src/Pure/Isar/rule_insts.ML
author wenzelm
Sat, 05 Aug 2006 14:52:58 +0200
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permissions -rw-r--r--
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(*  Title:      Pure/Isar/rule_insts.ML
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    ID:         $Id$
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    Author:     Makarius
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Rule instantiations -- operations within a rule/subgoal context.
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*)
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signature RULE_INSTS =
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sig
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  val bires_inst_tac: bool -> Proof.context -> (indexname * string) list ->
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    thm -> int -> tactic
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end;
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structure RuleInsts: RULE_INSTS =
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struct
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(** reading instantiations **)
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local
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fun is_tvar (x, _) = String.isPrefix "'" x;
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fun error_var msg xi = error (msg ^ Syntax.string_of_vname xi);
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fun the_sort tvars xi = the (AList.lookup (op =) tvars xi)
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  handle Option.Option => error_var "No such type variable in theorem: " xi;
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fun the_type vars xi = the (AList.lookup (op =) vars xi)
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  handle Option.Option => error_var "No such variable in theorem: " xi;
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fun unify_vartypes thy vars (xi, u) (unifier, maxidx) =
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  let
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    val T = the_type vars xi;
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    val U = Term.fastype_of u;
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    val maxidx' = Term.maxidx_term u (Int.max (#2 xi, maxidx));
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  in
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    Sign.typ_unify thy (T, U) (unifier, maxidx')
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      handle Type.TUNIFY => error_var "Incompatible type for instantiation of " xi
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  end;
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fun instantiate inst =
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  Term.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 read_insts ctxt mixed_insts (tvars, vars) =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val cert = Thm.cterm_of thy;
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    val certT = Thm.ctyp_of thy;
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    val (type_insts, term_insts) = List.partition (is_tvar o fst) mixed_insts;
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    val internal_insts = term_insts |> map_filter
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      (fn (xi, Args.Term t) => SOME (xi, t)
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        | (_, Args.Name _) => NONE
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        | (xi, _) => error_var "Term argument expected for " xi);
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    val external_insts = term_insts |> map_filter
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      (fn (xi, Args.Name s) => SOME (xi, s) | _ => NONE);
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    (* mixed type instantiations *)
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    fun readT (xi, arg) =
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      let
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        val S = the_sort tvars xi;
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        val T =
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          (case arg of
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            Args.Name s => ProofContext.read_typ ctxt s
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          | Args.Typ T => T
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          | _ => error_var "Type argument expected for " xi);
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      in
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        if Sign.of_sort thy (T, S) then ((xi, S), T)
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        else error_var "Incompatible sort for typ instantiation of " xi
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      end;
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    val type_insts1 = map readT type_insts;
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    val instT1 = Term.instantiateT type_insts1;
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    val vars1 = map (apsnd instT1) vars;
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    (* internal term instantiations *)
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    val instT2 = Envir.norm_type
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      (#1 (fold (unify_vartypes thy vars1) internal_insts (Vartab.empty, 0)));
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    val vars2 = map (apsnd instT2) vars1;
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    val internal_insts2 = map (apsnd (map_term_types instT2)) internal_insts;
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    val inst2 = instantiate internal_insts2;
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    (* external term instantiations *)
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    val (xs, strs) = split_list external_insts;
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    val Ts = map (the_type vars2) xs;
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    val (ts, inferred) =   (* FIXME polymorphic!? schematic vs. 'for' context!? *)
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      ProofContext.read_termTs_schematic ctxt (K false) (K NONE) (K NONE) [] (strs ~~ Ts);
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    val instT3 = Term.typ_subst_TVars inferred;
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    val vars3 = map (apsnd instT3) vars2;
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    val internal_insts3 = map (apsnd (map_term_types instT3)) internal_insts2;
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    val external_insts3 = xs ~~ ts;
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    val inst3 = instantiate external_insts3;
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    (* results *)
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    val type_insts3 = map (fn ((a, _), T) => (a, instT3 (instT2 T))) type_insts1;
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    val term_insts3 = internal_insts3 @ external_insts3;
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    val inst_tvars = map_filter (make_instT (instT3 o instT2 o instT1)) tvars;
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    val inst_vars = map_filter (make_inst (inst3 o inst2)) vars3;
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  in
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    ((type_insts3, term_insts3),
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      (map (pairself certT) inst_tvars, map (pairself cert) inst_vars))
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  end;
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fun read_instantiate ctxt mixed_insts thm =
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  let
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    val ctxt' = ctxt |> Variable.declare_thm thm;
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    val tvars = Drule.fold_terms Term.add_tvars thm [];
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    val vars = Drule.fold_terms Term.add_vars thm [];
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    val ((type_insts, term_insts), insts) = read_insts ctxt' (map snd mixed_insts) (tvars, vars);
