(*  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 exporter

  exception CONTEXT of string * context

  val theory_of: context -> theory

  val sign_of: context -> theory    (*obsolete*)

  val is_fixed: context -> string -> bool

  val is_known: context -> string -> bool

  val fixed_names_of: context -> string list

  val assms_of: context -> term list

  val prems_of: context -> thm list

  val fact_index_of: context -> FactIndex.T

  val init: theory -> context

  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 default_type: context -> string -> typ option

  val used_types: context -> string list

  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_liberal: 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 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: 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 * context attribute list) * (thmref * context attribute list) list) list ->

      context -> (bstring * thm list) list * context

  val note_thmss_i:

    ((bstring * context attribute list) * (thm list * context attribute list) list) list ->

      context -> (bstring * thm list) list * context

  val export_assume: exporter

  val export_presume: exporter

  val assume: exporter

    -> ((string * context attribute list) * (string * (string list * string list)) list) list

    -> context -> (bstring * thm list) list * context

  val assume_i: exporter

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

    -> context -> (bstring * thm list) list * context

  val mk_def: context -> (string * term) list -> term list

  val cert_def: context -> term -> string * term

  val export_def: exporter

  val add_def: string * term -> context -> ((string * typ) * thm) * context

  val add_view: context -> cterm list -> context -> context

  val export_view: cterm list -> context -> context -> thm -> thm

  val read_vars: (string list * string option) -> context -> (string list * typ option) * context

  val cert_vars: (string list * typ option) -> context -> (string list * typ option) * context

  val read_vars_liberal: (string list * string option) -> context ->

    (string list * typ option) * context

  val cert_vars_liberal: (string list * typ option) -> context ->

    (string list * typ option) * context

  val fix: (string list * string option) list -> context -> context

  val fix_i: (string list * typ option) list -> context -> context

  val add_fixes: (string * typ option * Syntax.mixfix option) list -> context -> context

  val add_fixes_liberal: (string * typ option * Syntax.mixfix option) list -> context -> context

  val fix_frees: term list -> context -> context

  val auto_fix: context * (term list list * 'a) -> context * (term list list * 'a)

  val bind_skolem: context -> string list -> term -> term

  val apply_case: RuleCases.T -> context

    -> ((indexname * term option) list * (string * term list) list) * context

  val get_case: context -> string -> string option list -> RuleCases.T

  val add_cases: (string * RuleCases.T option) list -> context -> context

  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_asms: context -> Pretty.T list

  val pretty_context: context -> Pretty.T list

end;

structure ProofContext: PROOF_CONTEXT =

struct

(** generic proof contexts **)

type context = Context.proof;

exception CONTEXT = Context.PROOF;

val theory_of = Context.theory_of_proof;

val sign_of = theory_of;

val init = Context.init_proof;

(** Isar proof context information **)

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

datatype ctxt =

  Ctxt of

   {syntax: (Syntax.syntax * Syntax.syntax * (Syntax.syntax -> Syntax.syntax)) *

      string list * string list,                (*global/local syntax with structs and mixfixed*)

    asms:

      ((cterm list * exporter) list *           (*assumes and views: A ==> _*)

        (string * thm list) list) *             (*prems: A |- A *)

      (string * string) list,                   (*fixes: !!x. _*)

    binds: (term * typ) Vartab.table,           (*term bindings*)

    thms: NameSpace.naming *                    (*local thms*)

      thm list NameSpace.table * FactIndex.T,

    cases: (string * RuleCases.T) list,         (*local contexts*)

    defs:

      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, asms, binds, thms, cases, defs) =

  Ctxt {syntax = syntax, asms = asms, binds = binds, thms = thms, cases = cases, defs = defs};

structure ContextData = ProofDataFun

(struct

  val name = "Isar/context";

  type T = ctxt;

  fun init thy =

    make_ctxt (((Sign.syn_of thy, Sign.syn_of thy, I), [], []), (([], []), []),

      Vartab.empty, (NameSpace.default_naming, NameSpace.empty_table, FactIndex.empty), [],

      (Vartab.empty, Vartab.empty, [], Symtab.empty));

  fun print _ _ = ();

end);

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, asms, binds, thms, cases, defs} =>

  make_ctxt (f (syntax, asms, binds, thms, cases, defs)));

val syntax_of = #syntax o rep_context;

val assumptions_of = #1 o #1 o #asms 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 #1 o #asms o rep_context;

val fixes_of = #2 o #asms o rep_context;

val fixed_names_of = map #2 o fixes_of;

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 = #defs 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;

