src/Pure/Isar/proof_context.ML

renamed export to export_standard (again!), because it includes Drule.local_standard';
added abs_def (from locale.ML);

(*  Title:      Pure/Isar/proof_context.ML
    ID:         $Id$
    Author:     Markus Wenzel, TU Muenchen

The key concept of Isar proof contexts.
*)

val show_structs = ref false;

signature PROOF_CONTEXT =
sig
  type context (*= Context.proof*)
  type export
  val theory_of: context -> theory
  val init: theory -> context
  val set_body: bool -> context -> context
  val restore_body: context -> context -> context
  val assms_of: context -> term list
  val prems_of: context -> thm list
  val fact_index_of: context -> FactIndex.T
  val is_fixed: context -> string -> bool
  val is_known: context -> string -> bool
  val transfer: theory -> context -> context
  val pretty_term: context -> term -> Pretty.T
  val pretty_typ: context -> typ -> Pretty.T
  val pretty_sort: context -> sort -> Pretty.T
  val pp: context -> Pretty.pp
  val pretty_thm: context -> thm -> Pretty.T
  val pretty_thms: context -> thm list -> Pretty.T
  val pretty_fact: context -> string * thm list -> Pretty.T
  val pretty_proof: context -> Proofterm.proof -> Pretty.T
  val pretty_proof_of: context -> bool -> thm -> Pretty.T
  val string_of_typ: context -> typ -> string
  val string_of_term: context -> term -> string
  val string_of_thm: context -> thm -> string
  val used_types: context -> string list
  val default_type: context -> string -> typ option
  val read_typ: context -> string -> typ
  val read_typ_syntax: context -> string -> typ
  val read_typ_abbrev: context -> string -> typ
  val cert_typ: context -> typ -> typ
  val cert_typ_syntax: context -> typ -> typ
  val cert_typ_abbrev: context -> typ -> typ
  val get_skolem: context -> string -> string
  val revert_skolem: context -> string -> string
  val extern_skolem: context -> term -> term
  val read_termTs: context -> (string -> bool) -> (indexname -> typ option)
    -> (indexname -> sort option) -> string list -> (string * typ) list
    -> term list * (indexname * typ) list
  val read_termTs_schematic: context -> (string -> bool) -> (indexname -> typ option)
    -> (indexname -> sort option) -> string list -> (string * typ) list
    -> term list * (indexname * typ) list
  val read_term_legacy: context -> string -> term
  val read_term: context -> string -> term
  val read_prop: context -> string -> term
  val read_prop_schematic: context -> string -> term
  val read_terms: context -> string list -> term list
  val read_term_pats: typ -> context -> string list -> term list
  val read_prop_pats: context -> string list -> term list
  val cert_term: context -> term -> term
  val cert_prop: context -> term -> term
  val cert_term_pats: typ -> context -> term list -> term list
  val cert_prop_pats: context -> term list -> term list
  val declare_term: term -> context -> context
  val infer_type: context -> string -> typ
  val inferred_param: string -> context -> (string * typ) * context
  val inferred_fixes: context -> (string * typ) list * context
  val read_tyname: context -> string -> typ
  val read_const: context -> string -> term
  val warn_extra_tfrees: context -> context -> context
  val generalize: context -> context -> term list -> term list
  val export_standard: context -> context -> thm -> thm
  val exports: context -> context -> thm -> thm Seq.seq
  val goal_exports: context -> context -> thm -> thm Seq.seq
  val drop_schematic: indexname * term option -> indexname * term option
  val add_binds: (indexname * string option) list -> context -> context
  val add_binds_i: (indexname * term option) list -> context -> context
  val auto_bind_goal: term list -> context -> context
  val auto_bind_facts: term list -> context -> context
  val match_bind: bool -> (string list * string) list -> context -> term list * context
  val match_bind_i: bool -> (term list * term) list -> context -> term list * context
  val read_propp: context * (string * (string list * string list)) list list
    -> context * (term * (term list * term list)) list list
  val cert_propp: context * (term * (term list * term list)) list list
    -> context * (term * (term list * term list)) list list
  val read_propp_schematic: context * (string * (string list * string list)) list list
    -> context * (term * (term list * term list)) list list
  val cert_propp_schematic: context * (term * (term list * term list)) list list
    -> context * (term * (term list * term list)) list list
  val bind_propp: context * (string * (string list * string list)) list list
    -> context * (term list list * (context -> context))
  val bind_propp_i: context * (term * (term list * term list)) list list
    -> context * (term list list * (context -> context))
  val bind_propp_schematic: context * (string * (string list * string list)) list list
    -> context * (term list list * (context -> context))
  val bind_propp_schematic_i: context * (term * (term list * term list)) list list
    -> context * (term list list * (context -> context))
  val fact_tac: thm list -> int -> tactic
  val some_fact_tac: context -> int -> tactic
  val get_thm: context -> thmref -> thm
  val get_thm_closure: context -> thmref -> thm
  val get_thms: context -> thmref -> thm list
  val get_thms_closure: context -> thmref -> thm list
  val valid_thms: context -> string * thm list -> bool
  val lthms_containing: context -> FactIndex.spec -> (string * thm list) list
  val extern_thm: context -> string -> xstring
  val qualified_names: context -> context
  val no_base_names: context -> context
  val custom_accesses: (string list -> string list list) -> context -> context
  val restore_naming: context -> context -> context
  val hide_thms: bool -> string list -> context -> context
  val put_thms: string * thm list option -> context -> context
  val note_thmss:
    ((bstring * attribute list) * (thmref * attribute list) list) list ->
      context -> (bstring * thm list) list * context
  val note_thmss_i:
    ((bstring * attribute list) * (thm list * attribute list) list) list ->
      context -> (bstring * thm list) list * context
  val read_vars: (string * string option * mixfix) list -> context ->
    (string * typ option * mixfix) list * context
  val cert_vars: (string * typ option * mixfix) list -> context ->
    (string * typ option * mixfix) list * context
  val read_vars_legacy: (string * string option * mixfix) list -> context ->
    (string * typ option * mixfix) list * context
  val cert_vars_legacy: (string * typ option * mixfix) list -> context ->
    (string * typ option * mixfix) list * context
  val add_fixes: (string * string option * mixfix) list -> context -> string list * context
  val add_fixes_i: (string * typ option * mixfix) list -> context -> string list * context
  val add_fixes_legacy: (string * typ option * mixfix) list -> context -> string list * context
  val fix_frees: term -> context -> context
  val auto_fixes: context * (term list list * 'a) -> context * (term list list * 'a)
  val bind_fixes: string list -> context -> (term -> term) * context
  val add_assms: export ->
    ((string * attribute list) * (string * (string list * string list)) list) list ->
    context -> (bstring * thm list) list * context
  val add_assms_i: export ->
    ((string * attribute list) * (term * (term list * term list)) list) list ->
    context -> (bstring * thm list) list * context
  val assume_export: export
  val presume_export: export
  val add_view: context -> cterm list -> context -> context
  val export_view: cterm list -> context -> context -> thm -> thm
  val mk_def: context -> (string * term) list -> term list
  val cert_def: context -> term -> string * term
  val abs_def: term -> (string * typ) * term
  val def_export: export
  val add_def: string * term -> context -> ((string * typ) * thm) * context
  val add_cases: bool -> (string * RuleCases.T option) list -> context -> context
  val apply_case: RuleCases.T -> context -> (string * term list) list * context
  val get_case: context -> string -> string option list -> RuleCases.T
  val verbose: bool ref
  val setmp_verbose: ('a -> 'b) -> 'a -> 'b
  val print_syntax: context -> unit
  val print_binds: context -> unit
  val print_lthms: context -> unit
  val print_cases: context -> unit
  val prems_limit: int ref
  val pretty_ctxt: context -> Pretty.T list
  val pretty_context: context -> Pretty.T list
end;

