author  paulson 
Mon, 26 May 1997 12:28:30 +0200  
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parent 3302  404fe31fd8d2 
child 3391  5e45dd3b64e9 
permissions  rwrr 
3302  1 
(* Title: TFL/post 
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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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Postprocessing of TFL definitions 

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*) 

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(* 
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Three postprocessors are applied to the definition: 
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 a wellfoundedness prover (WF_TAC) 
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 a simplifier (tries to eliminate the language of termination expressions) 
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 a termination prover 
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**) 
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3191  16 
signature TFL = 
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sig 

2112  18 
structure Prim : TFL_sig 
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3191  20 
val tgoalw : theory > thm list > thm list > thm list 
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val tgoal: theory > thm list > thm list 

2112  22 

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val WF_TAC : thm list > tactic 

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val simplifier : thm > thm 

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val std_postprocessor : theory 

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> {induction:thm, rules:thm, TCs:term list list} 

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> {induction:thm, rules:thm, nested_tcs:thm list} 

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3331  30 
val define_i : theory > string > term > term 
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> theory * (thm * Prim.pattern list) 

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val define : theory > string > string > string list 

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> theory * Prim.pattern list 

2112  35 

3191  36 
val simplify_defn : theory * (string * Prim.pattern list) 
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> {rules:thm list, induct:thm, tcs:term list} 

2112  38 

3191  39 
(* 
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val function : theory > term > {theory:theory, eq_ind : thm} 

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val lazyR_def: theory > term > {theory:theory, eqns : thm} 

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**) 

2112  43 

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val tflcongs : theory > thm list 

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3191  46 
end; 
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structure Tfl: TFL = 

2112  50 
struct 
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structure Prim = Prim 

3191  52 
structure S = Prim.USyntax 
2112  53 

3191  54 
(* 
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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 (Logic.freeze_vars 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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let val L = termination_goals rules 

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open USyntax 
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val g = cterm_of (sign_of thy) (HOLogic.mk_Trueprop(list_mk_conj L)) 
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in goalw_cterm defs g 
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end; 

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fun tgoal thy = tgoalw thy []; 
2112  74 

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(* 
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* Simple wellfoundedness prover. 

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**) 

2112  78 
fun WF_TAC thms = REPEAT(FIRST1(map rtac thms)) 
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val WFtac = WF_TAC[wf_measure, wf_inv_image, wf_lex_prod, wf_less_than, 
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wf_trancl]; 
2112  81 

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val terminator = simp_tac(!simpset addsimps [less_Suc_eq]) 1 
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THEN TRY(best_tac 
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(!claset addSDs [not0_implies_Suc] 
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addss (!simpset)) 1); 
3191  86 

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val simpls = [less_eq RS eq_reflection, 
3302  88 
lex_prod_def, measure_def, inv_image_def]; 
2112  89 

3191  90 
(* 
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* Does some standard things with the termination conditions of a definition: 

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

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* nonproven termination conditions; and finally attempts to prove the 

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* simplified termination conditions. 

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**) 

2112  96 
val std_postprocessor = Prim.postprocess{WFtac = WFtac, 
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terminator = terminator, 

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simplifier = Prim.Rules.simpl_conv simpls}; 

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val simplifier = rewrite_rule (simpls @ #simps(rep_ss (!simpset)) @ 
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[pred_list_def]); 
3191  102 

2112  103 
fun tflcongs thy = Prim.Context.read() @ (#case_congs(Thry.extract_info thy)); 
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val concl = #2 o Prim.Rules.dest_thm; 

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(* 

3191  109 
* Defining a function with an associated termination relation. 
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**) 

3331  111 
fun define_i thy fid R eqs = 
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let val dummy = require_thy thy "WF_Rel" "recursive function definitions" 

3191  113 
val {functional,pats} = Prim.mk_functional thy eqs 
3331  114 
val (thm,thry) = Prim.wfrec_definition0 thy fid R functional 
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in (thry,(thm,pats)) 
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end; 

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(*lcp's version: takes strings; doesn't return "thm" 

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(whose signature is a draft and therefore useless) *) 
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fun define thy fid R eqs = 
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let fun read thy = readtm (sign_of thy) (TVar(("DUMMY",0),[])) 
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val (thy',(_,pats)) = 

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define_i thy fid (read thy R) 
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(fold_bal (app Ind_Syntax.conj) (map (read thy) eqs)) 
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in (thy',pats) end 
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handle Utils.ERR {mesg,...} => error mesg; 

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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. 

