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(* Title: HOL/Tools/inductive_realizer.ML 
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Author: Stefan Berghofer, TU Muenchen 
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Porgram extraction from proofs involving inductive predicates: 
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Realizers for induction and elimination rules. 
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*) 
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signature INDUCTIVE_REALIZER = 
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sig 
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val add_ind_realizers: string > string list > theory > theory 
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val setup: theory > theory 
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end; 
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structure InductiveRealizer : INDUCTIVE_REALIZER = 
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struct 
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(* FIXME: LocalTheory.note should return theorems with proper names! *) (* FIXME ?? *) 
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fun name_of_thm thm = 
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(case Proofterm.fold_proof_atoms false (fn PThm (_, ((name, _, _), _)) => cons name  _ => I) 
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[Thm.proof_of thm] [] of 
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[name] => name 
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 _ => error ("name_of_thm: bad proof of theorem\n" ^ Display.string_of_thm thm)); 

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val all_simps = map (symmetric o mk_meta_eq) (thms "HOL.all_simps"); 
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fun prf_of thm = 
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let 
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val thy = Thm.theory_of_thm thm; 
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val thm' = Reconstruct.reconstruct_proof thy (Thm.prop_of thm) (Thm.proof_of thm); 
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in Reconstruct.expand_proof thy [("", NONE)] thm' end; (* FIXME *) 
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fun forall_intr_prf t prf = 
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let val (a, T) = (case t of Var ((a, _), T) => (a, T)  Free p => p) 
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in Abst (a, SOME T, Proofterm.prf_abstract_over t prf) end; 
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fun subsets [] = [[]] 
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 subsets (x::xs) = 
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let val ys = subsets xs 
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in ys @ map (cons x) ys end; 
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val pred_of = fst o dest_Const o head_of; 
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fun strip_all' used names (Const ("all", _) $ Abs (s, T, t)) = 
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let val (s', names') = (case names of 

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[] => (Name.variant used s, []) 

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 name :: names' => (name, names')) 

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in strip_all' (s'::used) names' (subst_bound (Free (s', T), t)) end 

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 strip_all' used names ((t as Const ("==>", _) $ P) $ Q) = 

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t $ strip_all' used names Q 

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 strip_all' _ _ t = t; 

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fun strip_all t = strip_all' (Term.add_free_names t []) [] t; 
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fun strip_one name (Const ("all", _) $ Abs (s, T, Const ("==>", _) $ P $ Q)) = 

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(subst_bound (Free (name, T), P), subst_bound (Free (name, T), Q)) 

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 strip_one _ (Const ("==>", _) $ P $ Q) = (P, Q); 

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fun relevant_vars prop = List.foldr (fn 
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(Var ((a, i), T), vs) => (case strip_type T of 
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(_, Type (s, _)) => if s mem ["bool"] then (a, T) :: vs else vs 
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 _ => vs) 
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 (_, vs) => vs) [] (OldTerm.term_vars prop); 
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fun dt_of_intrs thy vs nparms intrs = 
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let 
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val iTs = OldTerm.term_tvars (prop_of (hd intrs)); 
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val Tvs = map TVar iTs; 
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val (Const (s, _), ts) = strip_comb (HOLogic.dest_Trueprop 
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(Logic.strip_imp_concl (prop_of (hd intrs)))); 

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val params = map dest_Var (Library.take (nparms, ts)); 

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val tname = Binding.name (space_implode "_" (Long_Name.base_name s ^ "T" :: vs)); 
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fun constr_of_intr intr = (Binding.name (Long_Name.base_name (name_of_thm intr)), 
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map (Logic.unvarifyT o snd) (rev (Term.add_vars (prop_of intr) []) \\ params) @ 
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filter_out (equal Extraction.nullT) (map 
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(Logic.unvarifyT o Extraction.etype_of thy vs []) (prems_of intr)), 
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NoSyn); 
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in (map (fn a => "'" ^ a) vs @ map (fst o fst) iTs, tname, NoSyn, 
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map constr_of_intr intrs) 
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end; 
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fun mk_rlz T = Const ("realizes", [T, HOLogic.boolT] > HOLogic.boolT); 
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(** turn "P" into "%r x. realizes r (P x)" **) 
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fun gen_rvar vs (t as Var ((a, 0), T)) = 
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if body_type T <> HOLogic.boolT then t else 
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let 

