(*  Title:      Pure/Isar/proof_context.ML

    ID:         $Id$

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

  val naming_of: Proof.context -> NameSpace.naming

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

  val consts_of: Proof.context -> Consts.T

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

  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 theorems_of: Proof.context -> thm list NameSpace.table

  val fact_index_of: Proof.context -> FactIndex.T

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

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

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

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

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

  val pretty_typ: Proof.context -> typ -> Pretty.T

  val pretty_sort: Proof.context -> sort -> Pretty.T

  val pretty_classrel: Proof.context -> class list -> Pretty.T

  val pretty_arity: Proof.context -> arity -> Pretty.T

  val pp: Proof.context -> Pretty.pp

  val pretty_thm_legacy: thm -> Pretty.T

  val pretty_thm: Proof.context -> thm -> Pretty.T

  val pretty_thms: Proof.context -> thm list -> Pretty.T

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

  val pretty_proof: Proof.context -> Proofterm.proof -> Pretty.T

  val pretty_proof_of: Proof.context -> bool -> thm -> Pretty.T

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

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

  val string_of_thm: Proof.context -> thm -> string

  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 revert_skolems: Proof.context -> term -> term

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

  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 read_termTs_schematic: Proof.context -> (string -> bool) -> (indexname -> typ option)

    -> (indexname -> sort option) -> string list -> (string * typ) list

    -> term list * (indexname * typ) list

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

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

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

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

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

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

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

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

  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 add_binds: (indexname * string option) list -> Proof.context -> Proof.context

  val add_binds_i: (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_thm: Proof.context -> thmref -> thm

  val get_thm_closure: Proof.context -> thmref -> thm

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

  val get_thms_closure: Proof.context -> thmref -> thm list

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

  val lthms_containing: Proof.context -> FactIndex.spec -> (string * thm list) list

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

  val no_base_names: Proof.context -> Proof.context

  val qualified_names: Proof.context -> Proof.context

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

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

  val reset_naming: Proof.context -> Proof.context

  val hide_thms: bool -> string list -> Proof.context -> Proof.context

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

  val note_thmss: string ->

    ((bstring * attribute list) * (thmref * attribute list) list) list ->

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

  val note_thmss_i: string ->

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

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

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

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

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

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

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

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

  val cert_vars_legacy: (string * typ option * mixfix) list -> Proof.context ->

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

  val add_fixes: (string * string option * mixfix) list ->

    Proof.context -> string list * Proof.context

  val add_fixes_i: (string * typ option * mixfix) list ->

    Proof.context -> string list * Proof.context

  val add_fixes_legacy: (string * 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 ->

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

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

  val add_assms_i: Assumption.export ->

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

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

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

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

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

  val add_notation: Syntax.mode -> (term * mixfix) list ->

    Proof.context -> Proof.context

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

    Context.generic -> Context.generic

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

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

  val verbose: bool ref

  val setmp_verbose: ('a -> 'b) -> 'a -> 'b

  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 ref

  val prems_limit: int ref

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

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

end;

structure ProofContext: PROOF_CONTEXT =

struct

val theory_of = Context.theory_of_proof;

val tsig_of = Sign.tsig_of o theory_of;

val init = Context.init_proof;

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

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

    consts: Consts.T * Consts.T,                      (*global/local consts*)

    thms: thm list NameSpace.table * FactIndex.T,     (*local thms*)

    cases: (string * (RuleCases.T * bool)) list};     (*local contexts*)

fun make_ctxt (mode, naming, syntax, consts, thms, cases) =

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

    consts = consts, thms = thms, cases = cases};

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

structure ContextData = ProofDataFun

(

  type T = ctxt;

  fun init thy =

    make_ctxt (mode_default, local_naming, LocalSyntax.init thy,

      (Sign.consts_of thy, Sign.consts_of thy),

      (NameSpace.empty_table, FactIndex.empty), []);

);