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    val _ = (*assign internalized values*)
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      mixed_insts |> List.app (fn (arg, (xi, _)) =>
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        if is_tvar xi then
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          Args.assign (SOME (Args.Typ (the (AList.lookup (op =) type_insts xi)))) arg
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        else
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          Args.assign (SOME (Args.Term (the (AList.lookup (op =) term_insts xi)))) arg);
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  in
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    Drule.instantiate insts thm |> RuleCases.save thm
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  end;
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fun read_instantiate' ctxt (args, concl_args) 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) ((arg, SOME t) :: rest) = (arg, (x, 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 read_instantiate ctxt insts thm end;
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end;
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(** attributes **)
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(* where: named instantiation *)
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local
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val value =
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  Args.internal_typ >> Args.Typ ||
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  Args.internal_term >> Args.Term ||
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  Args.name >> Args.Name;
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val inst = Args.var -- (Args.$$$ "=" |-- Args.ahead -- value)
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  >> (fn (xi, (a, v)) => (a, (xi, v)));
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in
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val where_att = Attrib.syntax (Args.and_list (Scan.lift inst) >> (fn args =>
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  Thm.rule_attribute (fn context => read_instantiate (Context.proof_of context) args)));
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end;
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(* of: positional instantiation (terms only) *)
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local
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val value =
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  Args.internal_term >> Args.Term ||
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  Args.name >> Args.Name;
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val inst = Args.ahead -- Args.maybe value;
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val concl = Args.$$$ "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 of_att = Attrib.syntax (Scan.lift insts >> (fn args =>
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  Thm.rule_attribute (fn context => read_instantiate' (Context.proof_of context) args)));
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end;
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(* setup *)
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val _ = Context.add_setup (Attrib.add_attributes
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 [("where", where_att, "named instantiation of theorem"),
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  ("of", of_att, "positional instantiation of theorem")]);
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(** methods **)
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(* rule_tac etc. -- refer to dynamic goal state!! *)   (* FIXME cleanup!! *)
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fun bires_inst_tac bires_flag ctxt insts thm =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    (* Separate type and term insts *)
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    fun has_type_var ((x, _), _) = (case Symbol.explode x of
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          "'"::cs => true | cs => false);
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    val Tinsts = List.filter has_type_var insts;
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    val tinsts = filter_out has_type_var insts;
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    (* Tactic *)
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    fun tac i st =
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      let
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        (* Preprocess state: extract environment information:
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           - variables and their types
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           - type variables and their sorts
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           - parameters and their types *)
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        val (types, sorts) = types_sorts st;
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    (* Process type insts: Tinsts_env *)
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    fun absent xi = error
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          ("No such variable in theorem: " ^ Syntax.string_of_vname xi);
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    val (rtypes, rsorts) = types_sorts thm;
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    fun readT (xi, s) =
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        let val S = case rsorts xi of SOME S => S | NONE => absent xi;
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            val T = Sign.read_typ (thy, sorts) s;
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            val U = TVar (xi, S);
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        in if Sign.typ_instance thy (T, U) then (U, T)
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           else error
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             ("Instantiation of " ^ Syntax.string_of_vname xi ^ " fails")
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        end;
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    val Tinsts_env = map readT Tinsts;
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    (* Preprocess rule: extract vars and their types, apply Tinsts *)
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    fun get_typ xi =
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      (case rtypes xi of
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           SOME T => typ_subst_atomic Tinsts_env T
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         | NONE => absent xi);
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    val (xis, ss) = Library.split_list tinsts;
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    val Ts = map get_typ xis;
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        val (_, _, Bi, _) = dest_state(st,i)
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        val params = Logic.strip_params Bi
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                             (* params of subgoal i as string typ pairs *)
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        val params = rev(Term.rename_wrt_term Bi params)
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                           (* as they are printed: bound variables with *)
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                           (* the same name are renamed during printing *)
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        fun types' (a, ~1) = (case AList.lookup (op =) params a of
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                NONE => types (a, ~1)
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              | some => some)
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          | types' xi = types xi;
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        fun internal x = is_some (types' (x, ~1));
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        val used = Drule.add_used thm (Drule.add_used st []);
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        val (ts, envT) =
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          ProofContext.read_termTs_schematic ctxt internal types' sorts used (ss ~~ Ts);
