10769

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(* Title: TFL/post.ML


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ID: $Id$


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Author: Konrad Slind, Cambridge University Computer Laboratory


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Copyright 1997 University of Cambridge


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Second part of main module (postprocessing of TFL definitions).


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*)


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signature TFL =


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sig


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val trace: bool ref


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val quiet_mode: bool ref


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val message: string > unit


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val tgoalw: theory > thm list > thm list > thm list


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val tgoal: theory > thm list > thm list

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val define_i: bool > theory > claset > simpset > thm list > thm list > xstring >

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term > term list > theory * {rules: (thm * int) list, induct: thm, tcs: term list}

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val define: bool > theory > claset > simpset > thm list > thm list > xstring >

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string > string list > theory * {rules: (thm * int) list, induct: thm, tcs: term list}


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val defer_i: theory > thm list > xstring > term list > theory * thm


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val defer: theory > thm list > xstring > string list > theory * thm


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end;


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structure Tfl: TFL =


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struct


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structure S = USyntax


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(* messages *)


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val trace = Prim.trace


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val quiet_mode = ref false;


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fun message s = if ! quiet_mode then () else writeln s;


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(* misc *)


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val read_term = Thm.term_of oo (HOLogic.read_cterm o Theory.sign_of);

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(*


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* Extract termination goals so that they can be put it into a goalstack, or


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* have a tactic directly applied to them.


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**)


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fun termination_goals rules =


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map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop)


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(foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));


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(*


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* Finds the termination conditions in (highly massaged) definition and


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* puts them into a goalstack.


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**)


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fun tgoalw thy defs rules =


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case termination_goals rules of


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[] => error "tgoalw: no termination conditions to prove"


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 L => goalw_cterm defs


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(Thm.cterm_of (Theory.sign_of thy)


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(HOLogic.mk_Trueprop(USyntax.list_mk_conj L)));


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fun tgoal thy = tgoalw thy [];


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(*


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* Three postprocessors are applied to the definition. It


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* attempts to prove wellfoundedness of the given relation, simplifies the


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* nonproved termination conditions, and finally attempts to prove the


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* simplified termination conditions.


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**)

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fun std_postprocessor strict cs ss wfs =


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Prim.postprocess strict

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{wf_tac = REPEAT (ares_tac wfs 1),


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terminator = asm_simp_tac ss 1

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THEN TRY (silent_arith_tac 1 ORELSE

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fast_tac (cs addSDs [not0_implies_Suc] addss ss) 1),

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simplifier = Rules.simpl_conv ss []};


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val concl = #2 o Rules.dest_thm;


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(*


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* Postprocess a definition made by "define". This is a separate stage of


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* processing from the definition stage.


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**)


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local


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structure R = Rules


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structure U = Utils


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(* The rest of these local definitions are for the tricky nested case *)


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val solved = not o can S.dest_eq o #2 o S.strip_forall o concl


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fun id_thm th =


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let val {lhs,rhs} = S.dest_eq (#2 (S.strip_forall (#2 (R.dest_thm th))));


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in lhs aconv rhs end


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handle U.ERR _ => false;


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fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);


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val P_imp_P_iff_True = prover "P > (P= True)" RS mp;


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val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;


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fun mk_meta_eq r = case concl_of r of


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Const("==",_)$_$_ => r


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 _ $(Const("op =",_)$_$_) => r RS eq_reflection


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 _ => r RS P_imp_P_eq_True


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(*Is this the best way to invoke the simplifier??*)


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fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))


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fun join_assums th =


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let val {sign,...} = rep_thm th


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val tych = cterm_of sign


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val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))


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val cntxtl = (#1 o S.strip_imp) lhs (* cntxtl should = cntxtr *)


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val cntxtr = (#1 o S.strip_imp) rhs (* but union is solider *)


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val cntxt = gen_union (op aconv) (cntxtl, cntxtr)


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in


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R.GEN_ALL


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(R.DISCH_ALL


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(rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))


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end


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val gen_all = S.gen_all


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in

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fun proof_stage strict cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} =

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let


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val _ = message "Proving induction theorem ..."


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val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}


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val _ = message "Postprocessing ...";


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val {rules, induction, nested_tcs} =

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std_postprocessor strict cs ss wfs theory {rules=rules, induction=ind, TCs=TCs}

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in


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case nested_tcs


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of [] => {induction=induction, rules=rules,tcs=[]}


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 L => let val dummy = message "Simplifying nested TCs ..."


