(*  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

  val is_stmt: Proof.context -> bool

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

  val restore_stmt: Proof.context -> 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 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: bool -> 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 read_termTs: Proof.context -> (string -> bool) -> (indexname -> typ option)

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

    -> term list * (indexname * typ) list

  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 read_term: Proof.context -> string -> term

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

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

  val read_term_pats: typ -> Proof.context -> string list -> term list

  val read_prop_pats: Proof.context -> string list -> term list

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

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

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

  val cert_term_pats: typ -> Proof.context -> term list -> term list

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

  val infer_types: Proof.context -> (term * typ) list -> (term * typ) list

  val infer_types_pat: Proof.context -> (term * typ) list -> (term * typ) list

  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 set_expand_abbrevs: bool -> Proof.context -> Proof.context

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

  val target_abbrev: Syntax.mode -> (string * mixfix) * term -> morphism ->

    Context.generic -> Context.generic

  val local_abbrev: string * 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;

(** Isar proof context information **)

datatype ctxt =

  Ctxt of

   {is_stmt: bool,                                (*inner statement 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 (is_stmt, naming, syntax, consts, thms, cases) =

  Ctxt {is_stmt = is_stmt, naming = naming, syntax = syntax,

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

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

structure ContextData = ProofDataFun

(

  val name = "Isar/context";

  type T = ctxt;

  fun init thy =

    make_ctxt (false, local_naming, LocalSyntax.init thy,

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

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

  fun print _ _ = ();

);

val _ = Context.add_setup ContextData.init;

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

fun map_context f =

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

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

fun set_stmt b =

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

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

fun map_naming f =

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

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

fun map_syntax f =

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

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

fun map_consts f =

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

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

fun map_thms f =

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

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

fun map_cases f =

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

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

val is_stmt = #is_stmt o rep_context;

fun restore_stmt ctxt = set_stmt (is_stmt ctxt);

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 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 warn thy rews t =

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

  else (if warn then warning "Printing malformed term -- cannot expand abbreviations" 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 true thy (Consts.abbrevs_of consts (! print_mode @ [""]))

      |> do_abbrevs ? rewrite_term false 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 quote th =

  let

    val thy = Thm.theory_of_thm th;

    val pp =

      if Theory.eq_thy (thy, ProtoPure.thy) then Sign.pp thy

      else pp (init thy);

  in Display.pretty_thm_aux pp quote false [] th end;

fun pretty_thm ctxt th =

  let

    val thy = theory_of ctxt;

    val (pp, asms) =

      if Theory.eq_thy (thy, ProtoPure.thy) then (Sign.pp thy, [])

      else (pp ctxt, map Thm.term_of (Assumption.assms_of ctxt));

  in Display.pretty_thm_aux pp 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 **)

local

fun read_typ_aux read ctxt s =

  read (syn_of ctxt) ctxt (Variable.def_sort ctxt) s;

fun cert_typ_aux cert ctxt raw_T =

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

in

val read_typ        = read_typ_aux Sign.read_typ';

val read_typ_syntax = read_typ_aux Sign.read_typ_syntax';

val read_typ_abbrev = read_typ_aux Sign.read_typ_abbrev';

val cert_typ        = cert_typ_aux Sign.certify_typ;

val cert_typ_syntax = cert_typ_aux Sign.certify_typ_syntax;

val cert_typ_abbrev = cert_typ_aux Sign.certify_typ_abbrev;

end;

(* internalize Skolem constants *)

val lookup_skolem = AList.lookup (op =) o 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 **)

(*

  (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 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_term_thy freeze pp syn thy defaults fixed s =

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

fun read_prop_thy freeze pp syn thy defaults fixed s =

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

fun read_terms_thy freeze pp syn thy defaults fixed =

  #1 o read_def_termTs freeze pp syn thy defaults fixed o map (rpair dummyT);

fun read_props_thy freeze pp syn thy defaults fixed =

  #1 o read_def_termTs freeze pp syn thy defaults fixed o map (rpair propT);

