(*  Title:      Pure/variable.ML

    Author:     Makarius

Fixed type/term variables and polymorphic term abbreviations.

*)

signature VARIABLE =

sig

  val is_body: Proof.context -> bool

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

  val restore_body: Proof.context -> Proof.context -> Proof.context

  val names_of: Proof.context -> Name.context

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

  val binds_of: Proof.context -> (typ * term) Vartab.table

  val maxidx_of: Proof.context -> int

  val sorts_of: Proof.context -> sort list

  val constraints_of: Proof.context -> typ Vartab.table * sort Vartab.table

  val is_declared: Proof.context -> string -> bool

  val is_fixed: Proof.context -> string -> bool

  val newly_fixed: Proof.context -> Proof.context -> string -> bool

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

  val default_type: Proof.context -> string -> typ option

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

  val def_sort: Proof.context -> indexname -> sort option

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

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

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

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

  val declare_prf: Proofterm.proof -> Proof.context -> Proof.context

  val declare_thm: thm -> Proof.context -> Proof.context

  val thm_context: thm -> Proof.context

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

  val bind_term: indexname * term option -> Proof.context -> Proof.context

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

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

  val is_const: Proof.context -> string -> bool

  val declare_const: string * string -> Proof.context -> Proof.context

  val add_fixes: string list -> Proof.context -> string list * Proof.context

  val add_fixes_direct: string list -> Proof.context -> Proof.context

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

  val variant_fixes: string list -> Proof.context -> string list * Proof.context

  val invent_types: sort list -> Proof.context -> (string * sort) list * Proof.context

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

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

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

  val export_prf: Proof.context -> Proof.context -> Proofterm.proof -> Proofterm.proof

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

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

  val importT_inst: term list -> Proof.context -> ((indexname * sort) * typ) list * Proof.context

  val import_inst: bool -> term list -> Proof.context ->

    (((indexname * sort) * typ) list * ((indexname * typ) * term) list) * Proof.context

  val importT_terms: term list -> Proof.context -> term list * Proof.context

  val import_terms: bool -> term list -> Proof.context -> term list * Proof.context

  val importT: thm list -> Proof.context -> (ctyp list * thm list) * Proof.context

  val import_prf: bool -> Proofterm.proof -> Proof.context -> Proofterm.proof * Proof.context

  val import: bool -> thm list -> Proof.context ->

    ((ctyp list * cterm list) * thm list) * Proof.context

  val tradeT: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list

  val trade: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list

  val focus: cterm -> Proof.context -> (cterm list * cterm) * Proof.context

  val focus_subgoal: int -> thm -> Proof.context -> (cterm list * cterm) * Proof.context

  val warn_extra_tfrees: Proof.context -> Proof.context -> unit

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

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

end;

structure Variable: VARIABLE =

struct

(** local context data **)

datatype data = Data of

 {is_body: bool,                        (*inner body mode*)

  names: Name.context,                  (*type/term variable names*)

  consts: string Symtab.table,          (*consts within the local scope*)

  fixes: (string * string) list,        (*term fixes -- extern/intern*)

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

  type_occs: string list Symtab.table,  (*type variables -- possibly within term variables*)

  maxidx: int,                          (*maximum var index*)

  sorts: sort OrdList.T,                (*declared sort occurrences*)

  constraints:

    typ Vartab.table *                  (*type constraints*)

    sort Vartab.table};                 (*default sorts*)

fun make_data (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =

  Data {is_body = is_body, names = names, consts = consts, fixes = fixes, binds = binds,

    type_occs = type_occs, maxidx = maxidx, sorts = sorts, constraints = constraints};

structure Data = ProofDataFun

(

  type T = data;

  fun init thy =

    make_data (false, Name.context, Symtab.empty, [], Vartab.empty, Symtab.empty,

      ~1, [], (Vartab.empty, Vartab.empty));

);

fun map_data f =

  Data.map (fn Data {is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints} =>

    make_data (f (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints)));

fun map_names f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, f names, consts, fixes, binds, type_occs, maxidx, sorts, constraints));

fun map_consts f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, f consts, fixes, binds, type_occs, maxidx, sorts, constraints));

fun map_fixes f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, consts, f fixes, binds, type_occs, maxidx, sorts, constraints));

fun map_binds f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, consts, fixes, f binds, type_occs, maxidx, sorts, constraints));

fun map_type_occs f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, consts, fixes, binds, f type_occs, maxidx, sorts, constraints));

fun map_maxidx f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, consts, fixes, binds, type_occs, f maxidx, sorts, constraints));

fun map_sorts f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, consts, fixes, binds, type_occs, maxidx, f sorts, constraints));

fun map_constraints f =

  map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, f constraints));

