author  wenzelm 
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changeset 33368  b1cf34f1855c 
parent 33317  b4534348b8fd 
child 36950  75b8f26f2f07 
permissions  rwrr 
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(* Title: Pure/Isar/rule_insts.ML 
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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 BASIC_RULE_INSTS = 
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sig 
27236  9 
val read_instantiate: Proof.context > (indexname * string) list > thm > thm 
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val instantiate_tac: Proof.context > (indexname * string) list > tactic 
27120  11 
val res_inst_tac: Proof.context > (indexname * string) list > thm > int > tactic 
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val eres_inst_tac: Proof.context > (indexname * string) list > thm > int > tactic 

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val cut_inst_tac: Proof.context > (indexname * string) list > thm > int > tactic 
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val forw_inst_tac: Proof.context > (indexname * string) list > thm > int > tactic 
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val dres_inst_tac: Proof.context > (indexname * string) list > thm > int > tactic 
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val thin_tac: Proof.context > string > int > tactic 
27219  17 
val subgoal_tac: Proof.context > string > int > tactic 
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val subgoals_tac: Proof.context > string list > int > tactic 

30545  19 
val method: (Proof.context > (indexname * 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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signature RULE_INSTS = 
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sig 
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include BASIC_RULE_INSTS 
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val make_elim_preserve: thm > thm 
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end; 
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structure RuleInsts: RULE_INSTS = 
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struct 
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structure T = OuterLex; 
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structure P = OuterParse; 
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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 ^ Term.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 = 
31977  61 
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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27282  76 
val add_used = 
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(Thm.fold_terms o fold_types o fold_atyps) 

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

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

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 _ => I); 

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in 
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25333  84 
fun read_termTs ctxt schematic 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 (TypeInfer.constrain o TypeInfer.paramify_vars) Ts ts 

25333  90 
> Syntax.check_terms ((schematic ? ProofContext.set_mode ProofContext.mode_schematic) 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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in (ts', map (apsnd snd) (Vartab.dest tyenv)) end; 

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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, T.Term t) => SOME (xi, t) 
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 (_, T.Text _) => 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, T.Text 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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T.Text s => Syntax.read_typ ctxt s 
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 T.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_Subst.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_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) = read_termTs ctxt false 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_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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152 

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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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163 
end; 
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27236  165 
fun read_instantiate_mixed ctxt mixed_insts thm = 
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let 
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val ctxt' = ctxt > Variable.declare_thm thm 
27282  168 
> fold (fn a => Variable.declare_names (Logic.mk_type (TFree (a, dummyS)))) (add_used thm []); (* FIXME tmp *) 
22692  169 
val tvars = Thm.fold_terms Term.add_tvars thm []; 
170 
val vars = Thm.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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T.assign (SOME (T.Typ (the (AList.lookup (op =) type_insts xi)))) arg 
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else 
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T.assign (SOME (T.Term (the (AList.lookup (op =) term_insts xi)))) arg); 
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in 
33368  180 
Drule.instantiate insts thm > Rule_Cases.save thm 
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end; 
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27236  183 
fun read_instantiate_mixed' 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; 
27236  192 
in read_instantiate_mixed ctxt insts thm end; 
193 

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end; 
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(* instantiation of rule or goal state *) 
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27236  199 
fun read_instantiate ctxt args thm = 
200 
read_instantiate_mixed (ctxt > ProofContext.set_mode ProofContext.mode_schematic) (* FIXME !? *) 

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(map (fn (x, y) => (T.eof, (x, T.Text y))) args) thm; 
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fun instantiate_tac ctxt args = PRIMITIVE (read_instantiate ctxt args); 
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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 >> T.Typ  
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Args.internal_term >> T.Term  
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Args.name_source >> T.Text; 
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val inst = Args.var  (Args.$$$ "="  Scan.ahead P.not_eof  value) 
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>> (fn (xi, (a, v)) => (a, (xi, v))); 
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in 
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val _ = Context.>> (Context.map_theory 
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(Attrib.setup (Binding.name "where") 
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(Scan.lift (P.and_list inst) >> (fn args => 
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Thm.rule_attribute (fn context => read_instantiate_mixed (Context.proof_of context) args))) 
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"named instantiation of theorem")); 
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end; 
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230 

