src/HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML	Fri Aug 30 11:27:23 2013 +0200
@@ -0,0 +1,66 @@
+(*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML
+    Author:     Jasmin Blanchette, TU Muenchen
+    Copyright   2013
+
+Tactics for recursor and corecursor sugar.
+*)
+
+signature BNF_FP_REC_SUGAR_TACTICS =
+sig
+  val mk_primcorec_taut_tac: Proof.context -> tactic
+  val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
+    tactic
+  val mk_primcorec_dtr_to_ctr_tac: Proof.context -> int -> thm -> thm -> thm list -> tactic
+  val mk_primcorec_eq_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
+    thm list -> thm list -> thm list -> tactic
+  val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic
+end;
+
+structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =
+struct
+
+open BNF_Util
+open BNF_Tactics
+
+fun mk_primrec_tac ctxt num_extra_args map_id's map_comps fun_defs recx =
+  unfold_thms_tac ctxt fun_defs THEN
+  HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
+  unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_id's) THEN
+  HEADGOAL (rtac refl);
+
+fun mk_primcorec_taut_tac ctxt =
+  HEADGOAL (etac FalseE) ORELSE
+  unfold_thms_tac ctxt @{thms de_Morgan_conj de_Morgan_disj not_not not_False_eq_True} THEN
+  HEADGOAL (SOLVE o REPEAT o (atac ORELSE' resolve_tac @{thms disjI1 disjI2 conjI TrueI}));
+
+fun mk_primcorec_same_case_tac m =
+  HEADGOAL (if m = 0 then rtac TrueI
+    else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
+
+fun mk_primcorec_different_case_tac ctxt excl =
+  unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN
+  HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_taut_tac ctxt));
+
+fun mk_primcorec_cases_tac ctxt k m exclsss =
+  let val n = length exclsss in
+    EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
+        | [excl] => mk_primcorec_different_case_tac ctxt excl)
+      (take k (nth exclsss (k - 1))))
+  end;
+
+fun mk_primcorec_prelude ctxt defs thm =
+  unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};
+
+fun mk_primcorec_disc_tac ctxt defs disc k m exclsss =
+  mk_primcorec_prelude ctxt defs disc THEN mk_primcorec_cases_tac ctxt k m exclsss;
+
+fun mk_primcorec_eq_tac ctxt defs sel k m exclsss maps map_id's map_comps =
+  mk_primcorec_prelude ctxt defs (sel RS trans) THEN mk_primcorec_cases_tac ctxt k m exclsss THEN
+  unfold_thms_tac ctxt (@{thms if_if_True if_if_False if_True if_False o_def split_def sum.cases} @
+    maps @ map_comps @ map_id's) THEN HEADGOAL (rtac refl);
+
+fun mk_primcorec_dtr_to_ctr_tac ctxt m collapse disc sels =
+  HEADGOAL (rtac (collapse RS sym RS trans) THEN' rtac disc THEN' REPEAT_DETERM_N m o atac) THEN
+  unfold_thms_tac ctxt sels THEN HEADGOAL (rtac refl);
+
+end;