src/Pure/Tools/rule_insts.ML
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(*  Title:      Pure/Tools/rule_insts.ML
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    Author:     Makarius
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Rule instantiations -- operations within implicit rule / subgoal context.
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*)
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signature BASIC_RULE_INSTS =
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sig
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  val res_inst_tac: Proof.context ->
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    ((indexname * Position.T) * string) list -> thm -> int -> tactic
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  val eres_inst_tac: Proof.context ->
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    ((indexname * Position.T) * string) list -> thm -> int -> tactic
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  val cut_inst_tac: Proof.context ->
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    ((indexname * Position.T) * string) list -> thm -> int -> tactic
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  val forw_inst_tac: Proof.context ->
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    ((indexname * Position.T) * string) list -> thm -> int -> tactic
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  val dres_inst_tac: Proof.context ->
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    ((indexname * Position.T) * string) list -> thm -> int -> tactic
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  val thin_tac: Proof.context -> string -> int -> tactic
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  val subgoal_tac: Proof.context -> string -> int -> tactic
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end;
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signature RULE_INSTS =
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sig
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  include BASIC_RULE_INSTS
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  val where_rule: Proof.context ->
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    ((indexname * Position.T) * string) list ->
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    (binding * string option * mixfix) list -> thm -> thm
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  val of_rule: Proof.context -> string option list * string option list ->
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    (binding * string option * mixfix) list -> thm -> thm
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  val read_instantiate: Proof.context ->
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    ((indexname * Position.T) * string) list -> string list -> thm -> thm
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  val instantiate_tac: Proof.context ->
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    ((indexname * Position.T) * string) list -> string list -> tactic
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  val make_elim_preserve: Proof.context -> thm -> thm
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  val method:
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    (Proof.context -> ((indexname * Position.T) * string) list -> thm -> int -> tactic) ->
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    (Proof.context -> thm list -> int -> tactic) -> (Proof.context -> Proof.method) context_parser
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end;
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structure Rule_Insts: RULE_INSTS =
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struct
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(** reading instantiations **)
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val partition_insts = List.partition (fn (((x, _), _), _) => String.isPrefix "'" x);
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fun error_var msg (xi, pos) =
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  error (msg ^ quote (Term.string_of_vname xi) ^ Position.here pos);
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fun the_sort tvars (xi, pos) : sort =
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  (case AList.lookup (op =) tvars xi of
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    SOME S => S
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  | NONE => error_var "No such type variable in theorem: " (xi, pos));
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fun the_type vars (xi, pos) : typ =
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  (case AList.lookup (op =) vars xi of
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    SOME T => T
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  | NONE => error_var "No such variable in theorem: " (xi, pos));
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local
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fun instantiate inst =
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  Term_Subst.instantiate ([], map (fn (xi, t) => ((xi, Term.fastype_of t), t)) inst) #>
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  Envir.beta_norm;
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fun make_instT f v =
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  let
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    val T = TVar v;
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    val T' = f T;
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  in if T = T' then NONE else SOME (T, T') end;
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fun make_inst f v =
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  let
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    val t = Var v;
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    val t' = f t;
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  in if t aconv t' then NONE else SOME (t, t') end;
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in
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fun readT ctxt tvars ((xi, pos), s) =
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  let
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    val S = the_sort tvars (xi, pos);
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    val T = Syntax.read_typ ctxt s;
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  in
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    if Sign.of_sort (Proof_Context.theory_of ctxt) (T, S) then ((xi, S), T)
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    else error_var "Incompatible sort for typ instantiation of " (xi, pos)
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  end;
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fun read_termTs ctxt ss Ts =
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  let
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    fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;
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    val ts = map2 parse Ts ss;
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    val ts' =
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      map2 (Type.constraint o Type_Infer.paramify_vars) Ts ts
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      |> Syntax.check_terms ctxt
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      |> Variable.polymorphic ctxt;
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    val Ts' = map Term.fastype_of ts';
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    val tyenv = fold Type.raw_match (Ts ~~ Ts') Vartab.empty;
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    val tyenv' = Vartab.fold (fn (xi, (S, T)) => cons ((xi, S), T)) tyenv [];
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  in (ts', tyenv') end;
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fun read_insts ctxt (tvars, vars) mixed_insts =
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  let
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    val (type_insts, term_insts) = partition_insts mixed_insts;
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    (* type instantiations *)
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    val instT1 = Term_Subst.instantiateT (map (readT ctxt tvars) type_insts);
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    val vars1 = map (apsnd instT1) vars;
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    (* term instantiations *)
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    val (xs, ss) = split_list term_insts;
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    val Ts = map (the_type vars1) xs;
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    val (ts, inferred) = read_termTs ctxt ss Ts;