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231 

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(* of: positional instantiation (terms only) *) 
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local 
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235 

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val value = 
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Args.internal_term >> T.Term  
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Args.name_source >> T.Text; 
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239 

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val inst = Scan.ahead P.not_eof  Args.maybe value; 
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val concl = Args.$$$ "concl"  Args.colon; 
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242 

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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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246 

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in 
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248 

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val _ = Context.>> (Context.map_theory 
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(Attrib.setup (Binding.name "of") 
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(Scan.lift insts >> (fn args => 
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Thm.rule_attribute (fn context => read_instantiate_mixed' (Context.proof_of context) args))) 
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"positional instantiation of theorem")); 
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end; 
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256 

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257 

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258 

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(** tactics **) 
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(* resolution after lifting and instantation; may refer to parameters of the subgoal *) 
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262 

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(* FIXME cleanup this mess!!! *) 
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264 

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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 *) 
32784  269 
fun has_type_var ((x, _), _) = 
270 
(case Symbol.explode x of "'" :: _ => true  _ => false); 

33317  271 
val Tinsts = filter has_type_var insts; 
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val tinsts = filter_out has_type_var insts; 
25333  273 

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(* Tactic *) 
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fun tac i st = 
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let 
25333  277 
val (_, _, Bi, _) = Thm.dest_state (st, i); 
278 
val params = Logic.strip_params Bi; (*params of subgoal i as string typ pairs*) 

279 
val params = rev (Term.rename_wrt_term Bi params) 

280 
(*as they are printed: bound variables with*) 

281 
(*the same name are renamed during printing*) 

282 

283 
val (param_names, ctxt') = ctxt 

284 
> Variable.declare_thm thm 

285 
> Thm.fold_terms Variable.declare_constraints st 

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> ProofContext.add_fixes (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params); 
25333  287 

288 
(* Process type insts: Tinsts_env *) 

289 
fun absent xi = error 

290 
("No such variable in theorem: " ^ Term.string_of_vname xi); 

291 
val (rtypes, rsorts) = Drule.types_sorts thm; 

292 
fun readT (xi, s) = 

293 
let val S = case rsorts xi of SOME S => S  NONE => absent xi; 

294 
val T = Syntax.read_typ ctxt' s; 

295 
val U = TVar (xi, S); 

296 
in if Sign.typ_instance thy (T, U) then (U, T) 

297 
else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails") 

298 
end; 

299 
val Tinsts_env = map readT Tinsts; 

300 
(* Preprocess rule: extract vars and their types, apply Tinsts *) 

301 
fun get_typ xi = 

302 
(case rtypes xi of 

303 
SOME T => typ_subst_atomic Tinsts_env T 

304 
 NONE => absent xi); 

305 
val (xis, ss) = Library.split_list tinsts; 

306 
val Ts = map get_typ xis; 

307 

308 
val (ts, envT) = read_termTs ctxt' true 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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317 
(xis ~~ ts)); 
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318 
(* Lift and instantiate rule *) 
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319 
val {maxidx, ...} = rep_thm st; 
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val paramTs = map #2 params 
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321 
and inc = maxidx+1 
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322 
fun liftvar (Var ((a,j), T)) = 
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Var((a, j+inc), paramTs > Logic.incr_tvar inc T) 
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324 
 liftvar t = raise TERM("Variable expected", [t]); 
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fun liftterm t = list_abs_free 
25333  326 
(param_names ~~ paramTs, Logic.incr_indexes(paramTs,inc) t) 
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327 
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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330 
val rule = Drule.instantiate 
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331 
(map lifttvar envT', map liftpair cenv) 
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332 
(Thm.lift_rule (Thm.cprem_of st i) thm) 
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333 
in 
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334 
if i > nprems_of st then no_tac st 
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335 
else st > 
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336 
compose_tac (bires_flag, rule, nprems_of thm) i 
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337 
end 
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338 
handle TERM (msg,_) => (warning msg; no_tac st) 
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339 
 THM (msg,_,_) => (warning msg; no_tac st); 
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340 
in tac end; 
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341 

27120  342 
val res_inst_tac = bires_inst_tac false; 
343 
val eres_inst_tac = bires_inst_tac true; 

344 

345 

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346 
(* forward resolution *) 
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347 