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val U = TVar (("'" ^ a, 0), HOLogic.typeS) 

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val Ts = binder_types T; 

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val i = length Ts; 

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val xs = map (pair "x") Ts; 

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val u = list_comb (t, map Bound (i  1 downto 0)) 

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in 

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if a mem vs then 

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list_abs (("r", U) :: xs, mk_rlz U $ Bound i $ u) 

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else list_abs (xs, mk_rlz Extraction.nullT $ Extraction.nullt $ u) 

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end 

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 gen_rvar _ t = t; 
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fun mk_realizes_eqn n vs nparms intrs = 
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let 
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val concl = HOLogic.dest_Trueprop (concl_of (hd intrs)); 
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val iTs = OldTerm.term_tvars concl; 
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val Tvs = map TVar iTs; 
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val (h as Const (s, T), us) = strip_comb concl; 
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val params = List.take (us, nparms); 

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val elTs = List.drop (binder_types T, nparms); 

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val predT = elTs > HOLogic.boolT; 

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val used = map (fst o fst o dest_Var) params; 

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val xs = map (Var o apfst (rpair 0)) 

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(Name.variant_list used (replicate (length elTs) "x") ~~ elTs); 

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val rT = if n then Extraction.nullT 
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else Type (space_implode "_" (s ^ "T" :: vs), 
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map (fn a => TVar (("'" ^ a, 0), HOLogic.typeS)) vs @ Tvs); 
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val r = if n then Extraction.nullt else Var ((Long_Name.base_name s, 0), rT); 
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val S = list_comb (h, params @ xs); 
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val rvs = relevant_vars S; 
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val vs' = map fst rvs \\ vs; 
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val rname = space_implode "_" (s ^ "R" :: vs); 
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fun mk_Tprem n v = 
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let val T = (the o AList.lookup (op =) rvs) v 
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in (Const ("typeof", T > Type ("Type", [])) $ Var ((v, 0), T), 
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Extraction.mk_typ (if n then Extraction.nullT 
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else TVar (("'" ^ v, 0), HOLogic.typeS))) 
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end; 
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val prems = map (mk_Tprem true) vs' @ map (mk_Tprem false) vs; 
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val ts = map (gen_rvar vs) params; 
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val argTs = map fastype_of ts; 
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in ((prems, (Const ("typeof", HOLogic.boolT > Type ("Type", [])) $ S, 
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Extraction.mk_typ rT)), 
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(prems, (mk_rlz rT $ r $ S, 
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if n then list_comb (Const (rname, argTs > predT), ts @ xs) 

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else list_comb (Const (rname, argTs @ [rT] > predT), ts @ [r] @ xs)))) 

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end; 
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fun fun_of_prem thy rsets vs params rule ivs intr = 
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let 
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val ctxt = ProofContext.init thy 
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val args = map (Free o apfst fst o dest_Var) ivs; 

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val args' = map (Free o apfst fst) 
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(Term.add_vars (prop_of intr) [] \\ params); 
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val rule' = strip_all rule; 
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val conclT = Extraction.etype_of thy vs [] (Logic.strip_imp_concl rule'); 
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val used = map (fst o dest_Free) args; 
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val is_rec = exists_Const (fn (c, _) => member (op =) rsets c); 
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fun is_meta (Const ("all", _) $ Abs (s, _, P)) = is_meta P 
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 is_meta (Const ("==>", _) $ _ $ Q) = is_meta Q 
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 is_meta (Const ("Trueprop", _) $ t) = (case head_of t of 
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Const (s, _) => can (InductivePackage.the_inductive ctxt) s 

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 _ => true) 