(* local abbreviations *)

fun certify_consts ctxt =

  Consts.certify (pp ctxt) (tsig_of ctxt) (consts_of ctxt);

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 schematic =

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

(* schematic type variables *)

val reject_tvars = (Term.map_types o Term.map_atyps)

  (fn TVar (xi, _) => error ("Illegal schematic type variable: " ^ Term.string_of_vname xi)

    | T => T);

(* dummy patterns *)

val prepare_dummies =

  let val next = ref 1 in

    fn t =>

      let val (i, u) = Term.replace_dummy_patterns (! next, t)

      in next := i; u end

  end;

fun reject_dummies t = Term.no_dummy_patterns t

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

(* read terms *)

local

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

fun legacy_intern_skolem ctxt internal x =

  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 (Variable.default_type ctxt x);

  in

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

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

      if is_internal andalso is_declared then SOME x else NONE)

  end;

fun gen_read' read app pattern schematic

    ctxt internal more_types more_sorts more_used s =

  let

    val types = append_env (Variable.def_type ctxt pattern) 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) s

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

    |> app (certify_consts ctxt)

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

    |> app (if pattern orelse schematic then I else reject_tvars)

    |> app (if pattern then prepare_dummies else reject_dummies)

  end;

fun gen_read read app pattern schematic ctxt =

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

in

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

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

fun read_term_pats T ctxt =

  #1 o gen_read (read_def_termTs false) (apfst o map) true false ctxt o map (rpair T);

val read_prop_pats = read_term_pats propT;

fun read_prop_legacy ctxt =

  gen_read' (read_prop_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 prop pattern schematic ctxt t = t

  |> certify_consts ctxt

  |> (if pattern then I else expand_binds ctxt schematic)

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

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

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

in

val cert_term = gen_cert false false false;

val cert_prop = gen_cert true false false;

val cert_props = map oo gen_cert true false;

fun cert_term_pats _ = map o gen_cert false true false;

val cert_prop_pats = map o gen_cert true true false;

end;

(* type inference *)

local

fun gen_infer_types pattern ctxt =

  TypeInfer.infer_types (pp ctxt) (tsig_of ctxt) (try (Consts.the_constraint (consts_of ctxt)))

    (Variable.def_type ctxt pattern) (Variable.names_of ctxt) (not pattern) #> #1;

in

val infer_types = gen_infer_types false;

val infer_types_pat = gen_infer_types true;

end;

(* inferred types of parameters *)

fun infer_type ctxt x =

  #2 (singleton (infer_types ctxt) (Free (x, dummyT), 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);

(** 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 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 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' = Variable.declare_term t ctxt;

    val pats = prep_pats (Term.fastype_of t) ctxt' raw_pats;

    val binds = simult_matches ctxt' (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 flat (fold_map (prep_bind prep_pats) (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

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_pats) (ctxt, prop :: props) =

          let val ctxt' = Variable.declare_term prop ctxt

          in ((prop, prep_pats ctxt' raw_pats), (ctxt', props)) end

      | prep _ _ = sys_error "prep_propp";

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

      (context, prep_props schematic context (maps (map fst) args));

  in (context', propp) end;

fun gen_bind_propp prepp (ctxt, raw_args) =

  let

    val (ctxt', args) = prepp (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 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 = 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 th = Goal.prove ctxt [] [] (read_prop ctxt s) (K (ALLGOALS (some_fact_tac ctxt)))

          handle ERROR msg => cat_error msg "Failed to retrieve literal fact.";

      in pick "" [th] end

  | retrieve_thms from_thy pick ctxt xthmref =

      let

        val thy = theory_of ctxt;

        val (space, tab) = #1 (thms_of ctxt);