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    val instT2 = Term_Subst.instantiateT inferred;
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    val vars2 = map (apsnd instT2) vars1;
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    val inst2 = instantiate (map #1 xs ~~ ts);
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    (* result *)
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    val inst_tvars = map_filter (make_instT (instT2 o instT1)) tvars;
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    val inst_vars = map_filter (make_inst inst2) vars2;
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  in
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    (map (apply2 (Thm.ctyp_of ctxt)) inst_tvars,
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     map (apply2 (Thm.cterm_of ctxt)) inst_vars)
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  end;
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fun where_rule ctxt mixed_insts fixes thm =
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  let
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    val ctxt' = ctxt
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      |> Proof_Context.read_vars fixes |-> Proof_Context.add_fixes |> #2
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      |> Variable.declare_thm thm;
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    val tvars = Thm.fold_terms Term.add_tvars thm [];
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    val vars = Thm.fold_terms Term.add_vars thm [];
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    val insts = read_insts ctxt' (tvars, vars) mixed_insts;
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  in
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    Drule.instantiate_normalize insts thm
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    |> singleton (Proof_Context.export ctxt' ctxt)
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    |> Rule_Cases.save thm
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  end;
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fun of_rule ctxt (args, concl_args) fixes thm =
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  let
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    fun zip_vars _ [] = []
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      | zip_vars (_ :: xs) (NONE :: rest) = zip_vars xs rest
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      | zip_vars ((x, _) :: xs) (SOME t :: rest) = ((x, Position.none), t) :: zip_vars xs rest
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      | zip_vars [] _ = error "More instantiations than variables in theorem";
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    val insts =
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      zip_vars (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @
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      zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) concl_args;
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  in where_rule ctxt insts fixes thm end;
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end;
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(* instantiation of rule or goal state *)
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fun read_instantiate ctxt insts xs =
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  where_rule ctxt insts (map (fn x => (Binding.name x, NONE, NoSyn)) xs);
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fun instantiate_tac ctxt insts fixes =
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  PRIMITIVE (read_instantiate ctxt insts fixes);
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(** attributes **)
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(* where: named instantiation *)
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val _ = Theory.setup
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  (Attrib.setup @{binding "where"}
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    (Scan.lift
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      (Parse.and_list (Parse.position Args.var -- (Args.$$$ "=" |-- Args.name_inner_syntax))
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        -- Parse.for_fixes) >> (fn (insts, fixes) =>
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          Thm.rule_attribute (fn context => where_rule (Context.proof_of context) insts fixes)))
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    "named instantiation of theorem");
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(* of: positional instantiation (terms only) *)
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local
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val inst = Args.maybe Args.name_inner_syntax;
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val concl = Args.$$$ "concl" -- Args.colon;
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val insts =
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  Scan.repeat (Scan.unless concl inst) --
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  Scan.optional (concl |-- Scan.repeat inst) [];
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in
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val _ = Theory.setup
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  (Attrib.setup @{binding "of"}
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    (Scan.lift (insts -- Parse.for_fixes) >> (fn (args, fixes) =>
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      Thm.rule_attribute (fn context => of_rule (Context.proof_of context) args fixes)))
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    "positional instantiation of theorem");
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end;
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(** tactics **)
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(* resolution after lifting and instantiation; may refer to parameters of the subgoal *)
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fun bires_inst_tac bires_flag ctxt mixed_insts thm i st = CSUBGOAL (fn (cgoal, _) =>
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  let
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    val (Tinsts, tinsts) = partition_insts mixed_insts;
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    (* goal context *)
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    val goal = Thm.term_of cgoal;
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    val params =
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      Logic.strip_params goal
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      (*as they are printed: bound variables with the same name are renamed*)
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      |> Term.rename_wrt_term goal
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      |> rev;
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    val (param_names, ctxt') = ctxt
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      |> Variable.declare_thm thm
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      |> Thm.fold_terms Variable.declare_constraints st
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      |> Proof_Context.add_fixes (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params);
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    (* preprocess rule *)
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    val tvars = Thm.fold_terms Term.add_tvars thm [];
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    val vars = Thm.fold_terms Term.add_vars thm [];
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    val Tinsts_env = map (readT ctxt' tvars) Tinsts;
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    val (xis, ss) = split_list tinsts;
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    val Ts = map (Term_Subst.instantiateT Tinsts_env o the_type vars) xis;
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    val (ts, envT) =
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      read_termTs (Proof_Context.set_mode Proof_Context.mode_schematic ctxt') ss Ts;
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    val envT' = map (fn (v, T) => (TVar v, T)) (envT @ Tinsts_env);
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    val cenv =
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      map (fn ((xi, _), t) => apply2 (Thm.cterm_of ctxt') (Var (xi, fastype_of t), t))
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        (distinct
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          (fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)
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          (xis ~~ ts));