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 is_meta _ = false; 
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fun fun_of ts rts args used (prem :: prems) = 
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let 
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val T = Extraction.etype_of thy vs [] prem; 
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val [x, r] = Name.variant_list used ["x", "r"] 
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in if T = Extraction.nullT 
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then fun_of ts rts args used prems 
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else if is_rec prem then 
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if is_meta prem then 
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let 
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val prem' :: prems' = prems; 
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val U = Extraction.etype_of thy vs [] prem'; 
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in if U = Extraction.nullT 
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then fun_of (Free (x, T) :: ts) 
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(Free (r, binder_types T > HOLogic.unitT) :: rts) 
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(Free (x, T) :: args) (x :: r :: used) prems' 
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else fun_of (Free (x, T) :: ts) (Free (r, U) :: rts) 
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(Free (r, U) :: Free (x, T) :: args) (x :: r :: used) prems' 
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end 
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else (case strip_type T of 
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(Ts, Type ("*", [T1, T2])) => 
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let 
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val fx = Free (x, Ts > T1); 
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val fr = Free (r, Ts > T2); 
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val bs = map Bound (length Ts  1 downto 0); 
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val t = list_abs (map (pair "z") Ts, 
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HOLogic.mk_prod (list_comb (fx, bs), list_comb (fr, bs))) 
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in fun_of (fx :: ts) (fr :: rts) (t::args) 
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(x :: r :: used) prems 
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end 
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 (Ts, U) => fun_of (Free (x, T) :: ts) 
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(Free (r, binder_types T > HOLogic.unitT) :: rts) 
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(Free (x, T) :: args) (x :: r :: used) prems) 
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else fun_of (Free (x, T) :: ts) rts (Free (x, T) :: args) 
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(x :: used) prems 
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end 
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 fun_of ts rts args used [] = 
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let val xs = rev (rts @ ts) 
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in if conclT = Extraction.nullT 
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then list_abs_free (map dest_Free xs, HOLogic.unit) 
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else list_abs_free (map dest_Free xs, list_comb 
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(Free ("r" ^ Long_Name.base_name (name_of_thm intr), 
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map fastype_of (rev args) > conclT), rev args)) 
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end 
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in fun_of args' [] (rev args) used (Logic.strip_imp_prems rule') end; 
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fun indrule_realizer thy induct raw_induct rsets params vs rec_names rss intrs dummies = 
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let 
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val concls = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of raw_induct)); 
15570  207 
val premss = List.mapPartial (fn (s, rs) => if s mem rsets then 
22271  208 
SOME (rs, map (fn (_, r) => List.nth (prems_of raw_induct, 
15570  209 
find_index_eq (prop_of r) (map prop_of intrs))) rs) else NONE) rss; 
22271  210 
val fs = maps (fn ((intrs, prems), dummy) => 
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let 
22271  212 
val fs = map (fn (rule, (ivs, intr)) => 
213 
fun_of_prem thy rsets vs params rule ivs intr) (prems ~~ intrs) 

27982  214 
in if dummy then Const ("HOL.default_class.default", 
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HOLogic.unitT > body_type (fastype_of (hd fs))) :: fs 
22271  216 
else fs 
217 
end) (premss ~~ dummies); 

16861  218 
val frees = fold Term.add_frees fs []; 
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val Ts = map fastype_of fs; 
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fun name_of_fn intr = "r" ^ Long_Name.base_name (name_of_thm intr) 
22271  221 
in 
222 
fst (fold_map (fn concl => fn names => 

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let val T = Extraction.etype_of thy vs [] concl 
22271  224 
in if T = Extraction.nullT then (Extraction.nullt, names) else 
225 
let 

226 
val Type ("fun", [U, _]) = T; 

227 
val a :: names' = names 

228 
in (list_abs_free (("x", U) :: List.mapPartial (fn intr => 

229 
Option.map (pair (name_of_fn intr)) 

230 
(AList.lookup (op =) frees (name_of_fn intr))) intrs, 

231 
list_comb (Const (a, Ts > T), fs) $ Free ("x", U)), names') 

232 
end 

233 
end) concls rec_names) 

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end; 
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fun add_dummy name dname (x as (_, (vs, s, mfx, cs))) = 
30345  237 
if Binding.eq_name (name, s) then (true, (vs, s, mfx, (dname, [HOLogic.unitT], NoSyn) :: cs)) 
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else x; 
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18314  240 
fun add_dummies f [] _ thy = 
241 
(([], NONE), thy) 

242 
 add_dummies f dts used thy = 

243 
thy 

244 
> f (map snd dts) 

30345  245 
> (fn dtinfo => pair (map fst dts, SOME dtinfo)) 
18314  246 
handle DatatypeAux.Datatype_Empty name' => 
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let 
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val name = Long_Name.base_name name'; 
30345  249 
val dname = Name.variant used "Dummy"; 
18314  250 
in 
251 
thy 