structure ProofContext: PROOF_CONTEXT =
struct

type context = Context.proof;

val theory_of = Context.theory_of_proof;
val init = Context.init_proof;



(** Isar proof context information **)

type export = bool -> cterm list -> thm -> thm Seq.seq;

datatype ctxt =
  Ctxt of
   {syntax:                                      (*global/local syntax, structs, mixfixed*)
      (Syntax.syntax * Syntax.syntax * (Syntax.syntax -> Syntax.syntax)) *
      string list * string list,
    fixes: bool * (string * string) list,        (*fixes: !!x. _ with proof body flag*)
    assms:
      ((cterm list * export) list *              (*assumes and views: A ==> _*)
        (string * thm list) list),               (*prems: A |- A*)
    binds: (term * typ) Vartab.table,            (*term bindings*)
    thms: NameSpace.naming *                     (*local thms*)
      thm list NameSpace.table * FactIndex.T,
    cases: (string * (RuleCases.T * bool)) list, (*local contexts*)
    defaults:
      typ Vartab.table *                         (*type constraints*)
      sort Vartab.table *                        (*default sorts*)
      string list *                              (*used type variables*)
      term list Symtab.table};                   (*type variable occurrences*)

fun make_ctxt (syntax, fixes, assms, binds, thms, cases, defaults) =
  Ctxt {syntax = syntax, fixes = fixes, assms = assms, binds = binds,
    thms = thms, cases = cases, defaults = defaults};

structure ContextData = ProofDataFun
(
  val name = "Isar/context";
  type T = ctxt;
  fun init thy =
    make_ctxt (((Sign.syn_of thy, Sign.syn_of thy, I), [], []), (false, []), ([], []),
      Vartab.empty, (NameSpace.default_naming, NameSpace.empty_table, FactIndex.empty), [],
      (Vartab.empty, Vartab.empty, [], Symtab.empty));
  fun print _ _ = ();
);

val _ = Context.add_setup ContextData.init;

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

fun map_context f =
  ContextData.map (fn Ctxt {syntax, fixes, assms, binds, thms, cases, defaults} =>
    make_ctxt (f (syntax, fixes, assms, binds, thms, cases, defaults)));

fun map_syntax f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (f syntax, fixes, assms, binds, thms, cases, defaults));

fun map_fixes f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (syntax, f fixes, assms, binds, thms, cases, defaults));

fun map_assms f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (syntax, fixes, f assms, binds, thms, cases, defaults));

fun map_binds f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (syntax, fixes, assms, f binds, thms, cases, defaults));

fun map_thms f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (syntax, fixes, assms, binds, f thms, cases, defaults));

fun map_naming f = map_thms (fn (naming, table, index) => (f naming, table, index));

fun map_cases f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (syntax, fixes, assms, binds, thms, f cases, defaults));

fun map_defaults f = map_context (fn (syntax, fixes, assms, binds, thms, cases, defaults) =>
  (syntax, fixes, assms, binds, thms, cases, f defaults));

val syntax_of = #syntax o rep_context;

val is_body = #1 o #fixes o rep_context;
fun set_body b = map_fixes (fn (_, fixes) => (b, fixes));
fun restore_body ctxt = set_body (is_body ctxt);

val fixes_of = #2 o #fixes o rep_context;
val fixed_names_of = map #2 o fixes_of;

val assumptions_of = #1 o #assms o rep_context;
val assms_of = map Thm.term_of o List.concat o map #1 o assumptions_of;
val prems_of = List.concat o map #2 o #2 o #assms o rep_context;

val binds_of = #binds o rep_context;

val thms_of = #thms o rep_context;
val fact_index_of = #3 o thms_of;

val cases_of = #cases o rep_context;

val defaults_of = #defaults o rep_context;
val type_occs_of = #4 o defaults_of;

fun is_fixed ctxt x = exists (equal x o #2) (fixes_of ctxt);
fun is_known ctxt x = Vartab.defined (#1 (defaults_of ctxt)) (x, ~1) orelse is_fixed ctxt x;



(** syntax **)

(* translation functions *)

fun context_tr' ctxt =
  let
    val (_, structs, mixfixed) = syntax_of ctxt;

    fun tr' (t $ u) = tr' t $ tr' u
      | tr' (Abs (x, T, t)) = Abs (x, T, tr' t)
      | tr' (t as Free (x, T)) =
          let val i = Library.find_index_eq x structs + 1 in
            if i = 0 andalso member (op =) mixfixed x then Const (Syntax.fixedN ^ x, T)
            else if i = 1 andalso not (! show_structs) then
              Syntax.const "_struct" $ Syntax.const "_indexdefault"
            else t
          end
      | tr' a = a;
  in tr' end;