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    (* lift and instantiate rule *)
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    val maxidx = Thm.maxidx_of st;
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    val paramTs = map #2 params;
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    val inc = maxidx + 1;
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    fun lift_var (Var ((a, j), T)) = Var ((a, j + inc), paramTs ---> Logic.incr_tvar inc T)
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      | lift_var t = raise TERM ("Variable expected", [t]);
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    fun lift_term t =
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      fold_rev absfree (param_names ~~ paramTs) (Logic.incr_indexes (paramTs, inc) t);
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    fun lift_inst (cv, ct) = (cterm_fun lift_var cv, cterm_fun lift_term ct);
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    val lift_tvar = apply2 (Thm.ctyp_of ctxt' o Logic.incr_tvar inc);
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    val rule =
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      Drule.instantiate_normalize
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        (map lift_tvar envT', map lift_inst cenv)
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        (Thm.lift_rule cgoal thm);
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  in
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    compose_tac ctxt' (bires_flag, rule, Thm.nprems_of thm) i
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  end) i st;
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val res_inst_tac = bires_inst_tac false;
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val eres_inst_tac = bires_inst_tac true;
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(* forward resolution *)
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fun make_elim_preserve ctxt rl =
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  let
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    val maxidx = Thm.maxidx_of rl;
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    fun cvar xi = Thm.cterm_of ctxt (Var (xi, propT));
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    val revcut_rl' =
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      Drule.instantiate_normalize ([], [(cvar ("V", 0), cvar ("V", maxidx + 1)),
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        (cvar ("W", 0), cvar ("W", maxidx + 1))]) Drule.revcut_rl;
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  in
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    (case Seq.list_of
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      (Thm.bicompose (SOME ctxt) {flatten = true, match = false, incremented = false}
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        (false, rl, Thm.nprems_of rl) 1 revcut_rl')
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     of
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      [th] => th
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    | _ => raise THM ("make_elim_preserve", 1, [rl]))
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  end;
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(*instantiate and cut -- for atomic fact*)
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fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve ctxt rule);
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(*forward tactic applies a rule to an assumption without deleting it*)
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fun forw_inst_tac ctxt insts rule = cut_inst_tac ctxt insts rule THEN' assume_tac ctxt;
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(*dresolve tactic applies a rule to replace an assumption*)
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fun dres_inst_tac ctxt insts rule = eres_inst_tac ctxt insts (make_elim_preserve ctxt rule);
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(* derived tactics *)
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(*deletion of an assumption*)
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fun thin_tac ctxt s =
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  eres_inst_tac ctxt [((("V", 0), Position.none), s)] Drule.thin_rl;
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(*Introduce the given proposition as lemma and subgoal*)
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fun subgoal_tac ctxt A =
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  DETERM o res_inst_tac ctxt [((("psi", 0), Position.none), A)] cut_rl;
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(* method wrapper *)
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fun method inst_tac tac =
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  Args.goal_spec --
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  Scan.optional (Scan.lift
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    (Parse.and_list1 (Parse.position Args.var -- (Args.$$$ "=" |-- Parse.!!! Args.name_inner_syntax))
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      --| Args.$$$ "in")) [] --
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  Attrib.thms >>
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  (fn ((quant, insts), thms) => fn ctxt => METHOD (fn facts =>
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    if null insts then quant (Method.insert_tac facts THEN' tac ctxt thms)
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    else
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      (case thms of
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        [thm] => quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm)
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      | _ => error "Cannot have instantiations with multiple rules")));
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aac494583949 Rule instantiations -- operations within a rule/subgoal context.
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aac494583949 Rule instantiations -- operations within a rule/subgoal context.
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(* setup *)
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(*warning: rule_tac etc. refer to dynamic subgoal context!*)
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val _ = Theory.setup
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 (Method.setup @{binding rule_tac} (method res_inst_tac resolve_tac)
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    "apply rule (dynamic instantiation)" #>
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  Method.setup @{binding erule_tac} (method eres_inst_tac eresolve_tac)
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    "apply rule in elimination manner (dynamic instantiation)" #>
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  Method.setup @{binding drule_tac} (method dres_inst_tac dresolve_tac)
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    "apply rule in destruct manner (dynamic instantiation)" #>
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  Method.setup @{binding frule_tac} (method forw_inst_tac forward_tac)
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    "apply rule in forward manner (dynamic instantiation)" #>
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  Method.setup @{binding cut_tac} (method cut_inst_tac (K cut_rules_tac))
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    "cut rule (dynamic instantiation)" #>
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  Method.setup @{binding subgoal_tac}
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    (Args.goal_spec -- Scan.lift (Scan.repeat1 Args.name_inner_syntax) >>
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      (fn (quant, props) => fn ctxt =>
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        SIMPLE_METHOD'' quant (EVERY' (map (subgoal_tac ctxt) props))))
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    "insert subgoal (dynamic instantiation)" #>
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  Method.setup @{binding thin_tac}
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    (Args.goal_spec -- Scan.lift Args.name_inner_syntax >>
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      (fn (quant, prop) => fn ctxt => SIMPLE_METHOD'' quant (thin_tac ctxt prop)))
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      "remove premise (dynamic instantiation)");
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end;
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structure Basic_Rule_Insts: BASIC_RULE_INSTS = Rule_Insts;
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open Basic_Rule_Insts;