2112  131 
**) 
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local 

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structure R = Prim.Rules 

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structure U = Utils 

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3191  136 
(* The rest of these local definitions are for the tricky nested case *) 
2112  137 
val solved = not o U.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 S.aconv lhs rhs 

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end handle _ => 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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fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L)) 
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fun reducer thl = rewrite (map standard thl @ #simps(rep_ss (!simpset))) 
2112  153 

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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) 
2112  161 
in 
3191  162 
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))) 

2112  165 
end 
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val gen_all = S.gen_all 

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in 

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(* 
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* The "reducer" argument is 

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* (fn thl => rewrite (map standard thl @ #simps(rep_ss (!simpset)))); 
3191  171 
**) 
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fun proof_stage theory reducer {f, R, rules, full_pats_TCs, TCs} = 

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let val dummy = prs "Proving induction theorem.. " 
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val ind = Prim.mk_induction theory f R full_pats_TCs 
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val dummy = writeln "Proved induction theorem." 
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val pp = std_postprocessor theory 
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val dummy = prs "Postprocessing.. " 
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val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs} 
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in 

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case nested_tcs 

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of [] => (writeln "Postprocessing done."; 
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{induction=induction, rules=rules,tcs=[]}) 
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 L => let val dummy = prs "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 induction' = reducer (solved@simplified') induction 

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val rules' = reducer (solved@simplified') rules 

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val dummy = writeln "Postprocessing done." 
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in 
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{induction = induction', 

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rules = rules', 

3191  196 
tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl) 
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(simplified@stubborn)} 

2112  198 
end 
3191  199 
end handle (e as Utils.ERR _) => Utils.Raise e 
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 e => print_exn e; 

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3302  203 
(*lcp: curry the predicate of the induction rule*) 
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fun curry_rule rl = Prod_Syntax.split_rule_var 

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(head_of (HOLogic.dest_Trueprop (concl_of rl)), 
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rl); 
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(*lcp: put a theorem into Isabelle form, using metalevel connectives*) 
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val meta_outer = 

3302  210 
curry_rule o standard o 
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rule_by_tactic (REPEAT_FIRST (resolve_tac [allI, impI, conjI] 
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ORELSE' etac conjE)); 
3191  213 

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(*Strip off the outer !P*) 

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

2112  216 

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3191  218 
fun simplify_defn (thy,(id,pats)) = 
3208  219 
let val dummy = deny (id mem map ! (stamps_of_thy thy)) 
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("Recursive definition " ^ id ^ 

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" would clash with the theory of the same name!") 
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val def = freezeT(get_def thy id RS meta_eq_to_obj_eq) 
3191  223 
val {theory,rules,TCs,full_pats_TCs,patterns} = 
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Prim.post_definition (thy,(def,pats)) 
3191  225 
val {lhs=f,rhs} = S.dest_eq(concl def) 
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val (_,[R,_]) = S.strip_comb rhs 

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val {induction, rules, tcs} = 

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proof_stage theory reducer 

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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} 
3191  232 
val rules' = map (standard o normalize_thm [RSmp]) (R.CONJUNCTS rules) 
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in {induct = meta_outer 

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(normalize_thm [RSspec,RSmp] (induction RS spec')), 
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rules = rules', 
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tcs = (termination_goals rules') @ tcs} 
3191  237 
end 
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handle Utils.ERR {mesg,...} => error mesg 

2112  239 
end; 
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3191  241 
(* 
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* 

243 
* Definitions with synthesized termination relation temporarily 

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* deleted  it's not clear how to integrate this facility with 

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* the Isabelle theory file scheme, which restricts 

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* inference at theoryconstruction time. 

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* 

2112  248 

3208  249 
local structure R = Prim.Rules 
2112  250 
in 
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fun function theory eqs = 

3208  252 
let val dummy = prs "Making definition.. " 
2112  253 
val {rules,R,theory,full_pats_TCs,...} = Prim.lazyR_def theory eqs 
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val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules)) 

3208  255 
val dummy = prs "Definition made.\n" 
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val dummy = prs "Proving induction theorem.. " 

2112  257 
val induction = Prim.mk_induction theory f R full_pats_TCs 
3208  258 
val dummy = prs "Induction theorem proved.\n" 
2112  259 
in {theory = theory, 
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eq_ind = standard (induction RS (rules RS conjI))} 

261 
end 

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handle (e as Utils.ERR _) => Utils.Raise e 

263 
 e => print_exn e 

264 
end; 

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266 

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fun lazyR_def theory eqs = 

268 
let val {rules,theory, ...} = Prim.lazyR_def theory eqs 

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in {eqns=rules, theory=theory} 

270 
end 

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handle (e as Utils.ERR _) => Utils.Raise e 

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 e => print_exn e; 

3191  273 
* 
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* 

275 
**) 

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2112  278 

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3191  280 
(* 
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* Install the basic context notions. Others (for nat and list and prod) 

282 
* have already been added in thry.sml 

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**) 

284 
val () = Prim.Context.write[Thms.LET_CONG, Thms.COND_CONG]; 

2112  285 

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end; 