(* add syntax *)

local

fun check_mixfix (x, _, mx) =
  if mx <> NoSyn andalso mx <> Structure andalso
      (can Syntax.dest_internal x orelse can Syntax.dest_skolem x) then
    error ("Illegal mixfix syntax for internal/skolem constant " ^ quote x)
  else ();

fun mixfix x NONE mx = (Syntax.fixedN ^ x, TypeInfer.mixfixT mx, Syntax.fix_mixfix x mx)
  | mixfix x (SOME T) mx = (Syntax.fixedN ^ x, T, Syntax.fix_mixfix x mx);

fun prep_mixfix (_, _, Structure) = NONE
  | prep_mixfix (x, opt_T, mx) = SOME (mixfix x opt_T mx);

fun prep_mixfix' (_, _, Structure) = NONE
  | prep_mixfix' (x, _, NoSyn) = NONE
  | prep_mixfix' (x, opt_T, _) = SOME (x, mixfix x opt_T (Syntax.literal x));

fun prep_struct (x, _, Structure) = SOME x
  | prep_struct _ = NONE;

fun mk trs = map Syntax.mk_trfun trs;

fun extend_syntax thy extend (global_syn, syn, mk_syn) =
  let
    val thy_syn = Sign.syn_of thy;
    val mk_syn' = extend o mk_syn;
    val (global_syn', syn') =
      if Syntax.eq_syntax (global_syn, thy_syn)
      then (global_syn, extend syn)
      else (thy_syn, mk_syn' thy_syn);    (*potentially expensive*)
  in (global_syn', syn', mk_syn') end;

in

fun add_syntax decls ctxt = ctxt |> map_syntax (fn syntax =>
  let
    val (syns, structs, mixfixed) = syntax;
    val thy = theory_of ctxt;

    val is_logtype = Sign.is_logtype thy;
    val structs' = structs @ List.mapPartial prep_struct decls;
    val mxs = List.mapPartial (tap check_mixfix #> prep_mixfix) decls;
    val (fixed, mxs_output) = Library.split_list (List.mapPartial prep_mixfix' decls);

    val extend =
      Syntax.extend_const_gram is_logtype ("", false) mxs_output
      #> Syntax.extend_const_gram is_logtype ("", true) mxs;
    val syns' = extend_syntax thy extend syns;
  in (syns', structs', fixed @ mixfixed) end);

fun syn_of' thy ctxt =
  let
    val (syns, structs, _) = syntax_of ctxt;
    val (atrs, trs, trs', atrs') = Syntax.struct_trfuns structs;
    val extend = Syntax.extend_trfuns (mk atrs, mk trs, mk trs', mk atrs');
  in #2 (extend_syntax thy extend syns) end;

fun syn_of ctxt = syn_of' (theory_of ctxt) ctxt;

end;

fun transfer thy = add_syntax [] o Context.transfer_proof thy;



(** pretty printing **)

fun pretty_term' thy ctxt t = Sign.pretty_term' (syn_of' thy ctxt) thy (context_tr' ctxt t);
fun pretty_term ctxt t = pretty_term' (theory_of ctxt) ctxt (context_tr' ctxt t);
fun pretty_typ ctxt T = Sign.pretty_typ (theory_of ctxt) T;
fun pretty_sort ctxt S = Sign.pretty_sort (theory_of ctxt) S;
fun pretty_classrel ctxt cs = Sign.pretty_classrel (theory_of ctxt) cs;
fun pretty_arity ctxt ar = Sign.pretty_arity (theory_of ctxt) ar;

fun pp ctxt = Pretty.pp (pretty_term ctxt, pretty_typ ctxt, pretty_sort ctxt,
  pretty_classrel ctxt, pretty_arity ctxt);

fun pretty_thm ctxt th =
  Display.pretty_thm_aux (pp ctxt) false true (assms_of ctxt) th;

fun pretty_thms ctxt [th] = pretty_thm ctxt th
  | pretty_thms ctxt ths = Pretty.blk (0, Pretty.fbreaks (map (pretty_thm ctxt) ths));

fun pretty_fact ctxt ("", ths) = pretty_thms ctxt ths
  | pretty_fact ctxt (a, [th]) =
      Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1, pretty_thm ctxt th]
  | pretty_fact ctxt (a, ths) =
      Pretty.block (Pretty.fbreaks (Pretty.str (a ^ ":") :: map (pretty_thm ctxt) ths));

fun pretty_proof ctxt prf =
  pretty_term' (ProofSyntax.proof_syntax prf (theory_of ctxt)) ctxt
    (ProofSyntax.term_of_proof prf);

fun pretty_proof_of ctxt full th =
  pretty_proof ctxt (ProofSyntax.proof_of full th);

val string_of_typ = Pretty.string_of oo pretty_typ;
val string_of_term = Pretty.string_of oo pretty_term;
val string_of_thm = Pretty.string_of oo pretty_thm;



(** default sorts and types **)

val def_sort = Vartab.lookup o #2 o defaults_of;

fun def_type ctxt pattern xi =
  let val {binds, defaults = (types, _, _, _), ...} = rep_context ctxt in
    (case Vartab.lookup types xi of
      NONE =>
        if pattern then NONE
        else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #2)
    | some => some)
  end;

val used_types = #3 o defaults_of;

fun default_type ctxt x = Vartab.lookup (#1 (defaults_of ctxt)) (x, ~1);



(** prepare types **)

local

fun read_typ_aux read ctxt s =
  read (syn_of ctxt) (theory_of ctxt, def_sort ctxt) s;

fun cert_typ_aux cert ctxt raw_T =
  cert (theory_of ctxt) raw_T handle TYPE (msg, _, _) => error msg;

in

val read_typ        = read_typ_aux Sign.read_typ';
val read_typ_syntax = read_typ_aux Sign.read_typ_syntax';
val read_typ_abbrev = read_typ_aux Sign.read_typ_abbrev';
val cert_typ        = cert_typ_aux Sign.certify_typ;
val cert_typ_syntax = cert_typ_aux Sign.certify_typ_syntax;
val cert_typ_abbrev = cert_typ_aux Sign.certify_typ_abbrev;

end;


(* internalize Skolem constants *)

val lookup_skolem = AList.lookup (op =) o fixes_of;
fun get_skolem ctxt x = the_default x (lookup_skolem ctxt x);

fun no_skolem internal x =
  if can Syntax.dest_skolem x then
    error ("Illegal reference to internal Skolem constant: " ^ quote x)
  else if not internal andalso can Syntax.dest_internal x then
    error ("Illegal reference to internal variable: " ^ quote x)
  else x;

fun intern_skolem ctxt internal =
  let
    fun intern (t as Free (x, T)) =
          if internal x then t
          else
            (case lookup_skolem ctxt (no_skolem false x) of
              SOME x' => Free (x', T)
            | NONE => t)
      | intern (t $ u) = intern t $ intern u
      | intern (Abs (x, T, t)) = Abs (x, T, intern t)
      | intern a = a;
  in intern end;


