(*  Title:      Pure/Isar/rule_insts.ML

    Author:     Makarius

Rule instantiations -- operations within a rule/subgoal context.

*)

signature BASIC_RULE_INSTS =

sig

  val read_instantiate: Proof.context -> (indexname * string) list -> thm -> thm

  val instantiate_tac: Proof.context -> (indexname * string) list -> tactic

  val res_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic

  val eres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic

  val cut_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic

  val forw_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic

  val dres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic

  val thin_tac: Proof.context -> string -> int -> tactic

  val subgoal_tac: Proof.context -> string -> int -> tactic

  val subgoals_tac: Proof.context -> string list -> int -> tactic

  val method: (Proof.context -> (indexname * string) list -> thm -> int -> tactic) ->

    (Proof.context -> thm list -> int -> tactic) -> (Proof.context -> Proof.method) context_parser

end;

signature RULE_INSTS =

sig

  include BASIC_RULE_INSTS

  val make_elim_preserve: thm -> thm

end;

structure RuleInsts: RULE_INSTS =

struct

structure T = OuterLex;

structure P = OuterParse;

(** reading instantiations **)

local

fun is_tvar (x, _) = String.isPrefix "'" x;

fun error_var msg xi = error (msg ^ Term.string_of_vname xi);

fun the_sort tvars xi = the (AList.lookup (op =) tvars xi)

  handle Option.Option => error_var "No such type variable in theorem: " xi;

fun the_type vars xi = the (AList.lookup (op =) vars xi)

  handle Option.Option => error_var "No such variable in theorem: " xi;

fun unify_vartypes thy vars (xi, u) (unifier, maxidx) =

  let

    val T = the_type vars xi;

    val U = Term.fastype_of u;

    val maxidx' = Term.maxidx_term u (Int.max (#2 xi, maxidx));

  in

    Sign.typ_unify thy (T, U) (unifier, maxidx')

      handle Type.TUNIFY => error_var "Incompatible type for instantiation of " xi

  end;

fun instantiate inst =

  TermSubst.instantiate ([], map (fn (xi, t) => ((xi, Term.fastype_of t), t)) inst) #>

  Envir.beta_norm;

fun make_instT f v =

  let

    val T = TVar v;

    val T' = f T;

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

fun make_inst f v =

  let

    val t = Var v;

    val t' = f t;

  in if t aconv t' then NONE else SOME (t, t') end;

val add_used =

  (Thm.fold_terms o fold_types o fold_atyps)

    (fn TFree (a, _) => insert (op =) a

      | TVar ((a, _), _) => insert (op =) a

      | _ => I);

in

fun read_termTs ctxt schematic ss Ts =

  let

    fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;

    val ts = map2 parse Ts ss;

    val ts' =

      map2 (TypeInfer.constrain o TypeInfer.paramify_vars) Ts ts

      |> Syntax.check_terms ((schematic ? ProofContext.set_mode ProofContext.mode_schematic) ctxt)

      |> Variable.polymorphic ctxt;

    val Ts' = map Term.fastype_of ts';

    val tyenv = fold Type.raw_match (Ts ~~ Ts') Vartab.empty;

  in (ts', map (apsnd snd) (Vartab.dest tyenv)) end;

fun read_insts ctxt mixed_insts (tvars, vars) =

  let

    val thy = ProofContext.theory_of ctxt;

    val cert = Thm.cterm_of thy;

    val certT = Thm.ctyp_of thy;

    val (type_insts, term_insts) = List.partition (is_tvar o fst) mixed_insts;

    val internal_insts = term_insts |> map_filter

      (fn (xi, T.Term t) => SOME (xi, t)

        | (_, T.Text _) => NONE

        | (xi, _) => error_var "Term argument expected for " xi);

    val external_insts = term_insts |> map_filter

      (fn (xi, T.Text s) => SOME (xi, s) | _ => NONE);

    (* mixed type instantiations *)

    fun readT (xi, arg) =

      let

        val S = the_sort tvars xi;

        val T =

          (case arg of

            T.Text s => Syntax.read_typ ctxt s

          | T.Typ T => T

          | _ => error_var "Type argument expected for " xi);

      in

        if Sign.of_sort thy (T, S) then ((xi, S), T)

        else error_var "Incompatible sort for typ instantiation of " xi

      end;

    val type_insts1 = map readT type_insts;

    val instT1 = TermSubst.instantiateT type_insts1;

    val vars1 = map (apsnd instT1) vars;

