author  wenzelm 
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parent 25329  63e8de11c8e9 
child 25354  69560579abf1 
permissions  rwrr 
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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 ^ 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 = 
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TermSubst.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_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 

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> 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, Args.Term t) => SOME (xi, t) 
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 (_, Args.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, Args.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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Args.Text s => Syntax.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 = TermSubst.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 true (* FIXME 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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(* 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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> fold (fn a => Variable.declare_internal (Logic.mk_type (TFree (a, [])))) (Drule.add_used thm []); (* FIXME tmp *) 
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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 ((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.Text; 
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val inst = Args.var  (Args.$$$ "="  Args.ahead  value) 
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>> (fn (xi, (a, v)) => (a, (xi, v))); 
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in 
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val where_att = Attrib.syntax (Args.and_list (Scan.lift inst) >> (fn args => 
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Thm.rule_attribute (fn context => read_instantiate (Context.proof_of context) args))); 
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end; 
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(* of: positional instantiation (terms only) *) 
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local 
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val value = 
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Args.internal_term >> Args.Term  
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Args.name >> Args.Text; 
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val inst = Args.ahead  Args.maybe value; 
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val concl = Args.$$$ "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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val (_, _, Bi, _) = Thm.dest_state (st, i); 
244 
val params = Logic.strip_params Bi; (*params of subgoal i as string typ pairs*) 

245 
val params = rev (Term.rename_wrt_term Bi params) 

246 
(*as they are printed: bound variables with*) 

247 
(*the same name are renamed during printing*) 

248 

249 
val (param_names, ctxt') = ctxt 

250 
> Variable.declare_thm thm 

251 
> Thm.fold_terms Variable.declare_constraints st 

252 
> ProofContext.add_fixes_i (map (fn (x, T) => (x, SOME T, NoSyn)) params); 

253 

254 
(* Process type insts: Tinsts_env *) 

255 
fun absent xi = error 

256 
("No such variable in theorem: " ^ Term.string_of_vname xi); 

257 
val (rtypes, rsorts) = Drule.types_sorts thm; 

258 
fun readT (xi, s) = 

259 
let val S = case rsorts xi of SOME S => S  NONE => absent xi; 

260 
val T = Syntax.read_typ ctxt' s; 

261 
val U = TVar (xi, S); 

262 
in if Sign.typ_instance thy (T, U) then (U, T) 

263 
else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails") 

264 
end; 

265 
val Tinsts_env = map readT Tinsts; 

266 
(* Preprocess rule: extract vars and their types, apply Tinsts *) 

267 
fun get_typ xi = 

268 
(case rtypes xi of 

269 
SOME T => typ_subst_atomic Tinsts_env T 

270 
 NONE => absent xi); 

271 
val (xis, ss) = Library.split_list tinsts; 

272 
val Ts = map get_typ xis; 

273 

274 
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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(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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(param_names ~~ paramTs, 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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355 

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fun inst_args f src ctxt = 
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f ctxt (fst (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 (fst (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; 