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

val is_body = #is_body o rep_data;

fun set_body b =

  map_data (fn (_, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>

    (b, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints));

fun restore_body ctxt = set_body (is_body ctxt);

val names_of = #names o rep_data;

val fixes_of = #fixes o rep_data;

val binds_of = #binds o rep_data;

val type_occs_of = #type_occs o rep_data;

val maxidx_of = #maxidx o rep_data;

val sorts_of = #sorts o rep_data;

val constraints_of = #constraints o rep_data;

val is_declared = Name.is_declared o names_of;

fun is_fixed ctxt x = exists (fn (_, y) => x = y) (fixes_of ctxt);

fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);

fun add_fixed ctxt = Term.fold_aterms

  (fn Free (x, T) => if is_fixed ctxt x then insert (op =) (x, T) else I | _ => I);

(** declarations **)

(* default sorts and types *)

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

fun def_type ctxt pattern xi =

  let val {binds, constraints = (types, _), ...} = rep_data ctxt in

    (case Vartab.lookup types xi of

      NONE =>

        if pattern then NONE

        else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #1)

    | some => some)

  end;

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

(* names *)

fun declare_type_names t =

  map_names (fold_types (fold_atyps Term.declare_typ_names) t) #>

  map_maxidx (fold_types Term.maxidx_typ t);

fun declare_names t =

  declare_type_names t #>

  map_names (fold_aterms Term.declare_term_frees t) #>

  map_maxidx (Term.maxidx_term t);

(* type occurrences *)

fun decl_type_occsT T = fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I) T;

val decl_type_occs = fold_term_types

  (fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)

    | _ => decl_type_occsT);

val declare_type_occsT = map_type_occs o fold_types decl_type_occsT;

val declare_type_occs = map_type_occs o decl_type_occs;

(* constraints *)

fun constrain_tvar (xi, S) =

  if S = dummyS then Vartab.delete_safe xi else Vartab.update (xi, S);

fun declare_constraints t = map_constraints (fn (types, sorts) =>

  let

    val types' = fold_aterms

      (fn Free (x, T) => Vartab.update ((x, ~1), T)

        | Var v => Vartab.update v

        | _ => I) t types;

    val sorts' = fold_types (fold_atyps

      (fn TFree (x, S) => constrain_tvar ((x, ~1), S)

        | TVar v => constrain_tvar v

        | _ => I)) t sorts;

  in (types', sorts') end)

  #> declare_type_occsT t

  #> declare_type_names t;

(* common declarations *)

fun declare_internal t =

  declare_names t #>

  declare_type_occs t #>

  map_sorts (Sorts.insert_term t);

fun declare_term t =

  declare_internal t #>

  declare_constraints t;

val declare_typ = declare_term o Logic.mk_type;

val declare_prf = Proofterm.fold_proof_terms declare_internal (declare_internal o Logic.mk_type);

val declare_thm = Thm.fold_terms declare_internal;

fun thm_context th = declare_thm th (ProofContext.init (Thm.theory_of_thm th));

(* renaming term/type frees *)

fun variant_frees ctxt ts frees =

  let

    val names = names_of (fold declare_names ts ctxt);

    val xs = fst (Name.variants (map #1 frees) names);

  in xs ~~ map snd frees end;

(** term bindings **)

fun bind_term (xi, NONE) = map_binds (Vartab.delete_safe xi)

  | bind_term ((x, i), SOME t) =

      let

        val u = Term.close_schematic_term t;

        val U = Term.fastype_of u;

      in declare_term u #> map_binds (Vartab.update ((x, i), (U, u))) end;

fun expand_binds ctxt =

  let

    val binds = binds_of ctxt;

    val get = fn Var (xi, _) => Vartab.lookup binds xi | _ => NONE;

  in Envir.beta_norm o Envir.expand_term get end;

(** consts **)

val lookup_const = Symtab.lookup o #consts o rep_data;

val is_const = is_some oo lookup_const;

val declare_fixed = map_consts o Symtab.delete_safe;

val declare_const = map_consts o Symtab.update;