    (* internal term instantiations *)

    val instT2 = Envir.norm_type

      (#1 (fold (unify_vartypes thy vars1) internal_insts (Vartab.empty, 0)));

    val vars2 = map (apsnd instT2) vars1;

    val internal_insts2 = map (apsnd (map_types instT2)) internal_insts;

    val inst2 = instantiate internal_insts2;

    (* external term instantiations *)

    val (xs, strs) = split_list external_insts;

    val Ts = map (the_type vars2) xs;

    val (ts, inferred) = read_termTs ctxt false strs Ts;

    val instT3 = Term.typ_subst_TVars inferred;

    val vars3 = map (apsnd instT3) vars2;

    val internal_insts3 = map (apsnd (map_types instT3)) internal_insts2;

    val external_insts3 = xs ~~ ts;

    val inst3 = instantiate external_insts3;

    (* results *)

    val type_insts3 = map (fn ((a, _), T) => (a, instT3 (instT2 T))) type_insts1;

    val term_insts3 = internal_insts3 @ external_insts3;

    val inst_tvars = map_filter (make_instT (instT3 o instT2 o instT1)) tvars;

    val inst_vars = map_filter (make_inst (inst3 o inst2)) vars3;

  in

    ((type_insts3, term_insts3),

      (map (pairself certT) inst_tvars, map (pairself cert) inst_vars))

  end;

fun read_instantiate_mixed ctxt mixed_insts thm =

  let

    val ctxt' = ctxt |> Variable.declare_thm thm

      |> fold (fn a => Variable.declare_names (Logic.mk_type (TFree (a, dummyS)))) (add_used thm []);  (* FIXME tmp *)

    val tvars = Thm.fold_terms Term.add_tvars thm [];

    val vars = Thm.fold_terms Term.add_vars thm [];

    val ((type_insts, term_insts), insts) = read_insts ctxt' (map snd mixed_insts) (tvars, vars);

    val _ = (*assign internalized values*)

      mixed_insts |> List.app (fn (arg, (xi, _)) =>

        if is_tvar xi then

          T.assign (SOME (T.Typ (the (AList.lookup (op =) type_insts xi)))) arg

        else

          T.assign (SOME (T.Term (the (AList.lookup (op =) term_insts xi)))) arg);

  in

    Drule.instantiate insts thm |> RuleCases.save thm

  end;

fun read_instantiate_mixed' ctxt (args, concl_args) thm =

  let

    fun zip_vars _ [] = []

      | zip_vars (_ :: xs) ((_, NONE) :: rest) = zip_vars xs rest

      | zip_vars ((x, _) :: xs) ((arg, SOME t) :: rest) = (arg, (x, t)) :: zip_vars xs rest

      | zip_vars [] _ = error "More instantiations than variables in theorem";

    val insts =

      zip_vars (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @

      zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) concl_args;

  in read_instantiate_mixed ctxt insts thm end;

end;

(* instantiation of rule or goal state *)

fun read_instantiate ctxt args thm =

  read_instantiate_mixed (ctxt |> ProofContext.set_mode ProofContext.mode_schematic)  (* FIXME !? *)

    (map (fn (x, y) => (T.eof, (x, T.Text y))) args) thm;

fun instantiate_tac ctxt args = PRIMITIVE (read_instantiate ctxt args);

(** attributes **)

(* where: named instantiation *)

local

val value =

  Args.internal_typ >> T.Typ ||

  Args.internal_term >> T.Term ||

  Args.name_source >> T.Text;

val inst = Args.var -- (Args.$$$ "=" |-- Scan.ahead P.not_eof -- value)

  >> (fn (xi, (a, v)) => (a, (xi, v)));

in

val _ = Context.>> (Context.map_theory

  (Attrib.setup (Binding.name "where")

    (Scan.lift (P.and_list inst) >> (fn args =>

      Thm.rule_attribute (fn context => read_instantiate_mixed (Context.proof_of context) args)))