(* externalize Skolem constants -- approximation only! *)

fun rev_skolem ctxt =
  let val rev_fixes = map Library.swap (fixes_of ctxt)
  in AList.lookup (op =) rev_fixes end;

fun revert_skolem ctxt x =
  (case rev_skolem ctxt x of
    SOME x' => x'
  | NONE => perhaps (try Syntax.dest_skolem) x);

fun extern_skolem ctxt =
  let
    val revert = rev_skolem ctxt;
    fun extern (t as Free (x, T)) =
        (case revert x of
          SOME x' => Free (if lookup_skolem ctxt x' = SOME x then x' else NameSpace.hidden x', T)
        | NONE => t)
      | extern (t $ u) = extern t $ extern u
      | extern (Abs (x, T, t)) = Abs (x, T, extern t)
      | extern a = a;
  in extern end



(** prepare terms and propositions **)

(*
  (1) read / certify wrt. theory of context
  (2) intern Skolem constants
  (3) expand term bindings
*)


(* read wrt. theory *)     (*exception ERROR*)

fun read_def_termTs freeze pp syn thy (types, sorts, used) sTs =
  Sign.read_def_terms' pp (Sign.is_logtype thy) syn (thy, types, sorts) used freeze sTs;

fun read_def_termT freeze pp syn thy defaults sT =
  apfst hd (read_def_termTs freeze pp syn thy defaults [sT]);

fun read_term_thy freeze pp syn thy defaults s =
  #1 (read_def_termT freeze pp syn thy defaults (s, TypeInfer.logicT));

fun read_prop_thy freeze pp syn thy defaults s =
  #1 (read_def_termT freeze pp syn thy defaults (s, propT));

fun read_terms_thy freeze pp syn thy defaults =
  #1 o read_def_termTs freeze pp syn thy defaults o map (rpair TypeInfer.logicT);

fun read_props_thy freeze pp syn thy defaults =
  #1 o read_def_termTs freeze pp syn thy defaults o map (rpair propT);


(* norm_term *)

(*beta normal form for terms (not eta normal form), chase variables in
  bindings environment (code taken from Pure/envir.ML)*)

fun unifyT ctxt (T, U) =
  let val maxidx = Int.max (Term.maxidx_of_typ T, Term.maxidx_of_typ U)
  in #1 (Sign.typ_unify (theory_of ctxt) (T, U) (Vartab.empty, maxidx)) end;

fun norm_term ctxt schematic =
  let
    (*raised when norm has no effect on a term, to do sharing instead of copying*)
    exception SAME;

    val binds = binds_of ctxt;
    fun norm (t as Var (xi, T)) =
          (case Vartab.lookup binds xi of
            SOME (u, U) =>
              let
                val env = unifyT ctxt (T, U) handle Type.TUNIFY =>
                  raise TYPE ("norm_term: ill-typed variable assignment", [T, U], [t, u]);
                val u' = Envir.subst_TVars env u;
              in norm u' handle SAME => u' end
          | NONE =>
            if schematic then raise SAME
            else error ("Unbound schematic variable: " ^ Syntax.string_of_vname xi))
      | norm (Abs (a, T, body)) =  Abs (a, T, norm body)
      | norm (Abs (_, _, body) $ t) = normh (subst_bound (t, body))
      | norm (f $ t) =
          ((case norm f of
            Abs (_, _, body) => normh (subst_bound (t, body))
          | nf => nf $ (norm t handle SAME => t)) handle SAME => f $ norm t)
      | norm _ =  raise SAME
    and normh t = norm t handle SAME => t
  in normh end;


(* dummy patterns *)

val prepare_dummies =
  let val next = ref 1 in
    fn t =>
      let val (i, u) = Term.replace_dummy_patterns (! next, t)
      in next := i; u end
  end;

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


(* read terms *)

local

fun append_env e1 e2 x = (case e2 x of NONE => e1 x | some => some);

fun gen_read' read app pattern schematic
    ctxt internal more_types more_sorts more_used s =
  let
    val types = append_env (def_type ctxt pattern) more_types;
    val sorts = append_env (def_sort ctxt) more_sorts;
    val used = used_types ctxt @ more_used;
  in
    (read (pp ctxt) (syn_of ctxt) (theory_of ctxt) (types, sorts, used) s
      handle TERM (msg, _) => error msg)
    |> app (intern_skolem ctxt internal)
    |> app (if pattern then I else norm_term ctxt schematic)
    |> app (if pattern then prepare_dummies else reject_dummies)
  end;

fun gen_read read app pattern schematic ctxt =
  gen_read' read app pattern schematic ctxt (K false) (K NONE) (K NONE) [];

in

val read_termTs           = gen_read' (read_def_termTs false) (apfst o map) false false;
val read_termTs_schematic = gen_read' (read_def_termTs false) (apfst o map) false true;

fun read_term_pats T ctxt =
  #1 o gen_read (read_def_termTs false) (apfst o map) true false ctxt o map (rpair T);
val read_prop_pats = read_term_pats propT;

fun read_term_legacy ctxt =
  gen_read' (read_term_thy true) I false false ctxt (K true) (K NONE) (K NONE) [];

val read_term              = gen_read (read_term_thy true) I false false;
val read_prop              = gen_read (read_prop_thy true) I false false;
val read_prop_schematic    = gen_read (read_prop_thy true) I false true;
val read_terms             = gen_read (read_terms_thy true) map false false;
fun read_props schematic   = gen_read (read_props_thy true) map false schematic;

end;


(* certify terms *)

local

fun gen_cert cert pattern schematic ctxt t = t
  |> (if pattern then I else norm_term ctxt schematic)
  |> (fn t' => cert (pp ctxt) (theory_of ctxt) t'
    handle TYPE (msg, _, _) => error msg
      | TERM (msg, _) => error msg);

val certify_term = #1 ooo Sign.certify_term;
val certify_prop = #1 ooo Sign.certify_prop;

in

val cert_term = gen_cert certify_term false false;
val cert_prop = gen_cert certify_prop false false;
val cert_props = map oo gen_cert certify_prop false;

fun cert_term_pats _ = map o gen_cert certify_term true false;
val cert_prop_pats = map o gen_cert certify_prop true false;

end;


