(*  Title:      Pure/Isar/proof_context.ML

    Author:     Markus Wenzel, TU Muenchen

The key concept of Isar proof contexts: elevates primitive local

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

elements.  See also structure Variable and Assumption.

*)

signature PROOF_CONTEXT =

sig

  val theory_of: Proof.context -> theory

  val init_global: theory -> Proof.context

  type mode

  val mode_default: mode

  val mode_stmt: mode

  val mode_pattern: mode

  val mode_schematic: mode

  val mode_abbrev: mode

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

  val get_mode: Proof.context -> mode

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

  val abbrev_mode: Proof.context -> bool

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

  val local_naming: Name_Space.naming

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

  val naming_of: Proof.context -> Name_Space.naming

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

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

  val syntax_of: Proof.context -> Local_Syntax.T

  val syn_of: Proof.context -> Syntax.syntax

  val tsig_of: Proof.context -> Type.tsig

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

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

  val consts_of: Proof.context -> Consts.T

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

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

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

  val facts_of: Proof.context -> Facts.T

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  val allow_dummies: Proof.context -> Proof.context

  val get_sort: Proof.context -> (indexname * sort) list -> indexname -> sort

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

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

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

  val intern_skolem: Proof.context -> string -> string option

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

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

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

  val show_abbrevs_raw: Config.raw

  val show_abbrevs: bool Config.T

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  val fact_tac: thm list -> int -> tactic

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

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

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

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

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

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

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

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

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

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

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

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

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

    string list * Proof.context

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

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

  val add_assms: Assumption.export ->

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

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

  val add_assms_i: Assumption.export ->

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

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

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

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

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

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

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

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

    Context.generic -> Context.generic

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

    Context.generic -> Context.generic

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

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

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

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

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

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

  val print_syntax: Proof.context -> unit

  val print_abbrevs: Proof.context -> unit

  val print_binds: Proof.context -> unit

  val print_lthms: Proof.context -> unit

  val print_cases: Proof.context -> unit

  val debug: bool Unsynchronized.ref

  val verbose: bool Unsynchronized.ref

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

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

end;

structure ProofContext: PROOF_CONTEXT =

struct

open ProofContext;

(** inner syntax mode **)

datatype mode =

  Mode of

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

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

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

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

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

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

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

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

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

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

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

(** Isar proof context information **)

datatype ctxt =

  Ctxt of

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

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

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

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

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

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

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

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

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

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

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

structure Data = Proof_Data

(

  type T = ctxt;

  fun init thy =

    make_ctxt (mode_default, local_naming, Local_Syntax.init thy,

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

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

);

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

fun map_context f =

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

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

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

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

fun map_mode f =

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

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

fun map_naming f =

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

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

fun map_syntax f =

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

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

fun map_tsig f =

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

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

fun map_consts f =

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

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

fun map_facts f =

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

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

fun map_cases f =

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

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

val get_mode = #mode o rep_context;

val restore_mode = set_mode o get_mode;

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

fun set_stmt stmt =

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

val naming_of = #naming o rep_context;

val restore_naming = map_naming o K o naming_of

val full_name = Name_Space.full_name o naming_of;

val syntax_of = #syntax o rep_context;

val syn_of = Local_Syntax.syn_of o syntax_of;

val set_syntax_mode = map_syntax o Local_Syntax.set_mode;

val restore_syntax_mode = map_syntax o Local_Syntax.restore_mode o syntax_of;

val tsig_of = #1 o #tsig o rep_context;

val set_defsort = map_tsig o apfst o Type.set_defsort;

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

val consts_of = #1 o #consts o rep_context;

val the_const_constraint = Consts.the_constraint o consts_of;

val facts_of = #facts o rep_context;

val cases_of = #cases o rep_context;

(* theory transfer *)

fun transfer_syntax thy ctxt = ctxt |>

  map_syntax (Local_Syntax.rebuild thy) |>

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

    let val thy_tsig = Sign.tsig_of thy in

      if Type.eq_tsig (thy_tsig, global_tsig) then tsig

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

    end) |>

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

    let val thy_consts = Sign.consts_of thy in

      if Consts.eq_consts (thy_consts, global_consts) then consts

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

    end);

