author  wenzelm 
Mon, 21 Nov 2011 23:04:45 +0100  
changeset 45613  70e5b43535cd 
parent 45611  8e71b9228d2d 
child 46461  7524f3ac737c 
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 
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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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42806  29 
structure Rule_Insts: RULE_INSTS = 
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struct 
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(** reading instantiations **) 
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local 
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fun error_var msg xi = error (msg ^ quote (Term.string_of_vname xi)); 
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fun the_sort tvars (xi: indexname) = 
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(case AList.lookup (op =) tvars xi of 

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SOME S => S 

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 NONE => error_var "No such type variable in theorem: " xi); 

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fun the_type vars (xi: indexname) = 
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(case AList.lookup (op =) vars xi of 

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SOME T => T 

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 NONE => error_var "No such variable in theorem: " xi); 

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fun instantiate inst = 
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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  64 
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  72 
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' = 

39288  77 
map2 (Type.constraint o Type_Infer.paramify_vars) Ts ts 
42360  78 
> Syntax.check_terms ((schematic ? Proof_Context.set_mode Proof_Context.mode_schematic) ctxt) 
25329  79 
> 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 = Proof_Context.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 (String.isPrefix "'" o fst o fst) mixed_insts; 
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(* type instantiations *) 
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fun readT (xi, s) = 
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let 
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val S = the_sort tvars xi; 
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val T = Syntax.read_typ ctxt s; 
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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 instT1 = Term_Subst.instantiateT (map readT type_insts); 
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val vars1 = map (apsnd instT1) vars; 
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(* term instantiations *) 
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val (xs, ss) = split_list term_insts; 
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val Ts = map (the_type vars1) xs; 
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val (ts, inferred) = read_termTs ctxt false ss Ts; 
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val instT2 = Term.typ_subst_TVars inferred; 
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val vars2 = map (apsnd instT2) vars1; 
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val inst2 = instantiate (xs ~~ ts); 
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(* result *) 
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val inst_tvars = map_filter (make_instT (instT2 o instT1)) tvars; 
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val inst_vars = map_filter (make_inst inst2) vars2; 
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in 
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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_mixed ctxt mixed_insts thm = 
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let 
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val ctxt' = ctxt 
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> Variable.declare_thm thm 
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> fold (fn a => Variable.declare_names (Logic.mk_type (TFree (a, dummyS)))) (add_used thm []); (* FIXME !? *) 
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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 insts = read_insts ctxt' mixed_insts (tvars, vars); 
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in 
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Drule.instantiate_normalize insts thm 
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> Rule_Cases.save thm 
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end; 
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27236  140 
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) (SOME t :: rest) = (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_mixed ctxt insts thm end; 
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end; 
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152 

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(* instantiation of rule or goal state *) 
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fun read_instantiate ctxt = 
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read_instantiate_mixed (ctxt > Proof_Context.set_mode Proof_Context.mode_schematic); (* FIXME !? *) 
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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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val _ = Context.>> (Context.map_theory 
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(Attrib.setup (Binding.name "where") 
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(Scan.lift (Parse.and_list (Args.var  (Args.$$$ "="  Args.name_source))) >> 
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(fn args => 
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Thm.rule_attribute (fn context => read_instantiate_mixed (Context.proof_of context) args))) 
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"named instantiation of theorem")); 
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(* of: positional instantiation (terms only) *) 
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local 
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val inst = Args.maybe Args.name_source; 
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val concl = Args.$$$ "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 _ = 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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196 

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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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(* FIXME cleanup this mess!!! *) 
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fun bires_inst_tac bires_flag ctxt insts thm = 
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let 
42360  206 
val thy = Proof_Context.theory_of ctxt; 
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(* Separate type and term insts *) 
32784  208 
fun has_type_var ((x, _), _) = 
209 
(case Symbol.explode x of "'" :: _ => true  _ => false); 

33317  210 
val Tinsts = filter has_type_var insts; 
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val tinsts = filter_out has_type_var insts; 
25333  212 

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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); 
217 
val params = Logic.strip_params Bi; (*params of subgoal i as string typ pairs*) 

218 
val params = rev (Term.rename_wrt_term Bi params) 

219 
(*as they are printed: bound variables with*) 

220 
(*the same name are renamed during printing*) 