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348 
fun make_elim_preserve rl = 
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349 
let 
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val cert = Thm.cterm_of (Thm.theory_of_thm rl); 
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val maxidx = Thm.maxidx_of rl; 
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fun cvar xi = cert (Var (xi, propT)); 
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val revcut_rl' = 
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instantiate ([], [(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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356 
in 
31945  357 
(case Seq.list_of (Thm.bicompose false (false, rl, Thm.nprems_of rl) 1 revcut_rl') of 
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358 
[th] => th 
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 _ => raise THM ("make_elim_preserve", 1, [rl])) 
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360 
end; 
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361 

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362 
(*instantiate and cut  for atomic fact*) 
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363 
fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve rule); 
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364 

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365 
(*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; 
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367 

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368 
(*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 rule); 
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370 

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371 

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372 
(* derived tactics *) 
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373 

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374 
(*deletion of an assumption*) 
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375 
fun thin_tac ctxt s = eres_inst_tac ctxt [(("V", 0), s)] Drule.thin_rl; 
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376 

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377 
(*Introduce the given proposition as lemma and subgoal*) 
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378 
fun subgoal_tac ctxt A = DETERM o res_inst_tac ctxt [(("psi", 0), A)] cut_rl; 
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379 
fun subgoals_tac ctxt As = EVERY' (map (subgoal_tac ctxt) As); 
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380 

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381 

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382 

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383 
(** methods **) 
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384 

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385 
(* rule_tac etc.  refer to dynamic goal state! *) 
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386 

30545  387 
fun method inst_tac tac = 
30515  388 
Args.goal_spec  
389 
Scan.optional (Scan.lift 

390 
(P.and_list1 (Args.var  (Args.$$$ "="  P.!!! Args.name_source))  Args.$$$ "in")) []  

391 
Attrib.thms >> 

392 
(fn ((quant, insts), thms) => fn ctxt => METHOD (fn facts => 

30551  393 
if null insts then quant (Method.insert_tac facts THEN' tac ctxt thms) 
30515  394 
else 
395 
(case thms of 

396 
[thm] => quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm) 

397 
 _ => error "Cannot have instantiations with multiple rules"))); 

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398 

30551  399 
val res_inst_meth = method res_inst_tac (K Tactic.resolve_tac); 
400 
val eres_inst_meth = method eres_inst_tac (K Tactic.eresolve_tac); 

401 
val cut_inst_meth = method cut_inst_tac (K Tactic.cut_rules_tac); 

402 
val dres_inst_meth = method dres_inst_tac (K Tactic.dresolve_tac); 

403 
val forw_inst_meth = method forw_inst_tac (K Tactic.forward_tac); 

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404 

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405 

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406 
(* setup *) 
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407 

26463  408 
val _ = Context.>> (Context.map_theory 
30515  409 
(Method.setup (Binding.name "rule_tac") res_inst_meth "apply rule (dynamic instantiation)" #> 
410 
Method.setup (Binding.name "erule_tac") eres_inst_meth 

411 
"apply rule in elimination manner (dynamic instantiation)" #> 

412 
Method.setup (Binding.name "drule_tac") dres_inst_meth 

413 
"apply rule in destruct manner (dynamic instantiation)" #> 

414 
Method.setup (Binding.name "frule_tac") forw_inst_meth 

415 
"apply rule in forward manner (dynamic instantiation)" #> 

416 
Method.setup (Binding.name "cut_tac") cut_inst_meth "cut rule (dynamic instantiation)" #> 

417 
Method.setup (Binding.name "subgoal_tac") 

418 
(Args.goal_spec  Scan.lift (Scan.repeat1 Args.name_source) >> 

419 
(fn (quant, props) => fn ctxt => SIMPLE_METHOD'' quant (subgoals_tac ctxt props))) 

420 
"insert subgoal (dynamic instantiation)" #> 

421 
Method.setup (Binding.name "thin_tac") 

422 
(Args.goal_spec  Scan.lift Args.name_source >> 

423 
(fn (quant, prop) => fn ctxt => SIMPLE_METHOD'' quant (thin_tac ctxt prop))) 

424 
"remove premise (dynamic instantiation)")); 

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425 

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426 
end; 
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427 

27245
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428 
structure BasicRuleInsts: BASIC_RULE_INSTS = RuleInsts; 
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429 
open BasicRuleInsts; 