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

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

fun background_theory_result f ctxt =

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

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

(** pretty printing **)

(* extern *)

fun extern_fact ctxt name =

  let

    val local_facts = facts_of ctxt;

    val global_facts = Global_Theory.facts_of (theory_of ctxt);

  in

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

    then Facts.extern ctxt local_facts name

    else Facts.extern ctxt global_facts name

  end;

(* pretty *)

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

fun pretty_fact_name ctxt a = Pretty.block

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

fun pretty_fact_aux ctxt flag ("", ths) =

      Display.pretty_thms_aux ctxt flag ths

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

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

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

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

fun pretty_fact ctxt = pretty_fact_aux ctxt true;

(** prepare types **)

(* classes *)

fun read_class ctxt text =

  let

    val tsig = tsig_of ctxt;

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

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

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

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

  in c end;

(* type arities *)

local

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

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

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

in

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

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

end;

(* types *)

fun read_typ_mode mode ctxt s =

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

val read_typ = read_typ_mode Type.mode_default;

val read_typ_syntax = read_typ_mode Type.mode_syntax;

val read_typ_abbrev = read_typ_mode Type.mode_abbrev;

fun cert_typ_mode mode ctxt T =

  Type.cert_typ_mode mode (tsig_of ctxt) T

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

val cert_typ = cert_typ_mode Type.mode_default;

val cert_typ_syntax = cert_typ_mode Type.mode_syntax;

val cert_typ_abbrev = cert_typ_mode Type.mode_abbrev;

(** prepare variables **)

(* internalize Skolem constants *)

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

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

fun no_skolem internal x =

  if can Name.dest_skolem x then

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

  else if not internal andalso can Name.dest_internal x then

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

  else x;

(* revert Skolem constants -- if possible *)

fun revert_skolem ctxt x =

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

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

  | NONE => x);

(** prepare terms and propositions **)

(* inferred types of parameters *)

fun infer_type ctxt x =

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

fun inferred_param x ctxt =

  let val T = infer_type ctxt (x, dummyT)

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

fun inferred_fixes ctxt =

  let

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

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

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

(* type and constant names *)

local

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

fun prep_const_proper ctxt strict (c, pos) =

  let

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

    val consts = consts_of ctxt;

    val t as Const (d, _) =

      (case Variable.lookup_const ctxt c of

        SOME d =>

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

      | NONE => Consts.read_const consts c);

    val _ =

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

      else ();

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

  in t end;

in

fun read_type_name ctxt strict text =

  let

    val tsig = tsig_of ctxt;

    val (c, pos) = token_content text;

  in

    if Lexicon.is_tid c then

     (Context_Position.report ctxt pos Markup.tfree;

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

    else

      let

        val d = Type.intern_type tsig c;

        val decl = Type.the_decl tsig d;

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

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

        val args =

          (case decl of

            Type.LogicalType n => n

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

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

      in Type (d, replicate args dummyT) end

  end;

fun read_type_name_proper ctxt strict text =

  (case read_type_name ctxt strict text of

    T as Type _ => T

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

fun read_const_proper ctxt strict = prep_const_proper ctxt strict o token_content;

fun read_const ctxt strict ty text =

  let

    val (c, pos) = token_content text;

    val _ = no_skolem false c;

  in

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

      (SOME x, false) =>

        (Context_Position.report ctxt pos

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

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

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

  end;

end;

(* skolem variables *)

fun intern_skolem ctxt x =

  let

    val _ = no_skolem false x;

    val sko = lookup_skolem ctxt x;

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

    val is_declared = is_some (Variable.def_type ctxt false (x, ~1));

  in

    if Variable.is_const ctxt x then NONE

    else if is_some sko then sko

    else if not is_const orelse is_declared then SOME x

    else NONE

  end;