30345  252 
> add_dummies f (map (add_dummy (Binding.name name) (Binding.name dname)) dts) (dname :: used) 
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end; 
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22271  255 
fun mk_realizer thy vs (name, rule, rrule, rlz, rt) = 
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let 
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val rvs = map fst (relevant_vars (prop_of rule)); 
16861  258 
val xs = rev (Term.add_vars (prop_of rule) []); 
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val vs1 = map Var (filter_out (fn ((a, _), _) => a mem rvs) xs); 
16861  260 
val rlzvs = rev (Term.add_vars (prop_of rrule) []); 
17485  261 
val vs2 = map (fn (ixn, _) => Var (ixn, (the o AList.lookup (op =) rlzvs) ixn)) xs; 
22271  262 
val rs = map Var (subtract (op = o pairself fst) xs rlzvs); 
27330  263 
val rlz' = fold_rev Logic.all (vs2 @ rs) (prop_of rrule); 
264 
val rlz'' = fold_rev Logic.all vs2 rlz 

22271  265 
in (name, (vs, 
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if rt = Extraction.nullt then rt else 
30190  267 
List.foldr (uncurry lambda) rt vs1, 
22271  268 
ProofRewriteRules.un_hhf_proof rlz' rlz'' 
27330  269 
(fold_rev forall_intr_prf (vs2 @ rs) (prf_of rrule)))) 
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end; 
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fun rename tab = map (fn x => the_default x (AList.lookup op = tab x)); 
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fun add_ind_realizer rsets intrs induct raw_induct elims (thy, vs) = 
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let 
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val qualifier = Long_Name.qualifier (name_of_thm induct); 
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val inducts = PureThy.get_thms thy (Long_Name.qualify qualifier "inducts"); 
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val iTs = OldTerm.term_tvars (prop_of (hd intrs)); 
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val ar = length vs + length iTs; 
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val params = InductivePackage.params_of raw_induct; 
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val arities = InductivePackage.arities_of raw_induct; 
22271  282 
val nparms = length params; 
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val params' = map dest_Var params; 
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val rss = InductivePackage.partition_rules raw_induct intrs; 
22271  285 
val rss' = map (fn (((s, rs), (_, arity)), elim) => 
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(s, (InductivePackage.infer_intro_vars elim arity rs ~~ rs))) 
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(rss ~~ arities ~~ elims); 
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val (prfx, _) = split_last (Long_Name.explode (fst (hd rss))); 
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val tnames = map (fn s => space_implode "_" (s ^ "T" :: vs)) rsets; 
16123  290 

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val thy1 = thy > 
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Sign.root_path > 
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Sign.add_path (Long_Name.implode prfx); 
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val (ty_eqs, rlz_eqs) = split_list 
22271  295 
(map (fn (s, rs) => mk_realizes_eqn (not (s mem rsets)) vs nparms rs) rss); 
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val thy1' = thy1 > 
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Theory.copy > 
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Sign.add_types (map (fn s => (Binding.name (Long_Name.base_name s), ar, NoSyn)) tnames) > 
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fold (fn s => AxClass.axiomatize_arity 
19510  301 
(s, replicate ar HOLogic.typeS, HOLogic.typeS)) tnames > 
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Extraction.add_typeof_eqns_i ty_eqs; 
15570  303 
val dts = List.mapPartial (fn (s, rs) => if s mem rsets then 
22271  304 
SOME (dt_of_intrs thy1' vs nparms rs) else NONE) rss; 
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(** datatype representing computational content of inductive set **) 
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18314  308 
val ((dummies, dt_info), thy2) = 
18008  309 
thy1 
18314  310 
> add_dummies 
30345  311 
(DatatypePackage.add_datatype false false (map (Binding.name_of o #2) dts)) 
18314  312 
(map (pair false) dts) [] 
313 
> Extraction.add_typeof_eqns_i ty_eqs 

314 
> Extraction.add_realizes_eqns_i rlz_eqs; 

315 
fun get f = (these oo Option.map) f; 

