TFL/post.sml

+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;