(* declare terms *)

local

val ins_types = fold_aterms
  (fn Free (x, T) => Vartab.update ((x, ~1), T)
    | Var v => Vartab.update v
    | _ => I);

val ins_sorts = fold_types (fold_atyps
  (fn TFree (x, S) => Vartab.update ((x, ~1), S)
    | TVar v => Vartab.update v
    | _ => I));

val ins_used = fold_term_types (fn t =>
  fold_atyps (fn TFree (x, _) => insert (op =) x | _ => I));

val ins_occs = fold_term_types (fn t =>
  fold_atyps (fn TFree (x, _) => Symtab.update_multi (x, t) | _ => I));

fun ins_skolem def_ty = fold_rev (fn (x, x') =>
  (case def_ty x' of
    SOME T => Vartab.update ((x, ~1), T)
  | NONE => I));

in

fun declare_syntax t =
  map_defaults (fn (types, sorts, used, occ) => (ins_types t types, sorts, used, occ))
  #> map_defaults (fn (types, sorts, used, occ) => (types, ins_sorts t sorts, used, occ))
  #> map_defaults (fn (types, sorts, used, occ) => (types, sorts, ins_used t used, occ));

fun declare_var (x, opt_T, mx) =
  declare_syntax (Free (x, case opt_T of SOME T => T | NONE => TypeInfer.mixfixT mx));

fun declare_term t ctxt =
  ctxt
  |> declare_syntax t
  |> map_defaults (fn (types, sorts, used, occ) => (types, sorts, used, ins_occs t occ))
  |> map_defaults (fn (types, sorts, used, occ) =>
      (ins_skolem (fn x => Vartab.lookup types (x, ~1)) (fixes_of ctxt) types, sorts, used, occ));

end;


(* inferred types of parameters *)

fun infer_type ctxt x =
  (case try (fn () =>
      Sign.infer_types (pp ctxt) (theory_of ctxt) (def_type ctxt false) (def_sort ctxt)
        (used_types ctxt) true ([Free (x, dummyT)], TypeInfer.logicT)) () of
    SOME (Free (_, T), _) => T
  | _ => error ("Failed to infer type of fixed variable " ^ quote x));

fun inferred_param x ctxt =
  let val T = infer_type ctxt x
  in ((x, T), ctxt |> declare_term (Free (x, T))) end;

fun inferred_fixes ctxt =
  fold_map inferred_param (rev (fixed_names_of ctxt)) ctxt;


(* type and constant names *)

fun read_tyname ctxt c =
  if member (op =) (used_types ctxt) c then
    TFree (c, the_default (Sign.defaultS (theory_of ctxt)) (def_sort ctxt (c, ~1)))
  else Sign.read_tyname (theory_of ctxt) c;

fun read_const ctxt c =
  (case lookup_skolem ctxt c of
    SOME c' => Free (c', dummyT)
  | NONE => Sign.read_const (theory_of ctxt) c);



(** Hindley-Milner polymorphism **)

(* warn_extra_tfrees *)

fun warn_extra_tfrees ctxt1 ctxt2 =
  let
    fun occs_typ a (Type (_, Ts)) = exists (occs_typ a) Ts
      | occs_typ a (TFree (b, _)) = a = b
      | occs_typ _ (TVar _) = false;
    fun occs_free a (Free (x, _)) =
          (case def_type ctxt1 false (x, ~1) of
            SOME T => if occs_typ a T then I else cons (a, x)
          | NONE => cons (a, x))
      | occs_free _ _ = I;

    val occs1 = type_occs_of ctxt1 and occs2 = type_occs_of ctxt2;
    val extras = Symtab.fold (fn (a, ts) =>
      if Symtab.defined occs1 a then I else fold (occs_free a) ts) occs2 [];
    val tfrees = map #1 extras |> sort_distinct string_ord;
    val frees = map #2 extras |> sort_distinct string_ord;
  in
    if null extras then ()
    else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
      space_implode " or " (map (string_of_term ctxt2 o Syntax.free) frees));
    ctxt2
  end;


(* generalize type variables *)

fun generalize_tfrees inner outer =
  let
    val extra_fixes = fixed_names_of inner \\ fixed_names_of outer;
    fun still_fixed (Free (x, _)) = not (member (op =) extra_fixes x)
      | still_fixed _ = false;
    val occs_inner = type_occs_of inner;
    val occs_outer = type_occs_of outer;
    fun add a gen =
      if Symtab.defined occs_outer a orelse
        exists still_fixed (Symtab.lookup_multi occs_inner a)
      then gen else a :: gen;
  in fn tfrees => fold add tfrees [] end;

fun generalize inner outer ts =
  let
    val tfrees = generalize_tfrees inner outer (map #1 (fold Term.add_tfrees ts []));
    fun gen (x, S) = if member (op =) tfrees x then TVar ((x, 0), S) else TFree (x, S);
  in map (Term.map_term_types (Term.map_type_tfree gen)) ts end;



(** export theorems **)

fun common_exports is_goal inner outer =
  let
    val gen = generalize_tfrees inner outer;
    val fixes = fixed_names_of inner \\ fixed_names_of outer;
    val asms = Library.drop (length (assumptions_of outer), assumptions_of inner);
    val exp_asms = map (fn (cprops, exp) => exp is_goal cprops) asms;
  in
    Goal.norm_hhf_protect
    #> Seq.EVERY (rev exp_asms)
    #> Seq.map (fn rule =>
      let
        val thy = Thm.theory_of_thm rule;
        val prop = Thm.full_prop_of rule;
        val frees = map (Thm.cterm_of thy) (List.mapPartial (Term.find_free prop) fixes);
        val tfrees = gen (Term.add_term_tfree_names (prop, []));
      in
        rule
        |> Drule.forall_intr_list frees
        |> Goal.norm_hhf_protect
        |> Drule.tvars_intr_list tfrees |> #2
      end)
  end;

fun export_standard inner outer =
  let val exp = common_exports false inner outer in
    fn th =>
      (case Seq.pull (exp th) of
        SOME (th', _) => th' |> Drule.local_standard
      | NONE => sys_error "Failed to export theorem")
  end;

val exports = common_exports false;
val goal_exports = common_exports true;



(** bindings **)

(* delete_update_binds *)

local

val del_bind = map_binds o Vartab.delete_safe;

fun upd_bind ((x, i), t) =
  let
    val T = Term.fastype_of t;
    val t' =
      if null (Term.term_tvars t \\ Term.typ_tvars T) then t
      else Var ((x ^ "_has_extra_type_vars_on_rhs", i), T);
  in declare_term t' #> map_binds (Vartab.update ((x, i), (t', T))) end;

fun del_upd_bind (xi, NONE) = del_bind xi
  | del_upd_bind (xi, SOME t) = upd_bind (xi, t);

in

val delete_update_binds = fold del_upd_bind;

end;