(* read_term *)

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

val read_term_pattern   = read_term_mode mode_pattern;

val read_term_schematic = read_term_mode mode_schematic;

val read_term_abbrev    = read_term_mode mode_abbrev;

(* local abbreviations *)

local

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

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

fun expand_binds ctxt =

  let

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

    fun reject_schematic (t as Var _) =

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

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

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

      | reject_schematic _ = ();

  in

    if pattern then I

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

  end;

in

fun expand_abbrevs ctxt = certify_consts ctxt #> expand_binds ctxt;

end;

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

val show_abbrevs = Config.bool show_abbrevs_raw;

fun contract_abbrevs ctxt t =

  let

    val thy = theory_of ctxt;

    val consts = consts_of ctxt;

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

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

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

  in

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

    else Pattern.rewrite_term_top thy [] [match_abbrev] t

  end;

(* patterns *)

fun prepare_patternT ctxt T =

  let

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

    val _ =

      pattern orelse schematic orelse

        T |> Term.exists_subtype

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

            not (Type_Infer.is_param xi) andalso

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

          | _ => false)

  in T end;

local

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

fun check_dummies ctxt t =

  if Config.get ctxt dummies then t

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

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

in

val allow_dummies = Config.put dummies true;

fun prepare_patterns ctxt =

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

    Type_Infer.fixate ctxt #>

    pattern ? Variable.polymorphic ctxt #>

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

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

  end;

end;

(* sort constraints *)

fun get_sort ctxt raw_text =

  let

    val tsig = tsig_of ctxt;

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

    val _ =

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

        [] => ()

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

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

    fun lookup xi =

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

        NONE => NONE

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

    fun get xi =

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

        (NONE, NONE) => Type.defaultS tsig

      | (NONE, SOME S) => S

      | (SOME S, NONE) => S

      | (SOME S, SOME S') =>

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

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

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

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

  in get end;

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

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

(* certify terms *)

local

fun gen_cert prop ctxt t =

  t

  |> expand_abbrevs ctxt

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

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

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

in

val cert_term = gen_cert false;

val cert_prop = gen_cert true;

end;

(* type checking/inference *)

fun def_type ctxt =

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

  in Variable.def_type ctxt pattern end;

fun standard_infer_types ctxt =

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

local

fun standard_typ_check ctxt =

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

  map (prepare_patternT ctxt);

fun standard_term_check ctxt =

  standard_infer_types ctxt #>

  map (expand_abbrevs ctxt);

fun standard_term_uncheck ctxt =

  map (contract_abbrevs ctxt);

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

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

in

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

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

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

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

end;

(** export results **)

fun common_export is_goal inner outer =

  map (Assumption.export is_goal inner outer) #>

  Variable.export inner outer;

val goal_export = common_export true;

val export = common_export false;

fun export_morphism inner outer =

  Assumption.export_morphism inner outer $>

  Variable.export_morphism inner outer;

fun norm_export_morphism inner outer =

  export_morphism inner outer $>

  Morphism.thm_morphism Goal.norm_result;

(** term bindings **)

(* simult_matches *)

fun simult_matches ctxt (t, pats) =

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

    NONE => error "Pattern match failed!"

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

(* bind_terms *)

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

  ctxt

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

(* auto_bind *)

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

  | drop_schematic b = b;

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

val auto_bind_goal = auto_bind Auto_Bind.goal;

val auto_bind_facts = auto_bind Auto_Bind.facts;

(* match_bind(_i) *)

local

fun gen_bind prep_terms gen raw_binds ctxt =

  let

    fun prep_bind (raw_pats, t) ctxt1 =

      let

        val T = Term.fastype_of t;

        val ctxt2 = Variable.declare_term t ctxt1;

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

        val binds = simult_matches ctxt2 (t, pats);

      in (binds, ctxt2) end;

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

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

    val binds' =

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

      else binds;

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

    val ctxt'' =

      tap (Variable.warn_extra_tfrees ctxt)