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val rec_names = distinct (op =) (map (fst o dest_Const o head_of o fst o 
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HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) (get #rec_thms dt_info)); 
30190  318 
val (_, constrss) = Library.foldl_map (fn ((recs, dummies), (s, rs)) => 
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if s mem rsets then 
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let 
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val (d :: dummies') = dummies; 
19473  322 
val (recs1, recs2) = chop (length rs) (if d then tl recs else recs) 
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in ((recs2, dummies'), map (head_of o hd o rev o snd o strip_comb o 
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fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) recs1) 
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end 
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else ((recs, dummies), replicate (length rs) Extraction.nullt)) 
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((get #rec_thms dt_info, dummies), rss); 
18929  328 
val rintrs = map (fn (intr, c) => Envir.eta_contract 
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(Extraction.realizes_of thy2 vs 
22271  330 
(if c = Extraction.nullt then c else list_comb (c, map Var (rev 
331 
(Term.add_vars (prop_of intr) []) \\ params'))) (prop_of intr))) 

332 
(maps snd rss ~~ List.concat constrss); 

30345  333 
val (rlzpreds, rlzpreds') = 
334 
rintrs > map (fn rintr => 

22271  335 
let 
30345  336 
val Const (s, T) = head_of (HOLogic.dest_Trueprop (Logic.strip_assums_concl rintr)); 
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val s' = Long_Name.base_name s; 
30345  338 
val T' = Logic.unvarifyT T; 
339 
in (((s', T'), NoSyn), (Const (s, T'), Free (s', T'))) end) 

340 
> distinct (op = o pairself (#1 o #1)) 

341 
> map (apfst (apfst (apfst Binding.name))) 

342 
> split_list; 

343 

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val rlzparams = map (fn Var ((s, _), T) => (s, Logic.unvarifyT T)) 
22271  345 
(List.take (snd (strip_comb 
346 
(HOLogic.dest_Trueprop (Logic.strip_assums_concl (hd rintrs)))), nparms)); 

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(** realizability predicate **) 
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22271  350 
val (ind_info, thy3') = thy2 > 
26128  351 
InductivePackage.add_inductive_global (serial_string ()) 
28965  352 
{quiet_mode = false, verbose = false, kind = Thm.theoremK, alt_name = Binding.empty, 
29389  353 
coind = false, no_elim = false, no_ind = false, skip_mono = false, fork_mono = false} 
22271  354 
rlzpreds rlzparams (map (fn (rintr, intr) => 
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((Binding.name (Long_Name.base_name (name_of_thm intr)), []), 
22271  356 
subst_atomic rlzpreds' (Logic.unvarify rintr))) 
357 
(rintrs ~~ maps snd rss)) [] > 

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Sign.absolute_path; 
26663  359 
val thy3 = fold (PureThy.hide_fact false o name_of_thm) (#intrs ind_info) thy3'; 
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360 

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(** realizer for induction rule **) 
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22271  363 
val Ps = List.mapPartial (fn _ $ M $ P => if pred_of M mem rsets then 
15531  364 
SOME (fst (fst (dest_Var (head_of P)))) else NONE) 
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(HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of raw_induct))); 
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366 

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fun add_ind_realizer (thy, Ps) = 
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let 
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val vs' = rename (map (pairself (fst o fst o dest_Var)) 
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(params ~~ List.take (snd (strip_comb (HOLogic.dest_Trueprop 
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(hd (prems_of (hd inducts))))), nparms))) vs; 
22271  372 
val rs = indrule_realizer thy induct raw_induct rsets params' 
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(vs' @ Ps) rec_names rss' intrs dummies; 
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val rlzs = map (fn (r, ind) => Extraction.realizes_of thy (vs' @ Ps) r 
22271  375 
(prop_of ind)) (rs ~~ inducts); 
29281  376 
val used = fold Term.add_free_names rlzs []; 
22271  377 
val rnames = Name.variant_list used (replicate (length inducts) "r"); 
378 
val rnames' = Name.variant_list 

379 
(used @ rnames) (replicate (length intrs) "s"); 

380 
val rlzs' as (prems, _, _) :: _ = map (fn (rlz, name) => 

381 
let 

382 
val (P, Q) = strip_one name (Logic.unvarify rlz); 

383 
val Q' = strip_all' [] rnames' Q 

384 
in 

385 
(Logic.strip_imp_prems Q', P, Logic.strip_imp_concl Q') 

386 
end) (rlzs ~~ rnames); 

387 
val concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map 

388 
(fn (_, _ $ P, _ $ Q) => HOLogic.mk_imp (P, Q)) rlzs')); 