(* simult_matches *)

fun simult_matches ctxt [] = []
  | simult_matches ctxt pairs =
      let
        fun fail () = error "Pattern match failed!";

        val maxidx = fold (fn (t1, t2) => fn i =>
          Int.max (Int.max (Term.maxidx_of_term t1, Term.maxidx_of_term t2), i)) pairs ~1;
        val envs = Unify.smash_unifiers (theory_of ctxt, Envir.empty maxidx,
          map swap pairs);    (*prefer assignment of variables from patterns*)
        val env =
          (case Seq.pull envs of
            NONE => fail ()
          | SOME (env, _) => env);    (*ignore further results*)
        val domain =
          filter_out Term.is_replaced_dummy_pattern (map #1 (Drule.vars_of_terms (map #1 pairs)));
        val _ =    (*may not assign variables from text*)
          if null (map #1 (Envir.alist_of env) inter (map #1 (Drule.vars_of_terms (map #2 pairs))))
          then () else fail ();
        fun norm_bind (xi, (_, t)) =
          if member (op =) domain xi then SOME (xi, Envir.norm_term env t) else NONE;
      in List.mapPartial norm_bind (Envir.alist_of env) end;


(* add_binds(_i) *)

local

fun gen_bind prep (xi as (x, _), raw_t) ctxt =
  ctxt |> delete_update_binds [(xi, Option.map (prep ctxt) raw_t)];

in

fun drop_schematic (b as (xi, SOME t)) = if null (Term.term_vars t) then b else (xi, NONE)
  | drop_schematic b = b;

val add_binds = fold (gen_bind read_term);
val add_binds_i = fold (gen_bind cert_term);

fun auto_bind f ts ctxt = ctxt |> add_binds_i (map drop_schematic (f (theory_of ctxt) ts));
val auto_bind_goal = auto_bind AutoBind.goal;
val auto_bind_facts = auto_bind AutoBind.facts;

end;


(* match_bind(_i) *)

local

fun prep_bind prep_pats (raw_pats, t) ctxt =
  let
    val ctxt' = declare_term t ctxt;
    val pats = prep_pats (fastype_of t) ctxt' raw_pats;
    val binds = simult_matches ctxt' (map (rpair t) pats);
  in (binds, ctxt') end;

fun gen_binds prep_terms prep_pats gen raw_binds ctxt =
  let
    val ts = prep_terms ctxt (map snd raw_binds);
    val (binds, ctxt') =
      apfst List.concat (fold_map (prep_bind prep_pats) (map fst raw_binds ~~ ts) ctxt);
    val binds' =
      if gen then map #1 binds ~~ generalize ctxt' ctxt (map #2 binds)
      else binds;
    val binds'' = map (apsnd SOME) binds';
    val ctxt'' =
      warn_extra_tfrees ctxt
       (if gen then
          ctxt (*sic!*) |> fold declare_term (map #2 binds') |> add_binds_i binds''
        else ctxt' |> add_binds_i binds'');
  in (ts, ctxt'') end;

in

val match_bind = gen_binds read_terms read_term_pats;
val match_bind_i = gen_binds (map o cert_term) cert_term_pats;

end;


(* propositions with patterns *)

local

fun prep_propp schematic prep_props prep_pats (context, args) =
  let
    fun prep (_, (raw_pats1, raw_pats2)) (ctxt, prop :: props) =
          let
            val ctxt' = declare_term prop ctxt;
            val pats = prep_pats ctxt' (raw_pats1 @ raw_pats2);    (*simultaneous type inference!*)
          in ((prop, splitAt (length raw_pats1, pats)), (ctxt', props)) end
      | prep _ _ = sys_error "prep_propp";
    val (propp, (context', _)) = (fold_map o fold_map) prep args
      (context, prep_props schematic context (List.concat (map (map fst) args)));
  in (context', propp) end;

fun matches ctxt (prop, (pats1, pats2)) =
  simult_matches ctxt (map (rpair prop) pats1 @ map (rpair (Logic.strip_imp_concl prop)) pats2);

fun gen_bind_propp prepp (ctxt, raw_args) =
  let
    val (ctxt', args) = prepp (ctxt, raw_args);
    val binds = List.concat (List.concat (map (map (matches ctxt')) args));
    val propss = map (map #1) args;

    (*generalize result: context evaluated now, binds added later*)
    val gen = generalize ctxt' ctxt;
    fun gen_binds c = c |> add_binds_i (map #1 binds ~~ map SOME (gen (map #2 binds)));
  in (ctxt' |> add_binds_i (map (apsnd SOME) binds), (propss, gen_binds)) end;

in

val read_propp = prep_propp false read_props read_prop_pats;
val cert_propp = prep_propp false cert_props cert_prop_pats;
val read_propp_schematic = prep_propp true read_props read_prop_pats;
val cert_propp_schematic = prep_propp true cert_props cert_prop_pats;

val bind_propp = gen_bind_propp read_propp;
val bind_propp_i = gen_bind_propp cert_propp;
val bind_propp_schematic = gen_bind_propp read_propp_schematic;
val bind_propp_schematic_i = gen_bind_propp cert_propp_schematic;

end;



(** theorems **)

(* fact_tac *)

fun comp_incr_tac [] _ st = no_tac st
  | comp_incr_tac (th :: ths) i st =
      (Goal.compose_hhf_tac (Drule.incr_indexes st th) i APPEND comp_incr_tac ths i) st;

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

fun some_fact_tac ctxt = SUBGOAL (fn (goal, i) =>
  let
    val (_, _, index) = thms_of ctxt;
    val facts = FactIndex.could_unify index (Term.strip_all_body goal);
  in fact_tac facts i end);


(* get_thm(s) *)

fun retrieve_thms _ pick ctxt (Fact s) =
      let
        val thy = theory_of ctxt;
        val th = Goal.prove thy [] [] (read_prop ctxt s) (K (ALLGOALS (some_fact_tac ctxt)))
          handle ERROR msg => cat_error msg "Failed to retrieve literal fact.";
      in pick "" [th] end
  | retrieve_thms from_thy pick ctxt xthmref =
      let
        val thy = theory_of ctxt;
        val (_, (space, tab), _) = thms_of ctxt;
        val thmref = PureThy.map_name_of_thmref (NameSpace.intern space) xthmref;
        val name = PureThy.name_of_thmref thmref;
      in
        (case Symtab.lookup tab name of
          SOME ths => map (Thm.transfer thy) (PureThy.select_thm thmref ths)
        | NONE => from_thy thy xthmref) |> pick name
      end;

val get_thm = retrieve_thms PureThy.get_thms PureThy.single_thm;
val get_thm_closure = retrieve_thms PureThy.get_thms_closure PureThy.single_thm;
val get_thms = retrieve_thms PureThy.get_thms (K I);
val get_thms_closure = retrieve_thms PureThy.get_thms_closure (K I);


