(*  Title:      Pure/Isar/rule_insts.ML

    ID:         $Id$

    Author:     Makarius

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

*)

signature RULE_INSTS =

sig

  val bires_inst_tac: bool -> Proof.context -> (indexname * string) list ->

    thm -> int -> tactic

end;

structure RuleInsts: RULE_INSTS =

struct

(** reading instantiations **)

local

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

fun error_var msg xi = error (msg ^ Syntax.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;

in

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, Args.Term t) => SOME (xi, t)

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

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

    val external_insts = term_insts |> map_filter

      (fn (xi, Args.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

            Args.Text s => ProofContext.read_typ ctxt s

          | Args.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) =   (* FIXME polymorphic!? schematic vs. 'for' context!? *)

      ProofContext.read_termTs_schematic ctxt (K false) (K NONE) (K NONE) [] (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 ctxt mixed_insts thm =

  let

    val ctxt' = ctxt |> Variable.declare_thm thm

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

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

    val vars = Drule.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

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

        else

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

  in

    Drule.instantiate insts thm |> RuleCases.save thm

  end;

fun read_instantiate' 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 ctxt insts thm end;

end;

(** attributes **)

(* where: named instantiation *)

local

val value =

  Args.internal_typ >> Args.Typ ||

  Args.internal_term >> Args.Term ||

  Args.name >> Args.Text;

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

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

in

val where_att = Attrib.syntax (Args.and_list (Scan.lift inst) >> (fn args =>

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

end;

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

local

val value =

  Args.internal_term >> Args.Term ||

  Args.name >> Args.Text;

val inst = Args.ahead -- 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 of_att = Attrib.syntax (Scan.lift insts >> (fn args =>

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

end;

(* setup *)

val _ = Context.add_setup (Attrib.add_attributes

 [("where", where_att, "named instantiation of theorem"),

  ("of", of_att, "positional instantiation of theorem")]);

(** methods **)

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

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

        (* Preprocess state: extract environment information:

           - variables and their types

           - type variables and their sorts

           - parameters and their types *)

        val (types, sorts) = types_sorts st;

    (* Process type insts: Tinsts_env *)

    fun absent xi = error

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

    val (rtypes, rsorts) = types_sorts thm;

    fun readT (xi, s) =

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

            val T = Sign.read_typ (thy, sorts) s;

            val U = TVar (xi, S);

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

           else error

             ("Instantiation of " ^ Syntax.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 (_, _, Bi, _) = 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 *)

        fun types' (a, ~1) = (case AList.lookup (op =) params a of

                NONE => types (a, ~1)

              | some => some)

          | types' xi = types xi;

        fun internal x = is_some (types' (x, ~1));

        val used = Drule.add_used thm (Drule.add_used st []);

        val (ts, envT) =

          ProofContext.read_termTs_schematic ctxt internal types' sorts used (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

              (params, 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;

local

fun gen_inst _ tac _ (quant, ([], thms)) =

      Method.METHOD (fn facts => quant (Method.insert_tac facts THEN' tac thms))

  | gen_inst inst_tac _ ctxt (quant, (insts, [thm])) =

      Method.METHOD (fn facts =>

        quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm))

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

in

val res_inst_meth = gen_inst (bires_inst_tac false) Tactic.resolve_tac;

val eres_inst_meth = gen_inst (bires_inst_tac true) Tactic.eresolve_tac;

val cut_inst_meth =

  gen_inst

    (fn ctxt => fn insts => bires_inst_tac false ctxt insts o Tactic.make_elim_preserve)

    Tactic.cut_rules_tac;

val dres_inst_meth =

  gen_inst

    (fn ctxt => fn insts => bires_inst_tac true ctxt insts o Tactic.make_elim_preserve)

    Tactic.dresolve_tac;

val forw_inst_meth =

  gen_inst

    (fn ctxt => fn insts => fn rule =>

       bires_inst_tac false ctxt insts (Tactic.make_elim_preserve rule) THEN'

       assume_tac)

    Tactic.forward_tac;

fun subgoal_tac ctxt sprop =

  DETERM o bires_inst_tac false ctxt [(("psi", 0), sprop)] cut_rl;

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

fun thin_tac ctxt s =

  bires_inst_tac true ctxt [(("V", 0), s)] thin_rl;

(* method syntax *)

val insts =

  Scan.optional

    (Args.enum1 "and" (Scan.lift (Args.name -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|

      Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;

fun inst_args f src ctxt =

  f ctxt (fst (Method.syntax (Args.goal_spec HEADGOAL -- insts) src ctxt));

val insts_var =

  Scan.optional

    (Args.enum1 "and" (Scan.lift (Args.var -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|

      Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;

fun inst_args_var f src ctxt =

  f ctxt (fst (Method.syntax (Args.goal_spec HEADGOAL -- insts_var) src ctxt));

(* setup *)

val _ = Context.add_setup (Method.add_methods

 [("rule_tac", inst_args_var res_inst_meth,

    "apply rule (dynamic instantiation)"),

  ("erule_tac", inst_args_var eres_inst_meth,

    "apply rule in elimination manner (dynamic instantiation)"),

  ("drule_tac", inst_args_var dres_inst_meth,

    "apply rule in destruct manner (dynamic instantiation)"),

  ("frule_tac", inst_args_var forw_inst_meth,

    "apply rule in forward manner (dynamic instantiation)"),

  ("cut_tac", inst_args_var cut_inst_meth,

    "cut rule (dynamic instantiation)"),

  ("subgoal_tac", Method.goal_args_ctxt (Scan.repeat1 Args.name) subgoals_tac,

    "insert subgoal (dynamic instantiation)"),

  ("thin_tac", Method.goal_args_ctxt Args.name thin_tac,

    "remove premise (dynamic instantiation)")]);

end;

end;