(** fixes **)

local

fun no_dups [] = ()

  | no_dups dups = error ("Duplicate fixed variable(s): " ^ commas_quote dups);

fun new_fixes names' xs xs' =

  map_names (K names') #>

  fold declare_fixed xs #>

  map_fixes (fn fixes => (rev (xs ~~ xs') @ fixes)) #>

  fold (declare_constraints o Syntax.free) xs' #>

  pair xs';

in

fun add_fixes xs ctxt =

  let

    val _ =

      (case filter (can Name.dest_skolem) xs of [] => ()

      | bads => error ("Illegal internal Skolem constant(s): " ^ commas_quote bads));

    val _ = no_dups (duplicates (op =) xs);

    val (ys, zs) = split_list (fixes_of ctxt);

    val names = names_of ctxt;

    val (xs', names') =

      if is_body ctxt then Name.variants xs names |>> map Name.skolem

      else (no_dups (xs inter_string ys); no_dups (xs inter_string zs);

        (xs, fold Name.declare xs names));

  in ctxt |> new_fixes names' xs xs' end;

fun variant_fixes raw_xs ctxt =

  let

    val names = names_of ctxt;

    val xs = map (fn x => Name.clean x |> can Name.dest_internal x ? Name.internal) raw_xs;

    val (xs', names') = Name.variants xs names |>> (is_body ctxt ? map Name.skolem);

  in ctxt |> new_fixes names' xs xs' end;

end;

fun add_fixes_direct xs ctxt = ctxt

  |> set_body false

  |> (snd o add_fixes xs)

  |> restore_body ctxt;

fun fix_frees t ctxt = ctxt

  |> add_fixes_direct

      (rev (fold_aterms (fn Free (x, _) =>

        if is_fixed ctxt x then I else insert (op =) x | _ => I) t []));

fun auto_fixes t ctxt =

  (if is_body ctxt then ctxt else fix_frees t ctxt)

  |> declare_term t;

fun invent_types Ss ctxt =

  let

    val tfrees = Name.invents (names_of ctxt) Name.aT (length Ss) ~~ Ss;

    val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;

  in (tfrees, ctxt') end;

(** export -- generalize type/term variables (beware of closure sizes) **)

fun export_inst inner outer =

  let

    val declared_outer = is_declared outer;

    val fixes_inner = fixes_of inner;

    val fixes_outer = fixes_of outer;

    val gen_fixes = map #2 (Library.take (length fixes_inner - length fixes_outer, fixes_inner));

    val still_fixed = not o member (op =) gen_fixes;

    val type_occs_inner = type_occs_of inner;

    fun gen_fixesT ts =

      Symtab.fold (fn (a, xs) =>

        if declared_outer a orelse exists still_fixed xs

        then I else cons a) (fold decl_type_occs ts type_occs_inner) [];

  in (gen_fixesT, gen_fixes) end;

fun exportT_inst inner outer = #1 (export_inst inner outer);

fun exportT_terms inner outer =

  let val mk_tfrees = exportT_inst inner outer in

    fn ts => ts |> map

      (TermSubst.generalize (mk_tfrees ts, [])

        (fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1))

  end;

fun export_terms inner outer =

  let val (mk_tfrees, tfrees) = export_inst inner outer in

    fn ts => ts |> map

      (TermSubst.generalize (mk_tfrees ts, tfrees)

        (fold Term.maxidx_term ts ~1 + 1))

  end;

fun export_prf inner outer prf =

  let

    val (mk_tfrees, frees) = export_inst (declare_prf prf inner) outer;

    val tfrees = mk_tfrees [];

    val idx = Proofterm.maxidx_proof prf ~1 + 1;

    val gen_term = TermSubst.generalize_option (tfrees, frees) idx;

    val gen_typ = TermSubst.generalizeT_option tfrees idx;

  in Proofterm.map_proof_terms_option gen_term gen_typ prf end;

fun gen_export (mk_tfrees, frees) ths =

  let

    val tfrees = mk_tfrees (map Thm.full_prop_of ths);

    val maxidx = fold Thm.maxidx_thm ths ~1;

  in map (Thm.generalize (tfrees, frees) (maxidx + 1)) ths end;

fun exportT inner outer = gen_export (exportT_inst inner outer, []);

fun export inner outer = gen_export (export_inst inner outer);

fun export_morphism inner outer =

  let

    val fact = export inner outer;

    val term = singleton (export_terms inner outer);

    val typ = Logic.type_map term;

  in Morphism.morphism {binding = I, typ = typ, term = term, fact = fact} end;

