks

       (Pretty.str (name ^ ":") ::

         prt_sect "fix" [] (Pretty.str o fst) fixes @

         prt_sect "let" [Pretty.str "and"] prt_let

           (map_filter (fn (xi, SOME t) => SOME (xi, t) | _ => NONE) lets) @

         (if forall (null o #2) asms then []

           else prt_sect "assume" [Pretty.str "and"] prt_asm asms) @

         prt_sect "subcases:" [] (Pretty.str o fst) cs))

   end;

 in

 fun pretty_cases ctxt =

   let

     fun add_case (_, (_, false)) = I

       | add_case (name, (c as Rule_Cases.Case {fixes, ...}, true)) =

           cons (name, (fixes, case_result c ctxt));

     val cases = fold add_case (cases_of ctxt) [];

   in

     if null cases then []

     else [Pretty.big_list "cases:" (map pretty_case cases)]

   end;

 val print_cases = Pretty.writeln o Pretty.chunks o pretty_cases;

 end;

 (* core context *)

 val debug = Unsynchronized.ref false;

 val verbose = Unsynchronized.ref false;

 fun pretty_ctxt ctxt =

   if not (! debug) then []

   else

     let

       val prt_term = Syntax.pretty_term ctxt;

       (*structures*)

       val {structs, ...} = Local_Syntax.idents_of (syntax_of ctxt);

       val prt_structs =

         if null structs then []

         else [Pretty.block (Pretty.str "structures:" :: Pretty.brk 1 ::

           Pretty.commas (map Pretty.str structs))];

       (*fixes*)

       fun prt_fix (x, x') =

         if x = x' then Pretty.str x

         else Pretty.block [Pretty.str x, Pretty.str " =", Pretty.brk 1, prt_term (Syntax.free x')];

       val fixes =

         rev (filter_out ((can Name.dest_internal orf member (op =) structs) o #1)

           (Variable.fixes_of ctxt));

       val prt_fixes =

         if null fixes then []

         else [Pretty.block (Pretty.str "fixed variables:" :: Pretty.brk 1 ::

           Pretty.commas (map prt_fix fixes))];

       (*prems*)

       val prems = Assumption.all_prems_of ctxt;

       val prt_prems =

         if null prems then []

         else [Pretty.big_list "prems:" (map (Display.pretty_thm ctxt) prems)];

     in prt_structs @ prt_fixes @ prt_prems end;

 (* main context *)

 fun pretty_context ctxt =

   let

     val is_verbose = ! verbose;

     fun verb f x = if is_verbose then f (x ()) else [];

     val prt_term = Syntax.pretty_term ctxt;

     val prt_typ = Syntax.pretty_typ ctxt;

     val prt_sort = Syntax.pretty_sort ctxt;

     (*theory*)

     val pretty_thy = Pretty.block

       [Pretty.str "theory:", Pretty.brk 1, Context.pretty_thy (theory_of ctxt)];

     (*defaults*)

     fun prt_atom prt prtT (x, X) = Pretty.block

       [prt x, Pretty.str " ::", Pretty.brk 1, prtT X];

     fun prt_var (x, ~1) = prt_term (Syntax.free x)

       | prt_var xi = prt_term (Syntax.var xi);

     fun prt_varT (x, ~1) = prt_typ (TFree (x, []))

       | prt_varT xi = prt_typ (TVar (xi, []));

     val prt_defT = prt_atom prt_var prt_typ;

     val prt_defS = prt_atom prt_varT prt_sort;

     val (types, sorts) = Variable.constraints_of ctxt;

   in

     verb single (K pretty_thy) @

     pretty_ctxt ctxt @

     verb (pretty_abbrevs false) (K ctxt) @

     verb pretty_binds (K ctxt) @

     verb pretty_lthms (K ctxt) @

     verb pretty_cases (K ctxt) @

     verb single (fn () => Pretty.big_list "type constraints:" (map prt_defT (Vartab.dest types))) @

     verb single (fn () => Pretty.big_list "default sorts:" (map prt_defS (Vartab.dest sorts)))

   end;

 end;

 val show_abbrevs = ProofContext.show_abbrevs;