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val (solved,simplified,stubborn) =


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U.itlist (fn th => fn (So,Si,St) =>


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if (id_thm th) then (So, Si, th::St) else


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if (solved th) then (th::So, Si, St)


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else (So, th::Si, St)) nested_tcs ([],[],[])


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val simplified' = map join_assums simplified

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val dummy = (Prim.trace_thms "solved =" solved;


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Prim.trace_thms "simplified' =" simplified')

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val rewr = full_simplify (ss addsimps (solved @ simplified'));

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val dummy = Prim.trace_thms "Simplifying the induction rule..."


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[induction]

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val induction' = rewr induction

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val dummy = Prim.trace_thms "Simplifying the recursion rules..."


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[rules]


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val rules' = rewr rules


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val _ = message "... Postprocessing finished";

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in


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{induction = induction',


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rules = rules',


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tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)


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(simplified@stubborn)}


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end


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end;


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(*lcp: curry the predicate of the induction rule*)

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fun curry_rule rl =


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SplitRule.split_rule_var (Term.head_of (HOLogic.dest_Trueprop (concl_of rl)), rl);

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(*lcp: put a theorem into Isabelle form, using metalevel connectives*)


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val meta_outer =

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curry_rule o standard o


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rule_by_tactic (REPEAT (FIRSTGOAL (resolve_tac [allI, impI, conjI] ORELSE' etac conjE)));

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(*Strip off the outer !P*)


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val spec'= read_instantiate [("x","P::?'b=>bool")] spec;


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fun tracing true _ = ()


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 tracing false msg = writeln msg;


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fun simplify_defn strict thy cs ss congs wfs id pats def0 =

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let val def = freezeT def0 RS meta_eq_to_obj_eq

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val {theory,rules,rows,TCs,full_pats_TCs} =


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Prim.post_definition congs (thy, (def,pats))

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val {lhs=f,rhs} = S.dest_eq (concl def)


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val (_,[R,_]) = S.strip_comb rhs

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val dummy = Prim.trace_thms "congs =" congs


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(*the next step has caused simplifier looping in some cases*)

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val {induction, rules, tcs} =

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proof_stage strict cs ss wfs theory

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{f = f, R = R, rules = rules,


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full_pats_TCs = full_pats_TCs,


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TCs = TCs}

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val rules' = map (standard o ObjectLogic.rulify_no_asm)


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(R.CONJUNCTS rules)


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in {induct = meta_outer (ObjectLogic.rulify_no_asm (induction RS spec')),

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rules = ListPair.zip(rules', rows),


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tcs = (termination_goals rules') @ tcs}


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end


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handle U.ERR {mesg,func,module} =>


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error (mesg ^


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"\n (In TFL function " ^ module ^ "." ^ func ^ ")");


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(*


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* Defining a function with an associated termination relation.


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**)

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fun define_i strict thy cs ss congs wfs fid R eqs =

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let val {functional,pats} = Prim.mk_functional thy eqs


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val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional

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in (thy, simplify_defn strict thy cs ss congs wfs fid pats def) end;

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fun define strict thy cs ss congs wfs fid R seqs =


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define_i strict thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs)

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handle U.ERR {mesg,...} => error mesg;


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(*


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*


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* Definitions with synthesized termination relation


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*


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**)


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fun func_of_cond_eqn tm =


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#1 (S.strip_comb (#lhs (S.dest_eq (#2 (S.strip_forall (#2 (S.strip_imp tm)))))));


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fun defer_i thy congs fid eqs =


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let val {rules,R,theory,full_pats_TCs,SV,...} =


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Prim.lazyR_def thy (Sign.base_name fid) congs eqs


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val f = func_of_cond_eqn (concl (R.CONJUNCT1 rules handle U.ERR _ => rules));


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val dummy = message "Proving induction theorem ...";


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val induction = Prim.mk_induction theory


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{fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}


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in (theory,


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(*return the conjoined induction rule and recursion equations,


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with assumptions remaining to discharge*)


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standard (induction RS (rules RS conjI)))


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end


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fun defer thy congs fid seqs =


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defer_i thy congs fid (map (read_term thy) seqs)


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handle U.ERR {mesg,...} => error mesg;


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end;


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end;
