structure Tfl
:sig
structure Prim : TFL_sig
val tgoalw : theory -> thm list -> thm -> thm list
val tgoal: theory -> thm -> thm list
val WF_TAC : thm list -> tactic
val simplifier : thm -> thm
val std_postprocessor : theory
-> {induction:thm, rules:thm, TCs:term list list}
-> {induction:thm, rules:thm, nested_tcs:thm list}
val rfunction : theory
-> (thm list -> thm -> thm)
-> term -> term
-> {induction:thm, rules:thm,
tcs:term list, theory:theory}
val Rfunction : theory -> term -> term
-> {induction:thm, rules:thm,
theory:theory, tcs:term list}
val function : theory -> term -> {theory:theory, eq_ind : thm}
val lazyR_def : theory -> term -> {theory:theory, eqns : thm}
val tflcongs : theory -> thm list
end =
struct
structure Prim = Prim
fun tgoalw thy defs thm =
let val L = Prim.termination_goals thm
open USyntax
val g = cterm_of (sign_of thy) (mk_prop(list_mk_conj L))
in goalw_cterm defs g
end;
val tgoal = Utils.C tgoalw [];
fun WF_TAC thms = REPEAT(FIRST1(map rtac thms))
val WFtac = WF_TAC[wf_measure, wf_inv_image, wf_lex_prod,
wf_pred_nat, wf_pred_list, wf_trancl];
val terminator = simp_tac(HOL_ss addsimps[pred_nat_def,pred_list_def,
fst_conv,snd_conv,
mem_Collect_eq,lessI]) 1
THEN TRY(fast_tac set_cs 1);
val simpls = [less_eq RS eq_reflection,
lex_prod_def, measure_def, inv_image_def,
fst_conv RS eq_reflection, snd_conv RS eq_reflection,
mem_Collect_eq RS eq_reflection(*, length_Cons RS eq_reflection*)];
val std_postprocessor = Prim.postprocess{WFtac = WFtac,
terminator = terminator,
simplifier = Prim.Rules.simpl_conv simpls};
val simplifier = rewrite_rule (simpls @ #simps(rep_ss HOL_ss) @
[pred_nat_def,pred_list_def]);
fun tflcongs thy = Prim.Context.read() @ (#case_congs(Thry.extract_info thy));
local structure S = Prim.USyntax
in
fun func_of_cond_eqn tm =
#1(S.strip_comb(#lhs(S.dest_eq(#2(S.strip_forall(#2(S.strip_imp tm)))))))
end;
val concl = #2 o Prim.Rules.dest_thm;
(*---------------------------------------------------------------------------
* Defining a function with an associated termination relation. Lots of
* postprocessing takes place.
*---------------------------------------------------------------------------*)
local
structure S = Prim.USyntax
structure R = Prim.Rules
structure U = Utils
val solved = not o U.can S.dest_eq o #2 o S.strip_forall o concl
fun id_thm th =
let val {lhs,rhs} = S.dest_eq(#2(S.strip_forall(#2 (R.dest_thm th))))
in S.aconv lhs rhs
end handle _ => false
fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
fun mk_meta_eq r = case concl_of r of
Const("==",_)$_$_ => r
| _$(Const("op =",_)$_$_) => r RS eq_reflection
| _ => r RS P_imp_P_eq_True
fun rewrite L = rewrite_rule (map mk_meta_eq (Utils.filter(not o id_thm) L))
fun join_assums th =
let val {sign,...} = rep_thm th
val tych = cterm_of sign
val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
val cntxtl = (#1 o S.strip_imp) lhs (* cntxtl should = cntxtr *)
val cntxtr = (#1 o S.strip_imp) rhs (* but union is solider *)
val cntxt = U.union S.aconv cntxtl cntxtr
in
R.GEN_ALL
(R.DISCH_ALL
(rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
end
val gen_all = S.gen_all
in
fun rfunction theory reducer R eqs =
let val _ = prs "Making definition.. "
val {rules,theory, full_pats_TCs,
TCs,...} = Prim.gen_wfrec_definition theory {R=R,eqs=eqs}
val f = func_of_cond_eqn(concl(R.CONJUNCT1 rules handle _ => rules))
val _ = prs "Definition made.\n"
val _ = prs "Proving induction theorem.. "
val ind = Prim.mk_induction theory f R full_pats_TCs
val _ = prs "Proved induction theorem.\n"
val pp = std_postprocessor theory
val _ = prs "Postprocessing.. "
val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs}
val normal_tcs = Prim.termination_goals rules
in
case nested_tcs
of [] => (prs "Postprocessing done.\n";
{theory=theory, induction=induction, rules=rules,tcs=normal_tcs})
| L => let val _ = prs "Simplifying nested TCs.. "
val (solved,simplified,stubborn) =
U.itlist (fn th => fn (So,Si,St) =>
if (id_thm th) then (So, Si, th::St) else
if (solved th) then (th::So, Si, St)
else (So, th::Si, St)) nested_tcs ([],[],[])
val simplified' = map join_assums simplified
val induction' = reducer (solved@simplified') induction
val rules' = reducer (solved@simplified') rules
val _ = prs "Postprocessing done.\n"
in
{induction = induction',
rules = rules',
tcs = normal_tcs @
map (gen_all o S.rhs o #2 o S.strip_forall o concl)
(simplified@stubborn),
theory = theory}
end
end
handle (e as Utils.ERR _) => Utils.Raise e
| e => print_exn e
fun Rfunction thry =
rfunction thry
(fn thl => rewrite (map standard thl @ #simps(rep_ss HOL_ss)));
end;
local structure R = Prim.Rules
in
fun function theory eqs =
let val _ = prs "Making definition.. "
val {rules,R,theory,full_pats_TCs,...} = Prim.lazyR_def theory eqs
val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules))
val _ = prs "Definition made.\n"
val _ = prs "Proving induction theorem.. "
val induction = Prim.mk_induction theory f R full_pats_TCs
val _ = prs "Induction theorem proved.\n"
in {theory = theory,
eq_ind = standard (induction RS (rules RS conjI))}
end
handle (e as Utils.ERR _) => Utils.Raise e
| e => print_exn e
end;
fun lazyR_def theory eqs =
let val {rules,theory, ...} = Prim.lazyR_def theory eqs
in {eqns=rules, theory=theory}
end
handle (e as Utils.ERR _) => Utils.Raise e
| e => print_exn e;
val () = Prim.Context.write[Thms.LET_CONG, Thms.COND_CONG];
end;