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val rews = map mk_meta_eq 
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390 
(fst_conv :: snd_conv :: get #rec_thms dt_info); 
26711  391 
val thm = Goal.prove_global thy [] prems concl (fn {prems, ...} => EVERY 
22271  392 
[rtac (#raw_induct ind_info) 1, 
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393 
rewrite_goals_tac rews, 
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394 
REPEAT ((resolve_tac prems THEN_ALL_NEW EVERY' 
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[K (rewrite_goals_tac rews), ObjectLogic.atomize_prems_tac, 
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396 
DEPTH_SOLVE_1 o FIRST' [atac, etac allE, etac impE]]) 1)]); 
29579  397 
val (thm', thy') = PureThy.store_thm (Binding.name (space_implode "_" 
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(Long_Name.qualify qualifier "induct" :: vs' @ Ps @ ["correctness"])), thm) thy; 
22271  399 
val thms = map (fn th => zero_var_indexes (rotate_prems ~1 (th RS mp))) 
400 
(DatatypeAux.split_conj_thm thm'); 

401 
val ([thms'], thy'') = PureThy.add_thmss 

29579  402 
[((Binding.name (space_implode "_" 
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403 
(Long_Name.qualify qualifier "inducts" :: vs' @ Ps @ 
29579  404 
["correctness"])), thms), [])] thy'; 
22271  405 
val realizers = inducts ~~ thms' ~~ rlzs ~~ rs; 
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406 
in 
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407 
Extraction.add_realizers_i 
22271  408 
(map (fn (((ind, corr), rlz), r) => 
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409 
mk_realizer thy' (vs' @ Ps) (Thm.get_name ind, ind, corr, rlz, r)) 
22271  410 
realizers @ (case realizers of 
411 
[(((ind, corr), rlz), r)] => 

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412 
[mk_realizer thy' (vs' @ Ps) (Long_Name.qualify qualifier "induct", 
22271  413 
ind, corr, rlz, r)] 
414 
 _ => [])) thy'' 

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415 
end; 
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416 

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417 
(** realizer for elimination rules **) 
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418 

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419 
val case_names = map (fst o dest_Const o head_of o fst o HOLogic.dest_eq o 
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420 
HOLogic.dest_Trueprop o prop_of o hd) (get #case_thms dt_info); 
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421 

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422 
fun add_elim_realizer Ps 
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(((((elim, elimR), intrs), case_thms), case_name), dummy) thy = 
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424 
let 
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val (prem :: prems) = prems_of elim; 
22271  426 
fun reorder1 (p, (_, intr)) = 
27330  427 
Library.foldl (fn (t, ((s, _), T)) => Logic.all (Free (s, T)) t) 
16861  428 
(strip_all p, Term.add_vars (prop_of intr) [] \\ params'); 
22271  429 
fun reorder2 ((ivs, intr), i) = 
430 
let val fs = Term.add_vars (prop_of intr) [] \\ params' 

15570  431 
in Library.foldl (fn (t, x) => lambda (Var x) t) 
22271  432 
(list_comb (Bound (i + length ivs), ivs), fs) 
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433 
end; 
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434 
val p = Logic.list_implies 
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435 
(map reorder1 (prems ~~ intrs) @ [prem], concl_of elim); 
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436 
val T' = Extraction.etype_of thy (vs @ Ps) [] p; 
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437 
val T = if dummy then (HOLogic.unitT > body_type T') > T' else T'; 
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438 
val Ts = map (Extraction.etype_of thy (vs @ Ps) []) (prems_of elim); 
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439 
val r = if null Ps then Extraction.nullt 
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440 
else list_abs (map (pair "x") Ts, list_comb (Const (case_name, T), 
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441 
(if dummy then 
27982  442 
[Abs ("x", HOLogic.unitT, Const ("HOL.default_class.default", body_type T))] 
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443 
else []) @ 
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444 
map reorder2 (intrs ~~ (length prems  1 downto 0)) @ 
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445 
[Bound (length prems)])); 
22271  446 
val rlz = Extraction.realizes_of thy (vs @ Ps) r (prop_of elim); 
447 
val rlz' = strip_all (Logic.unvarify rlz); 