    "named instantiation of theorem"));

end;

(* of: positional instantiation (terms only) *)

local

val value =

  Args.internal_term >> T.Term ||

  Args.name_source >> T.Text;

val inst = Scan.ahead P.not_eof -- Args.maybe value;

val concl = Args.$$$ "concl" -- Args.colon;

val insts =

  Scan.repeat (Scan.unless concl inst) --

  Scan.optional (concl |-- Scan.repeat inst) [];

in

val _ = Context.>> (Context.map_theory

  (Attrib.setup (Binding.name "of")

    (Scan.lift insts >> (fn args =>

      Thm.rule_attribute (fn context => read_instantiate_mixed' (Context.proof_of context) args)))

    "positional instantiation of theorem"));

end;

(** tactics **)

(* resolution after lifting and instantation; may refer to parameters of the subgoal *)

(* FIXME cleanup this mess!!! *)

fun bires_inst_tac bires_flag ctxt insts thm =

  let

    val thy = ProofContext.theory_of ctxt;

    (* Separate type and term insts *)

    fun has_type_var ((x, _), _) = (case Symbol.explode x of

          "'"::cs => true | cs => false);

    val Tinsts = List.filter has_type_var insts;

    val tinsts = filter_out has_type_var insts;

    (* Tactic *)

    fun tac i st =

      let

        val (_, _, Bi, _) = Thm.dest_state (st, i);

        val params = Logic.strip_params Bi;  (*params of subgoal i as string typ pairs*)

        val params = rev (Term.rename_wrt_term Bi params)

          (*as they are printed: bound variables with*)

          (*the same name are renamed during printing*)

        val (param_names, ctxt') = ctxt

          |> Variable.declare_thm thm

          |> Thm.fold_terms Variable.declare_constraints st

          |> ProofContext.add_fixes_i (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params);

        (* Process type insts: Tinsts_env *)

        fun absent xi = error

              ("No such variable in theorem: " ^ Term.string_of_vname xi);

        val (rtypes, rsorts) = Drule.types_sorts thm;

        fun readT (xi, s) =

            let val S = case rsorts xi of SOME S => S | NONE => absent xi;

                val T = Syntax.read_typ ctxt' s;

                val U = TVar (xi, S);

            in if Sign.typ_instance thy (T, U) then (U, T)

               else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails")

            end;

        val Tinsts_env = map readT Tinsts;

        (* Preprocess rule: extract vars and their types, apply Tinsts *)

        fun get_typ xi =

          (case rtypes xi of

               SOME T => typ_subst_atomic Tinsts_env T

             | NONE => absent xi);

        val (xis, ss) = Library.split_list tinsts;

        val Ts = map get_typ xis;

        val (ts, envT) = read_termTs ctxt' true ss Ts;

        val envT' = map (fn (ixn, T) =>

          (TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;

        val cenv =

          map

            (fn (xi, t) =>

              pairself (Thm.cterm_of thy) (Var (xi, fastype_of t), t))

            (distinct

              (fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)

              (xis ~~ ts));

        (* Lift and instantiate rule *)

        val {maxidx, ...} = rep_thm st;

        val paramTs = map #2 params

        and inc = maxidx+1

        fun liftvar (Var ((a,j), T)) =

              Var((a, j+inc), paramTs ---> Logic.incr_tvar inc T)

          | liftvar t = raise TERM("Variable expected", [t]);

        fun liftterm t = list_abs_free

              (param_names ~~ paramTs, Logic.incr_indexes(paramTs,inc) t)

        fun liftpair (cv,ct) =

              (cterm_fun liftvar cv, cterm_fun liftterm ct)

        val lifttvar = pairself (ctyp_of thy o Logic.incr_tvar inc);

        val rule = Drule.instantiate

              (map lifttvar envT', map liftpair cenv)

              (Thm.lift_rule (Thm.cprem_of st i) thm)

      in

        if i > nprems_of st then no_tac st

        else st |>

          compose_tac (bires_flag, rule, nprems_of thm) i

      end

           handle TERM (msg,_)   => (warning msg; no_tac st)

                | THM  (msg,_,_) => (warning msg; no_tac st);

  in tac end;

val res_inst_tac = bires_inst_tac false;

val eres_inst_tac = bires_inst_tac true;