(* valid_thms *)

fun valid_thms ctxt (name, ths) =
  (case try (fn () => get_thms ctxt (Name name)) () of
    NONE => false
  | SOME ths' => Thm.eq_thms (ths, ths'));


(* lthms_containing *)

fun lthms_containing ctxt spec =
  FactIndex.find (fact_index_of ctxt) spec
  |> map ((not o valid_thms ctxt) ? apfst (fn name =>
    NameSpace.hidden (if name = "" then "unnamed" else name)));


(* name space operations *)

val extern_thm = NameSpace.extern o #1 o #2 o thms_of;

val qualified_names = map_naming NameSpace.qualified_names;
val no_base_names = map_naming NameSpace.no_base_names;
val custom_accesses = map_naming o NameSpace.custom_accesses;
val restore_naming = map_naming o K o #1 o thms_of;

fun hide_thms fully names = map_thms (fn (naming, (space, tab), index) =>
  (naming, (fold (NameSpace.hide fully) names space, tab), index));


(* put_thms *)

fun put_thms ("", NONE) ctxt = ctxt
  | put_thms ("", SOME ths) ctxt = ctxt |> map_thms (fn (naming, facts, index) =>
      let
        val index' = FactIndex.add_local (is_known ctxt) ("", ths) index;
      in (naming, facts, index') end)
  | put_thms (bname, NONE) ctxt = ctxt |> map_thms (fn (naming, (space, tab), index) =>
      let
        val name = NameSpace.full naming bname;
        val tab' = Symtab.delete_safe name tab;
      in (naming, (space, tab'), index) end)
  | put_thms (bname, SOME ths) ctxt = ctxt |> map_thms (fn (naming, (space, tab), index) =>
      let
        val name = NameSpace.full naming bname;
        val space' = NameSpace.declare naming name space;
        val tab' = Symtab.update (name, ths) tab;
        val index' = FactIndex.add_local (is_known ctxt) (name, ths) index;
      in (naming, (space', tab'), index') end);


(* note_thmss *)

local

fun gen_note_thmss get = fold_map (fn ((name, more_attrs), ths_attrs) => fn ctxt =>
  let
    fun app (th, attrs) (ct, ths) =
      let val (ct', th') = foldl_map (Thm.proof_attributes (attrs @ more_attrs)) (ct, get ctxt th)
      in (ct', th' :: ths) end;
    val (ctxt', rev_thms) = fold app ths_attrs (ctxt, []);
    val thms = List.concat (rev rev_thms);
  in ((name, thms), ctxt' |> put_thms (name, SOME thms)) end);

in

val note_thmss = gen_note_thmss get_thms;
val note_thmss_i = gen_note_thmss (K I);

val note_thmss_accesses = gen_note_thmss get_thms;
val note_thmss_accesses_i = gen_note_thmss (K I);

end;



(** parameters **)

(* variables *)

local

fun prep_vars prep_typ internal legacy =
  fold_map (fn (raw_x, raw_T, raw_mx) => fn ctxt =>
    let
      val x = Syntax.const_name raw_x raw_mx;
      val mx = Syntax.fix_mixfix raw_x raw_mx;
      val _ =
        if not legacy andalso not (Syntax.is_identifier (no_skolem internal x)) then
          error ("Illegal variable name: " ^ quote x)
        else ();

      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 prep_typ ctxt) raw_T;
      val var = (x, opt_T, mx);
    in (var, ctxt |> declare_var var) end);

in

val read_vars        = prep_vars read_typ false false;
val cert_vars        = prep_vars cert_typ true false;
val read_vars_legacy = prep_vars read_typ true true;
val cert_vars_legacy = prep_vars cert_typ true true;

end;


(* fixes *)

local

fun no_dups _ [] = ()
  | no_dups ctxt dups = error ("Duplicate variable(s): " ^ commas_quote dups);

fun gen_fixes prep raw_vars ctxt =
  let
    val (ys, zs) = split_list (fixes_of ctxt);
    val (vars, ctxt') = prep raw_vars ctxt;
    val xs = map #1 vars;
    val _ = no_dups ctxt (duplicates xs);
    val xs' =
      if is_body ctxt then Term.variantlist (map Syntax.skolem xs, zs)
      else (no_dups ctxt (xs inter_string ys); no_dups ctxt (xs inter_string zs); xs);
    val vars' = map2 (fn x' => fn (_, T, mx) => (x', T, mx)) xs' vars;
  in
    ctxt'
    |> map_fixes (fn (b, fixes) => (b, rev (xs ~~ xs') @ fixes))
    |> add_syntax vars'
    |> fold declare_var vars'
    |> pair xs'
  end;

in

val add_fixes = gen_fixes read_vars;
val add_fixes_i = gen_fixes cert_vars;
val add_fixes_legacy = gen_fixes cert_vars_legacy;

end;


(* fixes vs. frees *)

fun fix_frees t ctxt =
  let
    fun add (Free (x, T)) = if is_fixed ctxt x then I else insert (op =) (x, SOME T, NoSyn)
      | add _ = I;
    val fixes = rev (fold_aterms add t []);
  in ctxt |> set_body false |> add_fixes_i fixes |> snd |> restore_body ctxt end;

fun auto_fixes (arg as (ctxt, (propss, x))) =
  if is_body ctxt then arg
  else ((fold o fold) fix_frees propss ctxt, (propss, x));

fun bind_fixes xs ctxt =
  let
    val (_, ctxt') = ctxt |> add_fixes_i (map (fn x => (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 **)

(* generic assms *)

local

fun gen_assm ((name, attrs), props) ctxt =
  let
    val cprops = map (Thm.cterm_of (theory_of ctxt)) props;
    val asms = map (Goal.norm_hhf o Thm.assume) cprops;

    val ths = map (fn th => ([th], [])) asms;
    val ([(_, thms)], ctxt') =
      ctxt
      |> auto_bind_facts props
      |> note_thmss_i [((name, attrs), ths)];
  in ((cprops, (name, asms), (name, thms)), ctxt') end;

fun gen_assms prepp exp args ctxt =
  let
    val (propss, ctxt1) = swap (prepp (ctxt, map snd args));
    val (results, ctxt2) = fold_map gen_assm (map fst args ~~ propss) ctxt1;

    val new_asms = List.concat (map #1 results);
    val new_prems = map #2 results;
    val ctxt3 = ctxt2 |> map_assms (fn (asms, prems) => (asms @ [(new_asms, exp)], prems @ new_prems))
    val ctxt4 = ctxt3 |> put_thms ("prems", SOME (prems_of ctxt3));
  in (map #3 results, warn_extra_tfrees ctxt ctxt4) 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;