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448 
val rews = map mk_meta_eq case_thms; 
22271  449 
val thm = Goal.prove_global thy [] 
26711  450 
(Logic.strip_imp_prems rlz') (Logic.strip_imp_concl rlz') (fn {prems, ...} => EVERY 
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451 
[cut_facts_tac [hd prems] 1, 
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452 
etac elimR 1, 
22271  453 
ALLGOALS (asm_simp_tac HOL_basic_ss), 
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454 
rewrite_goals_tac rews, 
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455 
REPEAT ((resolve_tac prems THEN_ALL_NEW (ObjectLogic.atomize_prems_tac THEN' 
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456 
DEPTH_SOLVE_1 o FIRST' [atac, etac allE, etac impE])) 1)]); 
29579  457 
val (thm', thy') = PureThy.store_thm (Binding.name (space_implode "_" 
458 
(name_of_thm elim :: vs @ Ps @ ["correctness"])), thm) thy 

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459 
in 
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460 
Extraction.add_realizers_i 
22271  461 
[mk_realizer thy' (vs @ Ps) (name_of_thm elim, elim, thm', rlz, r)] thy' 
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462 
end; 
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463 

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464 
(** add realizers to theory **) 
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465 

15570  466 
val thy4 = Library.foldl add_ind_realizer (thy3, subsets Ps); 
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467 
val thy5 = Extraction.add_realizers_i 
22271  468 
(map (mk_realizer thy4 vs) (map (fn (((rule, rrule), rlz), c) => 
469 
(name_of_thm rule, rule, rrule, rlz, 

470 
list_comb (c, map Var (rev (Term.add_vars (prop_of rule) []) \\ params')))) 

471 
(List.concat (map snd rss) ~~ #intrs ind_info ~~ rintrs ~~ 

472 
List.concat constrss))) thy4; 

473 
val elimps = List.mapPartial (fn ((s, intrs), p) => 

474 
if s mem rsets then SOME (p, intrs) else NONE) 

475 
(rss' ~~ (elims ~~ #elims ind_info)); 

15570  476 
val thy6 = Library.foldl (fn (thy, p as (((((elim, _), _), _), _), _)) => thy > 
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477 
add_elim_realizer [] p > add_elim_realizer [fst (fst (dest_Var 
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478 
(HOLogic.dest_Trueprop (concl_of elim))))] p) (thy5, 
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479 
elimps ~~ get #case_thms dt_info ~~ case_names ~~ dummies) 
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480 

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481 
in Sign.restore_naming thy thy6 end; 
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482 

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483 
fun add_ind_realizers name rsets thy = 
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484 
let 
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485 
val (_, {intrs, induct, raw_induct, elims, ...}) = 
22271  486 
InductivePackage.the_inductive (ProofContext.init thy) name; 
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487 
val vss = sort (int_ord o pairself length) 
22271  488 
(subsets (map fst (relevant_vars (concl_of (hd intrs))))) 
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489 
in 
15570  490 
Library.foldl (add_ind_realizer rsets intrs induct raw_induct elims) (thy, vss) 
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491 
end 
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492 

20897  493 
fun rlz_attrib arg = Thm.declaration_attribute (fn thm => Context.mapping 
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494 
let 
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495 
fun err () = error "ind_realizer: bad rule"; 
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496 
val sets = 
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497 
(case HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of thm)) of 
22271  498 
[_] => [pred_of (HOLogic.dest_Trueprop (hd (prems_of thm)))] 
499 
 xs => map (pred_of o fst o HOLogic.dest_imp) xs) 

15570  500 
handle TERM _ => err ()  Empty => err (); 
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501 
in 
18728  502 
add_ind_realizers (hd sets) 
503 
(case arg of 

15531  504 
NONE => sets  SOME NONE => [] 
15703  505 
 SOME (SOME sets') => sets \\ sets') 
20897  506 
end I); 
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507 

18728  508 
val ind_realizer = Attrib.syntax 
15703  509 
((Scan.option (Scan.lift (Args.$$$ "irrelevant")  
510 
Scan.option (Scan.lift (Args.colon)  

18728  511 
Scan.repeat1 Args.const))) >> rlz_attrib); 
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512 

18708  513 
val setup = 
18728  514 
Attrib.add_attributes [("ind_realizer", ind_realizer, "add realizers for inductive set")]; 
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515 

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516 
end; 
15706  517 