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

fun map_context f =

  ContextData.map (fn Ctxt {mode, naming, syntax, consts, thms, cases} =>

    make_ctxt (f (mode, naming, syntax, consts, thms, cases)));

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

  (mode, naming, syntax, consts, thms, cases));

fun map_mode f =

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

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

fun map_naming f =

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

    (mode, f naming, syntax, consts, thms, cases));

fun map_syntax f =

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

    (mode, naming, f syntax, consts, thms, cases));

fun map_consts f =

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

    (mode, naming, syntax, f consts, thms, cases));

fun map_thms f =

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

    (mode, naming, syntax, consts, f thms, cases));

fun map_cases f =

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

    (mode, naming, syntax, consts, thms, f cases));

val get_mode = #mode o rep_context;

fun restore_mode ctxt = set_mode (get_mode ctxt);

fun set_stmt stmt =

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

val naming_of = #naming o rep_context;

val full_name = NameSpace.full o naming_of;

val syntax_of = #syntax o rep_context;

val syn_of = LocalSyntax.syn_of o syntax_of;

val set_syntax_mode = map_syntax o LocalSyntax.set_mode;

val restore_syntax_mode = map_syntax o LocalSyntax.restore_mode o syntax_of;

val consts_of = #2 o #consts o rep_context;

val const_syntax_name = Consts.syntax_name o consts_of;

val the_const_constraint = Consts.the_constraint o consts_of;

val thms_of = #thms o rep_context;

val theorems_of = #1 o thms_of;

val fact_index_of = #2 o thms_of;

val cases_of = #cases o rep_context;

(* theory transfer *)

fun transfer_syntax thy =

  map_syntax (LocalSyntax.rebuild thy) #>

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

    let val thy_consts = Sign.consts_of thy in

      if Consts.eq_consts (thy_consts, global_consts) then consts

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

    end);

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

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

fun theory_result f ctxt =

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

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

(** pretty printing **)

local

fun rewrite_term thy rews t =

  if can Term.type_of t then Pattern.rewrite_term thy rews [] t else t;

fun pretty_term' abbrevs ctxt t =

  let

    val thy = theory_of ctxt;

    val syntax = syntax_of ctxt;

    val consts = consts_of ctxt;

    val do_abbrevs = abbrevs andalso not (print_mode_active "no_abbrevs");

    val t' = t

      |> do_abbrevs ? rewrite_term thy (Consts.abbrevs_of consts (print_mode_value () @ [""]))

      |> do_abbrevs ? rewrite_term thy (Consts.abbrevs_of consts [Syntax.internalM])

      |> Sign.extern_term (Consts.extern_early consts) thy

      |> LocalSyntax.extern_term syntax;

  in Sign.pretty_term' ctxt (LocalSyntax.syn_of syntax) (Consts.extern consts) t' end;

in

val pretty_term = pretty_term' true;

val pretty_term_abbrev = pretty_term' false;

end;

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_legacy th =

  let val thy = Thm.theory_of_thm th

  in Display.pretty_thm_aux (pp (init thy)) true false [] th end;

fun pretty_thm ctxt th =

  let val asms = map Thm.term_of (Assumption.assms_of ctxt)

  in Display.pretty_thm_aux (pp ctxt) false true asms th end;

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_abbrev (ctxt |> transfer_syntax (ProofSyntax.proof_syntax prf (theory_of 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;

(** prepare types **)

(* read_typ *)

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;

(* cert_typ *)

fun cert_typ_mode mode ctxt T =

  Sign.certify_typ_mode mode (theory_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 -- approximation only! *)

fun revert_skolem ctxt =

  let

    val rev_fixes = map Library.swap (Variable.fixes_of ctxt);

    val revert = AList.lookup (op =) rev_fixes;

  in

    fn x =>

      (case revert x of

        SOME x' => x'

      | NONE => perhaps (try Name.dest_skolem) x)

   end;

fun revert_skolems ctxt =

  let

    val revert = revert_skolem ctxt;

    fun reverts (Free (x, T)) = Free (revert x, T)

      | reverts (t $ u) = reverts t $ reverts u

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

      | reverts a = a;

  in reverts end;