(** local 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 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 (_, _, NONE) = NONE

  | prep_mixfix (x, opt_T, SOME mx) = SOME (mixfix x opt_T mx);

fun prep_mixfix' (_, _, NONE) = NONE

  | prep_mixfix' (x, _, SOME Syntax.NoSyn) = NONE

  | prep_mixfix' (x, opt_T, _) = SOME (x, mixfix x opt_T (Syntax.literal x));

fun prep_struct (x, _, NONE) = 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_context (fn (syntax, asms, binds, thms, cases, defs) =>

  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 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), asms, binds, thms, cases, defs) 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, defs = (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;

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

val used_types = #3 o defaults_of;

(** prepare types **)

local

fun read_typ_aux read ctxt s =

  transform_error (read (syn_of ctxt) (theory_of ctxt, def_sort ctxt)) s

    handle ERROR_MESSAGE msg => raise CONTEXT (msg, ctxt);

fun cert_typ_aux cert ctxt raw_T =

  cert (theory_of ctxt) raw_T

    handle TYPE (msg, _, _) => raise CONTEXT (msg, ctxt);

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 ctxt x =

  if can Syntax.dest_skolem x then

    raise CONTEXT ("Illegal reference to internal Skolem constant: " ^ quote x, ctxt)

  else if not internal andalso can Syntax.dest_internal x then

    raise CONTEXT ("Illegal reference to internal variable: " ^ quote x, ctxt)

  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 ctxt 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 => Syntax.deskolem 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 defs sT =

  apfst hd (read_def_termTs freeze pp syn thy defs [sT]);

fun read_term_thy freeze pp syn thy defs s =

  #1 (read_def_termT freeze pp syn thy defs (s, TypeInfer.logicT));

fun read_prop_thy freeze pp syn thy defs s =

  #1 (read_def_termT freeze pp syn thy defs (s, propT));

fun read_terms_thy freeze pp syn thy defs =

  #1 o read_def_termTs freeze pp syn thy defs o map (rpair TypeInfer.logicT);

fun read_props_thy freeze pp syn thy defs =

  #1 o read_def_termTs freeze pp syn thy defs 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 raise CONTEXT ("Unbound schematic variable: " ^ Syntax.string_of_vname xi, ctxt))

      | 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 ctxt t = Term.no_dummy_patterns t

  handle TERM _ => raise CONTEXT ("Illegal dummy pattern(s) in term", ctxt);

(* 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

    (transform_error (read (pp ctxt) (syn_of ctxt) (theory_of ctxt) (types, sorts, used)) s

      handle TERM (msg, _) => raise CONTEXT (msg, ctxt)

        | ERROR_MESSAGE msg => raise CONTEXT (msg, ctxt))

    |> app (intern_skolem ctxt internal)

    |> app (if pattern then I else norm_term ctxt schematic)

    |> app (if pattern then prepare_dummies else reject_dummies ctxt)

  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_liberal 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, _, _) => raise CONTEXT (msg, ctxt)

      | TERM (msg, _) => raise CONTEXT (msg, ctxt));

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));

fun map_defaults f = map_context (fn (syntax, asms, binds, thms, cases, defs) =>

  (syntax, asms, binds, thms, cases, f defs));

in

fun declare_term_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_term t ctxt =

  ctxt

  |> declare_term_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;

(* 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 |> Library.sort_strings |> Library.unique_strings;

    val frees = map #2 extras |> Library.sort_strings |> Library.unique_strings;

  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 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

fun del_bind xi = map_context (fn (syntax, asms, binds, thms, cases, defs) =>

  (syntax, asms, Vartab.delete_safe xi binds, thms, cases, defs));

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

    map_context (fn (syntax, asms, binds, thms, cases, defs) =>

      (syntax, asms, Vartab.update ((x, i), (t', T)) binds, thms, cases, defs))

    o declare_term 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 () = raise CONTEXT ("Pattern match failed!", ctxt);

        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_MESSAGE msg =>

            raise CONTEXT (msg ^ "\nFailed to retrieve literal fact.", ctxt);

      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 (transform_error (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;

fun map_naming f = map_context (fn (syntax, asms, binds,

    (naming, table, index), cases, defs) =>

  (syntax, asms, binds, (f naming, table, index), cases, defs));

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_context

  (fn (syntax, asms, binds, (naming, (space, tab), index), cases, defs) =>

    (syntax, asms, binds,

      (naming, (fold (NameSpace.hide fully) names space, tab), index), cases, defs));

(* put_thms *)

fun put_thms ("", NONE) ctxt = ctxt

  | put_thms ("", SOME ths) ctxt = ctxt |> map_context