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        val envT' = map (fn (ixn, T) =>
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          (TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;
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        val cenv =
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          map
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            (fn (xi, t) =>
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              pairself (Thm.cterm_of thy) (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, ...} = rep_thm st;
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        val paramTs = map #2 params
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        and inc = maxidx+1
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        fun liftvar (Var ((a,j), T)) =
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              Var((a, j+inc), paramTs ---> Logic.incr_tvar inc T)
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          | liftvar t = raise TERM("Variable expected", [t]);
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        fun liftterm t = list_abs_free
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              (params, Logic.incr_indexes(paramTs,inc) t)
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        fun liftpair (cv,ct) =
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              (cterm_fun liftvar cv, cterm_fun liftterm ct)
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        val lifttvar = pairself (ctyp_of thy o Logic.incr_tvar inc);
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        val rule = Drule.instantiate
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              (map lifttvar envT', map liftpair cenv)
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              (Thm.lift_rule (Thm.cprem_of st i) thm)
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      in
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        if i > nprems_of st then no_tac st
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        else st |>
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          compose_tac (bires_flag, rule, nprems_of thm) i
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      end
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           handle TERM (msg,_)   => (warning msg; no_tac st)
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                | THM  (msg,_,_) => (warning msg; no_tac st);
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  in tac end;
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local
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fun gen_inst _ tac _ (quant, ([], thms)) =
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      Method.METHOD (fn facts => quant (Method.insert_tac facts THEN' tac thms))
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  | gen_inst inst_tac _ ctxt (quant, (insts, [thm])) =
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      Method.METHOD (fn facts =>
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        quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm))
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  | gen_inst _ _ _ _ = error "Cannot have instantiations with multiple rules";
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in
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val res_inst_meth = gen_inst (bires_inst_tac false) Tactic.resolve_tac;
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val eres_inst_meth = gen_inst (bires_inst_tac true) Tactic.eresolve_tac;
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val cut_inst_meth =
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  gen_inst
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    (fn ctxt => fn insts => bires_inst_tac false ctxt insts o Tactic.make_elim_preserve)
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    Tactic.cut_rules_tac;
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val dres_inst_meth =
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  gen_inst
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    (fn ctxt => fn insts => bires_inst_tac true ctxt insts o Tactic.make_elim_preserve)
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    Tactic.dresolve_tac;
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val forw_inst_meth =
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  gen_inst
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    (fn ctxt => fn insts => fn rule =>
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       bires_inst_tac false ctxt insts (Tactic.make_elim_preserve rule) THEN'
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       assume_tac)
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    Tactic.forward_tac;
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fun subgoal_tac ctxt sprop =
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  DETERM o bires_inst_tac false ctxt [(("psi", 0), sprop)] cut_rl;
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fun subgoals_tac ctxt sprops = EVERY' (map (subgoal_tac ctxt) sprops);
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fun thin_tac ctxt s =
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  bires_inst_tac true ctxt [(("V", 0), s)] thin_rl;
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(* method syntax *)
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val insts =
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  Scan.optional
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    (Args.enum1 "and" (Scan.lift (Args.name -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|
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      Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;
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fun inst_args f src ctxt =
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  f ctxt (#2 (Method.syntax (Args.goal_spec HEADGOAL -- insts) src ctxt));
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val insts_var =
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  Scan.optional
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    (Args.enum1 "and" (Scan.lift (Args.var -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|
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      Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;
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fun inst_args_var f src ctxt =
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  f ctxt (#2 (Method.syntax (Args.goal_spec HEADGOAL -- insts_var) src ctxt));
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(* setup *)
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val _ = Context.add_setup (Method.add_methods
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 [("rule_tac", inst_args_var res_inst_meth,
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    "apply rule (dynamic instantiation)"),
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  ("erule_tac", inst_args_var eres_inst_meth,
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    "apply rule in elimination manner (dynamic instantiation)"),
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  ("drule_tac", inst_args_var dres_inst_meth,
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    "apply rule in destruct manner (dynamic instantiation)"),
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  ("frule_tac", inst_args_var forw_inst_meth,
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    "apply rule in forward manner (dynamic instantiation)"),
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  ("cut_tac", inst_args_var cut_inst_meth,
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    "cut rule (dynamic instantiation)"),
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  ("subgoal_tac", Method.goal_args_ctxt (Scan.repeat1 Args.name) subgoals_tac,
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    "insert subgoal (dynamic instantiation)"),
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  ("thin_tac", Method.goal_args_ctxt Args.name thin_tac,
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    "remove premise (dynamic instantiation)")]);
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end;
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end;