(** prepare terms and propositions **)

(* 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 =

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

  in Consts.certify (pp ctxt) (tsig_of ctxt) (not abbrev) (consts_of ctxt) end;

fun reject_schematic (Var (xi, _)) =

      error ("Unbound schematic variable: " ^ Term.string_of_vname xi)

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

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

  | reject_schematic _ = ();

fun expand_binds ctxt =

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

(* patterns *)

fun prepare_patternT ctxt =

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

    if pattern orelse schematic then I

    else Term.map_atyps

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

            if not (TypeInfer.is_param xi)

            then error ("Illegal schematic type variable: " ^ Term.string_of_vname xi)

            else T

        | T => T)

  end;

local

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

fun reject_dummies t = Term.no_dummy_patterns t

  handle TERM _ => error "Illegal dummy pattern(s) in term";

in

fun prepare_patterns ctxt =

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

    TypeInfer.fixate_params (Variable.names_of ctxt) #>

    pattern ? Variable.polymorphic ctxt #>

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

    (if pattern then prepare_dummies else map reject_dummies)

  end;

end;

(* decoding raw terms (syntax trees) *)

fun legacy_intern_skolem ctxt internal def_type x =    (* FIXME cleanup this mess *)

  let

    val sko = lookup_skolem ctxt x;

    val is_const = can (Consts.read_const (consts_of ctxt)) x;

    val is_free = is_some sko orelse not is_const;

    val is_internal = internal x;

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

    val res =

      if is_free andalso not is_internal then (no_skolem false x; sko)

      else ((no_skolem false x; ()) handle ERROR msg =>

          legacy_feature (msg ^ ContextPosition.str_of ctxt);

        if is_internal andalso is_declared then SOME x else NONE);

  in if is_some res then res else if is_declared then SOME x else NONE end;

fun term_context ctxt =

  let val thy = theory_of ctxt in

   {get_sort = Sign.get_sort thy (Variable.def_sort ctxt),

    map_const = try (#1 o Term.dest_Const o Consts.read_const (consts_of ctxt)),

    map_free = legacy_intern_skolem ctxt (K false) (Variable.def_type ctxt false),

    map_type = Sign.intern_tycons thy,

    map_sort = Sign.intern_sort thy}

  end;

fun decode_term ctxt =

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

  in Syntax.decode_term get_sort map_const map_free map_type map_sort end;

(* read terms -- legacy *)

local

fun read_def_termTs freeze pp syn ctxt (types, sorts, used) fixed sTs =

  Sign.read_def_terms' pp (Sign.is_logtype (theory_of ctxt)) syn (consts_of ctxt) fixed

    ctxt (types, sorts) used freeze sTs;

fun read_def_termT freeze pp syn ctxt defaults fixed sT =

  apfst hd (read_def_termTs freeze pp syn ctxt defaults fixed [sT]);

fun read_prop_thy freeze pp syn thy defaults fixed s =

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

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

fun gen_read' read app schematic ctxt0 internal more_types more_sorts more_used s =

  let

    val ctxt = if schematic then set_mode mode_schematic ctxt0 else ctxt0;

    val types = append_env (Variable.def_type ctxt false) more_types;

    val sorts = append_env (Variable.def_sort ctxt) more_sorts;

    val used = fold Name.declare more_used (Variable.names_of ctxt);

  in

    (read (pp ctxt) (syn_of ctxt) ctxt (types, sorts, used)

        (legacy_intern_skolem ctxt internal types) s

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

    |> app (expand_abbrevs ctxt)

    |> app (singleton (prepare_patterns ctxt))

  end;

fun gen_read read app schematic ctxt =

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

in

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

fun read_prop_legacy ctxt =

  gen_read' (read_prop_thy true) I false ctxt (K true) (K NONE) (K NONE) [];

end;