(* forward resolution *)

fun make_elim_preserve rl =

  let

    val cert = Thm.cterm_of (Thm.theory_of_thm rl);

    val maxidx = Thm.maxidx_of rl;

    fun cvar xi = cert (Var (xi, propT));

    val revcut_rl' =

      instantiate ([], [(cvar ("V", 0), cvar ("V", maxidx + 1)),

        (cvar ("W", 0), cvar ("W", maxidx + 1))]) Drule.revcut_rl;

  in

    (case Seq.list_of (bicompose false (false, rl, Thm.nprems_of rl) 1 revcut_rl') of

      [th] => th

    | _ => raise THM ("make_elim_preserve", 1, [rl]))

  end;

(*instantiate and cut -- for atomic fact*)

fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve rule);

(*forward tactic applies a rule to an assumption without deleting it*)

fun forw_inst_tac ctxt insts rule = cut_inst_tac ctxt insts rule THEN' assume_tac;

(*dresolve tactic applies a rule to replace an assumption*)

fun dres_inst_tac ctxt insts rule = eres_inst_tac ctxt insts (make_elim_preserve rule);

(* derived tactics *)

(*deletion of an assumption*)

fun thin_tac ctxt s = eres_inst_tac ctxt [(("V", 0), s)] Drule.thin_rl;

(*Introduce the given proposition as lemma and subgoal*)

fun subgoal_tac ctxt A = DETERM o res_inst_tac ctxt [(("psi", 0), A)] cut_rl;

fun subgoals_tac ctxt As = EVERY' (map (subgoal_tac ctxt) As);

(** methods **)

(* rule_tac etc. -- refer to dynamic goal state! *)

fun method inst_tac tac =

  Args.goal_spec --

  Scan.optional (Scan.lift

    (P.and_list1 (Args.var -- (Args.$$$ "=" |-- P.!!! Args.name_source)) --| Args.$$$ "in")) [] --

  Attrib.thms >>

  (fn ((quant, insts), thms) => fn ctxt => METHOD (fn facts =>

    if null insts then quant (Method.insert_tac facts THEN' tac ctxt thms)

    else

      (case thms of

        [thm] => quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm)

      | _ => error "Cannot have instantiations with multiple rules")));

val res_inst_meth = method res_inst_tac (K Tactic.resolve_tac);

val eres_inst_meth = method eres_inst_tac (K Tactic.eresolve_tac);

val cut_inst_meth = method cut_inst_tac (K Tactic.cut_rules_tac);

val dres_inst_meth = method dres_inst_tac (K Tactic.dresolve_tac);

val forw_inst_meth = method forw_inst_tac (K Tactic.forward_tac);

(* setup *)

val _ = Context.>> (Context.map_theory

 (Method.setup (Binding.name "rule_tac") res_inst_meth "apply rule (dynamic instantiation)" #>

  Method.setup (Binding.name "erule_tac") eres_inst_meth

    "apply rule in elimination manner (dynamic instantiation)" #>

  Method.setup (Binding.name "drule_tac") dres_inst_meth

    "apply rule in destruct manner (dynamic instantiation)" #>

  Method.setup (Binding.name "frule_tac") forw_inst_meth

    "apply rule in forward manner (dynamic instantiation)" #>

  Method.setup (Binding.name "cut_tac") cut_inst_meth "cut rule (dynamic instantiation)" #>

  Method.setup (Binding.name "subgoal_tac")

    (Args.goal_spec -- Scan.lift (Scan.repeat1 Args.name_source) >>

      (fn (quant, props) => fn ctxt => SIMPLE_METHOD'' quant (subgoals_tac ctxt props)))

    "insert subgoal (dynamic instantiation)" #>

  Method.setup (Binding.name "thin_tac")

    (Args.goal_spec -- Scan.lift Args.name_source >>

      (fn (quant, prop) => fn ctxt => SIMPLE_METHOD'' quant (thin_tac ctxt prop)))

      "remove premise (dynamic instantiation)"));

end;

structure BasicRuleInsts: BASIC_RULE_INSTS = RuleInsts;

open BasicRuleInsts;