(* basic assumptions *)

fun assume_export true = Seq.single oo Drule.implies_intr_protected
  | assume_export false = Seq.single oo Drule.implies_intr_list;

fun presume_export _ = assume_export false;


(* additional views *)

fun add_view outer view = map_assms (fn (asms, prems) =>
  let
    val (asms1, asms2) = splitAt (length (assumptions_of outer), asms);
    val asms' = asms1 @ [(view, assume_export)] @ asms2;
  in (asms', prems) end);

fun export_view view inner outer = export_standard (add_view outer view inner) outer;


(* definitions *)

fun mk_def ctxt args =
  let
    val (xs, rhss) = split_list args;
    val (bind, _) = bind_fixes xs ctxt;
    val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;
  in map Logic.mk_equals (lhss ~~ rhss) end;

fun cert_def ctxt eq =
  let
    fun err msg = cat_error msg
      ("The error(s) above occurred in definition: " ^ string_of_term ctxt eq);
    val (lhs, rhs) = Logic.dest_equals (Term.strip_all_body eq)
      handle TERM _ => err "Not a meta-equality (==)";
    val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);
    val (c, _) = Term.dest_Free f handle TERM _ =>
      err "Head of lhs must be a free/fixed variable";

    fun is_free (Free (x, _)) = not (is_fixed ctxt x)
      | is_free _ = false;
    val extra_frees = List.filter is_free (term_frees rhs) \\ xs;
  in
    conditional (not (forall (is_Bound orf is_free) xs andalso null (duplicates xs))) (fn () =>
      err "Arguments of lhs must be distinct free/bound variables");
    conditional (f mem Term.term_frees rhs) (fn () =>
      err "Element to be defined occurs on rhs");
    conditional (not (null extra_frees)) (fn () =>
      err ("Extra free variables on rhs: " ^ commas_quote (map (#1 o dest_Free) extra_frees)));
    (c, Term.list_all_free (List.mapPartial (try Term.dest_Free) xs, eq))
  end;

fun abs_def eq =
  let
    val body = Term.strip_all_body eq;
    val vars = map Free (Term.rename_wrt_term body (Term.strip_all_vars eq));
    val (lhs, rhs) = Logic.dest_equals (Term.subst_bounds (vars, body));
    val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);
    val eq' = Term.list_abs_free (map Term.dest_Free xs, rhs);
  in (Term.dest_Free f, eq') end;


fun head_of_def cprop =
  #1 (Term.strip_comb (#1 (Logic.dest_equals (Term.strip_all_body (Thm.term_of cprop)))))
  |> Thm.cterm_of (Thm.theory_of_cterm cprop);

fun def_export _ cprops thm =
  thm
  |> Drule.implies_intr_list cprops
  |> Drule.forall_intr_list (map head_of_def cprops)
  |> Drule.forall_elim_vars 0
  |> RANGE (replicate (length cprops) (Tactic.rtac Drule.reflexive_thm)) 1;

fun add_def (x, t) ctxt =
  let
    val [eq] = mk_def ctxt [(x, t)];
    val x' = Term.dest_Free (fst (Logic.dest_equals eq));
  in
    ctxt
    |> add_fixes_i [(x, NONE, NoSyn)] |> snd
    |> add_assms_i def_export [(("", []), [(eq, ([], []))])]
    |>> (fn [(_, [th])] => (x', th))
  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 RuleCases.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
        RuleCases.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' |> declare_syntax t) end;

in

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

fun case_result c ctxt =
  let
    val RuleCases.Case {fixes, ...} = c;
    val (ts, ctxt') = ctxt |> fold_map fix fixes;
    val RuleCases.Case {assumes, binds, cases, ...} = RuleCases.apply ts c;
  in
    ctxt'
    |> add_binds_i (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 **)

val verbose = ref false;
fun verb f x = if ! verbose then f (x ()) else [];

fun setmp_verbose f x = Library.setmp verbose true f x;

fun pretty_items prt name items =
  let
    fun prt_itms (name, [x]) = Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, prt x]
      | prt_itms (name, xs) = Pretty.big_list (name ^ ":") (map prt xs);
  in
    if null items andalso not (! verbose) then []
    else [Pretty.big_list name (map prt_itms items)]
  end;


(* local syntax *)

val print_syntax = Syntax.print_syntax o syn_of;


(* term bindings *)

fun pretty_binds ctxt =
  let
    val binds = binds_of ctxt;
    fun prt_bind (xi, (t, T)) = pretty_term ctxt (Logic.mk_equals (Var (xi, T), t));
  in
    if Vartab.is_empty binds andalso not (! verbose) 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 =
  pretty_items (pretty_thm ctxt) "facts:" (NameSpace.extern_table (#2 (thms_of ctxt)));

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


(* local contexts *)

fun pretty_cases ctxt =
  let
    val prt_term = 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 ::
            List.concat (Library.separate sep (map (Library.single o prt) xs))))];

    fun prt_case (name, (fixes, (asms, (lets, cs)))) = Pretty.block (Pretty.fbreaks
      (Pretty.str (name ^ ":") ::
        prt_sect "fix" [] (Pretty.str o fst) fixes @
        prt_sect "let" [Pretty.str "and"] prt_let
          (List.mapPartial (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));

    fun add_case (_, (_, false)) = I
      | add_case (name, (c as RuleCases.Case {fixes, ...}, true)) =
          cons (name, (fixes, #1 (case_result c ctxt)));
    val cases = fold add_case (cases_of ctxt) [];
  in
    if null cases andalso not (! verbose) then []
    else [Pretty.big_list "cases:" (map prt_case cases)]
  end;

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


(* core context *)

val prems_limit = ref 10;

fun pretty_ctxt ctxt =
  let
    val prt_term = pretty_term ctxt;

    (*structures*)
    val (_, structs, _) = 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 Syntax.dest_internal orf member (op =) structs) o #1) (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 limit = ! prems_limit;
    val prems = prems_of ctxt;
    val len = length prems;
    val prt_prems = if null prems then []
      else [Pretty.big_list "prems:" ((if len <= limit then [] else [Pretty.str "..."]) @
        map (pretty_thm ctxt) (Library.drop (len - limit, prems)))];

  in prt_structs @ prt_fixes @ prt_prems end;


(* main context *)

fun pretty_context ctxt =
  let
    val prt_term = pretty_term ctxt;
    val prt_typ = pretty_typ ctxt;
    val prt_sort = 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, used, _) = defaults_of ctxt;
  in
    verb single (K pretty_thy) @
    pretty_ctxt 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))) @
    verb single (fn () => Pretty.strs ("used type variable names:" :: used))
  end;

end;