(** import -- fix schematic type/term variables **)

fun importT_inst ts ctxt =

  let

    val tvars = rev (fold Term.add_tvars ts []);

    val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;

  in (tvars ~~ map TFree tfrees, ctxt') end;

fun import_inst is_open ts ctxt =

  let

    val ren = Name.clean #> (if is_open then I else Name.internal);

    val (instT, ctxt') = importT_inst ts ctxt;

    val vars = map (apsnd (TermSubst.instantiateT instT)) (rev (fold Term.add_vars ts []));

    val (xs, ctxt'') = variant_fixes (map (ren o #1 o #1) vars) ctxt';

    val inst = vars ~~ map Free (xs ~~ map #2 vars);

  in ((instT, inst), ctxt'') end;

fun importT_terms ts ctxt =

  let val (instT, ctxt') = importT_inst ts ctxt

  in (map (TermSubst.instantiate (instT, [])) ts, ctxt') end;

fun import_terms is_open ts ctxt =

  let val (inst, ctxt') = import_inst is_open ts ctxt

  in (map (TermSubst.instantiate inst) ts, ctxt') end;

fun importT ths ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val certT = Thm.ctyp_of thy;

    val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;

    val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;

    val ths' = map (Thm.instantiate (instT', [])) ths;

  in ((map #2 instT', ths'), ctxt') end;

fun import_prf is_open prf ctxt =

  let

    val ts = rev (Proofterm.fold_proof_terms cons (cons o Logic.mk_type) prf []);

    val (insts, ctxt') = import_inst is_open ts ctxt;

  in (Proofterm.instantiate insts prf, ctxt') end;

fun import is_open ths ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val cert = Thm.cterm_of thy;

    val certT = Thm.ctyp_of thy;

    val ((instT, inst), ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;

    val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;

    val inst' = map (fn (v, t) => (cert (Var v), cert t)) inst;

    val ths' = map (Thm.instantiate (instT', inst')) ths;

  in (((map #2 instT', map #2 inst'), ths'), ctxt') end;

(* import/export *)

fun gen_trade imp exp f ctxt ths =

  let val ((_, ths'), ctxt') = imp ths ctxt

  in exp ctxt' ctxt (f ctxt' ths') end;

val tradeT = gen_trade importT exportT;

val trade = gen_trade (import true) export;

(* focus on outermost parameters *)

fun forall_elim_prop t prop =

  Thm.beta_conversion false (Thm.capply (Thm.dest_arg prop) t)

  |> Thm.cprop_of |> Thm.dest_arg;

fun focus goal ctxt =

  let

    val cert = Thm.cterm_of (Thm.theory_of_cterm goal);

    val t = Thm.term_of goal;

    val ps = Term.variant_frees t (Term.strip_all_vars t);   (*as they are printed :-*)

    val (xs, Ts) = split_list ps;

    val (xs', ctxt') = variant_fixes xs ctxt;

    val ps' = ListPair.map (cert o Free) (xs', Ts);

    val goal' = fold forall_elim_prop ps' goal;

    val ctxt'' = ctxt' |> fold (declare_constraints o Thm.term_of) ps';

  in ((ps', goal'), ctxt'') end;

fun focus_subgoal i st =

  let

    val all_vars = Thm.fold_terms Term.add_vars st [];

    val no_binds = map (fn (xi, _) => (xi, NONE)) all_vars;

  in

    fold bind_term no_binds #>

    fold (declare_constraints o Var) all_vars #>

    focus (Thm.cprem_of st i)

  end;

(** implicit polymorphism **)

(* warn_extra_tfrees *)

fun warn_extra_tfrees ctxt1 ctxt2 =

  let

    fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);

    fun occs_free a x =

      (case def_type ctxt1 false (x, ~1) of

        SOME T => if occs_typ a T then I else cons (a, x)

      | NONE => cons (a, x));

    val occs1 = type_occs_of ctxt1;

    val occs2 = type_occs_of ctxt2;

    val extras = Symtab.fold (fn (a, xs) =>

      if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];

    val tfrees = map #1 extras |> sort_distinct string_ord;

    val frees = map #2 extras |> sort_distinct string_ord;

  in

    if null extras then ()

    else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^

      space_implode " or " (map quote frees))

  end;

(* polymorphic terms *)

fun polymorphic_types ctxt ts =

  let

    val ctxt' = fold declare_term ts ctxt;

    val occs = type_occs_of ctxt;

    val occs' = type_occs_of ctxt';

    val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];

    val idx = maxidx_of ctxt' + 1;

    val Ts' = (fold o fold_types o fold_atyps)

      (fn T as TFree _ =>

          (case TermSubst.generalizeT types idx T of TVar v => insert (op =) v | _ => I)

        | _ => I) ts [];

    val ts' = map (TermSubst.generalize (types, []) idx) ts;

  in (rev Ts', ts') end;

fun polymorphic ctxt ts = snd (polymorphic_types ctxt ts);

end;