221 

222 
val (param_names, ctxt') = ctxt 

223 
> Variable.declare_thm thm 

224 
> Thm.fold_terms Variable.declare_constraints st 

42360  225 
> Proof_Context.add_fixes (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params); 
25333  226 

227 
(* Process type insts: Tinsts_env *) 

228 
fun absent xi = error 

229 
("No such variable in theorem: " ^ Term.string_of_vname xi); 

230 
val (rtypes, rsorts) = Drule.types_sorts thm; 

231 
fun readT (xi, s) = 

232 
let val S = case rsorts xi of SOME S => S  NONE => absent xi; 

233 
val T = Syntax.read_typ ctxt' s; 

234 
val U = TVar (xi, S); 

235 
in if Sign.typ_instance thy (T, U) then (U, T) 

236 
else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails") 

237 
end; 

238 
val Tinsts_env = map readT Tinsts; 

239 
(* Preprocess rule: extract vars and their types, apply Tinsts *) 

240 
fun get_typ xi = 

241 
(case rtypes xi of 

242 
SOME T => typ_subst_atomic Tinsts_env T 

243 
 NONE => absent xi); 

244 
val (xis, ss) = Library.split_list tinsts; 

245 
val Ts = map get_typ xis; 

246 

247 
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 *) 
44058  258 
val maxidx = Thm.maxidx_of 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]); 
44241  264 
fun liftterm t = 
265 
fold_rev absfree (param_names ~~ paramTs) (Logic.incr_indexes (paramTs, inc) t); 

266 
fun liftpair (cv, ct) = (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_normalize 
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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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27120  280 
val res_inst_tac = bires_inst_tac false; 
281 
val eres_inst_tac = bires_inst_tac true; 

282 

283 

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(* forward resolution *) 
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285 

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fun make_elim_preserve rl = 
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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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Drule.instantiate_normalize ([], [(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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in 
31945  295 
(case Seq.list_of (Thm.bicompose false (false, rl, Thm.nprems_of rl) 1 revcut_rl') of 
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[th] => th 
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 _ => raise THM ("make_elim_preserve", 1, [rl])) 
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end; 
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299 

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(*instantiate and cut  for atomic fact*) 
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fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve rule); 
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302 

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(*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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305 

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(*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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308 

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309 

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(* derived tactics *) 
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311 

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(*deletion of an assumption*) 
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fun thin_tac ctxt s = eres_inst_tac ctxt [(("V", 0), s)] Drule.thin_rl; 
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(*Introduce the given proposition as lemma and subgoal*) 
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fun subgoal_tac ctxt A = DETERM o res_inst_tac ctxt [(("psi", 0), A)] cut_rl; 
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fun subgoals_tac ctxt As = EVERY' (map (subgoal_tac ctxt) As); 
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(** methods **) 
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(* rule_tac etc.  refer to dynamic goal state! *) 
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30545  325 
fun method inst_tac tac = 
30515  326 
Args.goal_spec  
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Scan.optional (Scan.lift 

36950  328 
(Parse.and_list1 (Args.var  (Args.$$$ "="  Parse.!!! Args.name_source))  
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Args.$$$ "in")) []  

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

30551  332 
if null insts then quant (Method.insert_tac facts THEN' tac ctxt thms) 
30515  333 
else 
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(case thms of 

335 
[thm] => quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm) 

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

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30551  338 
val res_inst_meth = method res_inst_tac (K Tactic.resolve_tac); 
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val eres_inst_meth = method eres_inst_tac (K Tactic.eresolve_tac); 

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

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

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

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(* setup *) 
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26463  347 
val _ = Context.>> (Context.map_theory 
30515  348 
(Method.setup (Binding.name "rule_tac") res_inst_meth "apply rule (dynamic instantiation)" #> 
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Method.setup (Binding.name "erule_tac") eres_inst_meth 

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

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

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

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

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

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

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Method.setup (Binding.name "subgoal_tac") 

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

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

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"insert subgoal (dynamic instantiation)" #> 

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Method.setup (Binding.name "thin_tac") 

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

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

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"remove premise (dynamic instantiation)")); 

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end; 
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42806  367 
structure Basic_Rule_Insts: BASIC_RULE_INSTS = Rule_Insts; 
36950  368 
open Basic_Rule_Insts; 