       (if gen then

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

        else ctxt' |> bind_terms binds'');

  in (ts, ctxt'') end;

in

fun read_terms ctxt T =

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

val match_bind = gen_bind read_terms;

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

end;

(* propositions with patterns *)

local

fun prep_propp mode prep_props (context, args) =

  let

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

      let val ctxt' = Variable.declare_term prop ctxt

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

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

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

  in (context', propp) end;

fun gen_bind_propp mode parse_prop (ctxt, raw_args) =

  let

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

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

    val propss = map (map #1) args;

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

    val gen = Variable.exportT_terms ctxt' ctxt;

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

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

in

val read_propp           = prep_propp mode_default Syntax.read_props;

val cert_propp           = prep_propp mode_default (map o cert_prop);

val read_propp_schematic = prep_propp mode_schematic Syntax.read_props;

val cert_propp_schematic = prep_propp mode_schematic (map o cert_prop);

val bind_propp             = gen_bind_propp mode_default Syntax.read_props;

val bind_propp_i           = gen_bind_propp mode_default (map o cert_prop);

val bind_propp_schematic   = gen_bind_propp mode_schematic Syntax.read_props;

val bind_propp_schematic_i = gen_bind_propp mode_schematic (map o cert_prop);

end;

(** theorems **)

(* fact_tac *)

fun comp_incr_tac [] _ = no_tac

  | comp_incr_tac (th :: ths) i =

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

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

fun potential_facts ctxt prop =

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

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

(* get_thm(s) *)

local

fun retrieve_thms pick ctxt (Facts.Fact s) =

      let

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

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

          |> singleton (Variable.polymorphic ctxt);

        fun prove_fact th =

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

        val res =

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

            SOME res => res

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

              Syntax.string_of_term ctxt prop))

      in pick "" [res] end

  | retrieve_thms pick ctxt xthmref =

      let

        val thy = theory_of ctxt;

        val local_facts = facts_of ctxt;

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

        val name = Facts.name_of_ref thmref;

        val pos = Facts.pos_of_ref xthmref;

        val thms =

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

          else

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

              SOME (_, ths) =>

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

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

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

      in pick name thms end;

in

val get_fact = retrieve_thms (K I);

val get_fact_single = retrieve_thms Facts.the_single;

fun get_thms ctxt = get_fact ctxt o Facts.named;

fun get_thm ctxt = get_fact_single ctxt o Facts.named;

end;

(* facts *)

local

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

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

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

in

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

  let

    val pos = Binding.pos_of b;

    val name = full_name ctxt b;

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

    val facts = Global_Theory.name_thmss false name raw_facts;

    fun app (th, attrs) x =

      swap (Library.foldl_map

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

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

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

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

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

fun put_thms do_props thms ctxt = ctxt

  |> map_naming (K local_naming)

  |> Context_Position.set_visible false

  |> update_thms do_props (apfst Binding.name thms)

  |> Context_Position.restore_visible ctxt

  |> restore_naming ctxt;

end;

(** basic logical entities **)

(* variables *)

fun declare_var (x, opt_T, mx) ctxt =

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

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

local

fun prep_vars prep_typ internal =

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

    let

      val x = Variable.name b;

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

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

      fun cond_tvars T =

        if internal then T

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

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

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

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

in

val read_vars = prep_vars Syntax.parse_typ false;

val cert_vars = prep_vars (K I) true;

end;

(* notation *)

local

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

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

  | type_syntax _ = NONE;

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

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

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

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

      | NONE => NONE)

  | const_syntax _ _ = NONE;

fun gen_notation syntax add mode args ctxt =

  ctxt |> map_syntax

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

in

val type_notation = gen_notation (K type_syntax);

val notation = gen_notation const_syntax;

fun target_type_notation add mode args phi =

  let

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

      let

        val T' = Morphism.typ phi T;

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

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

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

fun target_notation add mode args phi =

  let

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

      let val t' = Morphism.term phi t

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

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

end;

(* aliases *)

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

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

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