(* certify terms *)

local

fun gen_cert prop ctxt t =

  t

  |> expand_abbrevs ctxt

  |> (fn t' => #1 (Sign.certify' prop (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 standard_infer_types ctxt ts =

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

    TypeInfer.infer_types (pp ctxt) (tsig_of ctxt) (Syntax.check_typs ctxt)

      (try (Consts.the_constraint (consts_of ctxt))) (Variable.def_type ctxt pattern)

      (Variable.names_of ctxt) (Variable.maxidx_of ctxt) NONE (map (rpair dummyT) ts)

    |> #1 |> map #1

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

  end;

local

fun standard_typ_check ctxt =

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

  map (prepare_patternT ctxt);

fun add_check add f = Context.add_setup

  (Context.theory_map (add (fn xs => fn ctxt => (f ctxt xs, ctxt))));

in

val _ = add_check (Syntax.add_term_check 0 "standard") standard_infer_types;

val _ = add_check (Syntax.add_term_check 50 "abbrevs") (map o expand_abbrevs);

val _ = add_check (Syntax.add_term_check 100 "fixate") prepare_patterns;

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

end;

(* inferred types of parameters *)

fun infer_type ctxt x =

  Term.fastype_of (singleton (Syntax.check_terms (set_mode mode_schematic ctxt))

    (Free (x, dummyT)));

fun inferred_param x ctxt =

  let val T = infer_type ctxt x

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

fun inferred_fixes ctxt =

  fold_map inferred_param (rev (map #2 (Variable.fixes_of ctxt))) ctxt;

(* type and constant names *)

fun read_tyname ctxt c =

  if Syntax.is_tid c then

    TFree (c, the_default (Sign.defaultS (theory_of ctxt)) (Variable.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 x => Free (x, infer_type ctxt x)

  | NONE => Consts.read_const (consts_of ctxt) c);

(** inner syntax operations **)

local

fun parse_sort ctxt str =

  Syntax.standard_parse_sort ctxt (syn_of ctxt) (Sign.intern_sort (theory_of ctxt)) str;

fun parse_typ ctxt str =

  let

    val thy = ProofContext.theory_of ctxt;

    val get_sort = Sign.get_sort thy (Variable.def_sort ctxt);

    val T = Sign.intern_tycons thy

      (Syntax.standard_parse_typ ctxt (syn_of ctxt) get_sort (Sign.intern_sort thy) str);

  in T end

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

fun parse_term T ctxt str =

  let

    val thy = theory_of ctxt;

    val infer = singleton (standard_infer_types (Type.set_mode Type.mode_default ctxt)) o

      TypeInfer.constrain T;

    fun check t = Exn.Result (infer t) handle ERROR msg => Exn.Exn (ERROR msg);

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

    val read = Syntax.standard_parse_term (pp ctxt) check get_sort map_const map_free map_type

      map_sort ctxt (Sign.is_logtype thy) (syn_of ctxt) ((#1 (TypeInfer.paramify_dummies T 0)));

  in read str 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 = undefined,

   unparse_typ = undefined,

   unparse_term = undefined};

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;

(** 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, _) => map (apsnd snd) (Envir.alist_of env));

(* add_binds(_i) *)

local

fun gen_bind prep (xi as (x, _), raw_t) ctxt =

  ctxt

  |> Variable.add_binds [(xi, Option.map (prep (set_mode mode_default ctxt)) raw_t)];

in

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

  | drop_schematic b = b;

val add_binds = fold (gen_bind Syntax.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 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') |> add_binds_i binds''

        else ctxt' |> add_binds_i binds'');

  in (ts, ctxt'') end;

in

fun read_terms ctxt T =

  map (Syntax.parse_term ctxt #> TypeInfer.constrain 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 |> 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 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 [] _ 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 = Goal.norm_hhf_tac THEN' comp_incr_tac facts;

