--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/TFL/post.sml Fri Oct 18 12:41:04 1996 +0200
@@ -0,0 +1,193 @@
+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 _ = output(std_out, "Making definition.. ")
+ val _ = flush_out std_out
+ 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 _ = output(std_out, "Definition made.\n")
+ val _ = output(std_out, "Proving induction theorem.. ")
+ val _ = flush_out std_out
+ val ind = Prim.mk_induction theory f R full_pats_TCs
+ val _ = output(std_out, "Proved induction theorem.\n")
+ val pp = std_postprocessor theory
+ val _ = output(std_out, "Postprocessing.. ")
+ val _ = flush_out std_out
+ val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs}
+ val normal_tcs = Prim.termination_goals rules
+ in
+ case nested_tcs
+ of [] => (output(std_out, "Postprocessing done.\n");
+ {theory=theory, induction=induction, rules=rules,tcs=normal_tcs})
+ | L => let val _ = output(std_out, "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 _ = output(std_out, "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 _ = output(std_out, "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 _ = output(std_out, "Definition made.\n")
+ val _ = output(std_out, "Proving induction theorem.. ")
+ val induction = Prim.mk_induction theory f R full_pats_TCs
+ val _ = output(std_out, "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;