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

        val name = PureThy.name_of_thmref thmref;

      in

        (case Symtab.lookup tab name of

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

        | NONE => from_thy thy xthmref) |> pick name

      end;

val get_thm = retrieve_thms PureThy.get_thms PureThy.single_thm;

val get_thm_closure = retrieve_thms PureThy.get_thms_closure PureThy.single_thm;

val get_thms = retrieve_thms PureThy.get_thms (K I);

val get_thms_closure = retrieve_thms PureThy.get_thms_closure (K I);

(* valid_thms *)

fun valid_thms ctxt (name, ths) =

  (case try (fn () => get_thms ctxt (Name name)) () of

    NONE => false

  | SOME ths' => Thm.eq_thms (ths, ths'));

(* lthms_containing *)

fun lthms_containing ctxt spec =

  FactIndex.find (fact_index_of ctxt) spec

  |> map (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);

  in ((bname, thms), ctxt' |> update_thms (is_stmt ctxt, 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 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 read_typ false false;

val cert_vars        = prep_vars cert_typ true false;

val read_vars_legacy = prep_vars read_typ true true;

val cert_vars_legacy = prep_vars cert_typ true true;

end;

(* 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

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

val _ = Context.add_setup

 (Sign.add_syntax

   [("_context_const", "id => 'a", Delimfix "CONST _"),

    ("_context_const", "longid => 'a", Delimfix "CONST _")] #>

  Sign.add_advanced_trfuns ([("_context_const", context_const_ast_tr)], [], [], []));

(* notation *)

fun add_notation mode args ctxt =

  ctxt |> map_syntax

    (LocalSyntax.add_modesyntax (theory_of ctxt) mode (map_filter (const_syntax ctxt) args));

fun target_notation mode args phi =

  let val args' = filter (fn (t, _) => Term.equiv_types (t, Morphism.term phi t)) args;

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

(* abbreviations *)

val set_expand_abbrevs = map_consts o apsnd o Consts.set_expand;

fun read_term_abbrev ctxt = read_term (set_expand_abbrevs false ctxt);

fun add_abbrev mode (c, raw_t) ctxt =

  let

    val t0 = cert_term (ctxt |> set_expand_abbrevs false) raw_t

      handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote c);

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

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

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

  in

    ctxt

    |> map_consts (apsnd (K consts'))

    |> Variable.declare_term rhs

    |> pair (lhs, rhs)

  end;

fun target_abbrev prmode ((c, mx), rhs) phi =

  let

    val c' = Morphism.name phi c;

    val rhs' = Morphism.term phi rhs;

    val arg' = (c', rhs');

  in

    Context.mapping_result

      (Sign.add_abbrev Syntax.internalM arg') (add_abbrev Syntax.internalM arg')

    #-> (fn (lhs, _) =>

      Term.equiv_types (rhs, rhs') ? Morphism.form (target_notation prmode [(lhs, mx)]))

  end;

fun local_abbrev (x, rhs) =

  Variable.add_fixes [x] #-> (fn [x'] =>

    let

      val T = Term.fastype_of rhs;

      val lhs = Free (x', T);

    in

      Variable.declare_term lhs #>

      Variable.declare_term rhs #>

      Assumption.add_assms (K (K (I, Envir.expand_term_frees [((x', T), rhs)]))) [] #> snd #>

      pair (lhs, rhs)

    end);

(* fixes *)

local

fun prep_mixfix (x, T, mx) =

  if mx <> NoSyn andalso mx <> Structure andalso

      (can Name.dest_internal x orelse can Name.dest_skolem x) then

    error ("Illegal mixfix syntax for internal/skolem constant " ^ quote x)

  else (true, (x, T, mx));

fun gen_fixes prep raw_vars ctxt =

  let

    val (vars, _) = prep raw_vars ctxt;

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

  in

    ctxt'

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

    |-> (map_syntax o LocalSyntax.add_syntax (theory_of ctxt) o map prep_mixfix)

    |> pair xs'

  end;

in

val add_fixes = gen_fixes read_vars;

val add_fixes_i = gen_fixes cert_vars;

val add_fixes_legacy = gen_fixes cert_vars_legacy;

end;

(* fixes vs. frees *)

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