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

  let

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

          |> singleton (Variable.polymorphic ctxt);

        val th = Goal.prove ctxt [] [] prop (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) = #1 (thms_of ctxt);

        val thmref = PureThy.map_name_of_thmref (NameSpace.intern space) xthmref;

        val name = PureThy.name_of_thmref thmref;

        val thms =

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

          else

            (case Symtab.lookup tab name of

              SOME ths => map (Thm.transfer thy) (PureThy.select_thm thmref ths)

            | NONE => from_thy thy xthmref);

      in pick name thms 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 (fn (name, ths) =>

    if valid_thms ctxt (name, ths) then (name, ths)

    else (NameSpace.hidden (if name = "" then "unnamed" else name), ths));

(* name space operations *)

val add_path        = map_naming o NameSpace.add_path;

val no_base_names   = map_naming NameSpace.no_base_names;

val qualified_names = map_naming NameSpace.qualified_names;

val sticky_prefix   = map_naming o NameSpace.sticky_prefix;

val restore_naming  = map_naming o K o naming_of;

val reset_naming    = map_naming (K local_naming);

fun hide_thms fully names = map_thms (fn ((space, tab), index) =>

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

(* put_thms *)

fun update_thms _ ("", NONE) ctxt = ctxt

  | update_thms opts ("", SOME ths) ctxt = ctxt |> map_thms (fn (facts, index) =>

      let

        val index' = uncurry FactIndex.add_local opts ("", ths) index;

      in (facts, index') end)

  | update_thms _ (bname, NONE) ctxt = ctxt |> map_thms (fn ((space, tab), index) =>

      let

        val name = full_name ctxt bname;

        val tab' = Symtab.delete_safe name tab;

      in ((space, tab'), index) end)

  | update_thms opts (bname, SOME ths) ctxt = ctxt |> map_thms (fn ((space, tab), index) =>

      let

        val name = full_name ctxt bname;

        val space' = NameSpace.declare (naming_of ctxt) name space;

        val tab' = Symtab.update (name, ths) tab;

        val index' = uncurry FactIndex.add_local opts (name, ths) index;

      in ((space', tab'), index') end);

fun put_thms thms ctxt =

  ctxt |> map_naming (K local_naming) |> update_thms (true, false) thms |> restore_naming ctxt;

(* note_thmss *)

local

fun gen_note_thmss get k = fold_map (fn ((bname, more_attrs), raw_facts) => fn ctxt =>

  let

    val name = full_name ctxt bname;

    val facts = PureThy.name_thmss false name (map (apfst (get ctxt)) raw_facts);

    fun app (th, attrs) x =

      swap (foldl_map (Thm.proof_attributes (attrs @ more_attrs @ [PureThy.kind k])) (x, th));

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

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

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

  in ((bname, thms), ctxt' |> update_thms (stmt, true) (bname, SOME thms)) end);

in

fun note_thmss k = gen_note_thmss get_thms k;

fun note_thmss_i k = gen_note_thmss (K I) k;

end;

(** parameters **)

(* 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 legacy =

  fold_map (fn (raw_x, raw_T, raw_mx) => fn ctxt =>

    let

      val (x, mx) = Syntax.const_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 cert_typ ctxt o prep_typ ctxt) raw_T;

      val var = (x, opt_T, mx);

    in (var, ctxt |> declare_var var |> #2) end);

in

val read_vars        = prep_vars Syntax.parse_typ false false;

val cert_vars        = prep_vars (K I) true false;

val read_vars_legacy = prep_vars Syntax.parse_typ true true;

val cert_vars_legacy = prep_vars (K I) true true;

end;

(* authentic constants *)

fun const_syntax ctxt (Free (x, T), mx) = SOME (true, (x, T, mx))

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

      Option.map (pair false) (try (Consts.syntax (consts_of ctxt)) (c, mx))

  | const_syntax _ _ = NONE;

fun context_const_ast_tr ctxt [Syntax.Variable c] =

      let

        val consts = consts_of ctxt;

        val c' = Consts.intern consts c;

        val _ = Consts.the_constraint consts c' handle TYPE (msg, _, _) => error msg;

      in Syntax.Constant (Syntax.constN ^ c') end