+(* FG: subst tactic *********************************************************)
+
+(* FG: This should be replaced by T.try_tactic *)
+let try_tactic ~tactic =
+ let try_tactic status =
+ try PET.apply_tactic tactic status with
+ | PET.Fail _ -> PET.apply_tactic T.id_tac status
+ in
+ PET.mk_tactic try_tactic
+
+let rec lift_rewrite_tac ~context ~direction ~pattern equality =
+ let lift_rewrite_tac status =
+ let (proof, goal) = status in
+ let (_, metasenv, _, _) = proof in
+ let _, new_context, _ = CicUtil.lookup_meta goal metasenv in
+ let n = List.length new_context - List.length context in
+ let equality = if n > 0 then S.lift n equality else equality in
+ PET.apply_tactic (rewrite_tac ~direction ~pattern equality) status
+ in
+ PET.mk_tactic lift_rewrite_tac
+
+
+let msg0 = lazy "Subst: not found in context"
+let msg1 = lazy "Subst: not a simple equality"
+let msg2 = lazy "Subst: recursive equation"
+
+let subst_tac ~hyp =
+ let hole = C.Implicit (Some `Hole) in
+ let subst_tac status =
+ let (proof, goal) = status in
+ let (_, metasenv, _, _) = proof in
+ let _, context, _ = CicUtil.lookup_meta goal metasenv in
+ let what = match PEH.get_rel context hyp with
+ | Some t -> t
+ | None -> raise (PET.Fail msg0)
+ in
+ let ty, _ = TC.type_of_aux' metasenv context what CicUniv.empty_ugraph in
+ let direction, i, t = match ty with
+ | (C.Appl [(C.MutInd (uri, 0, [])); _; C.Rel i; t])
+ when LO.is_eq_URI uri -> `LeftToRight, i, t
+ | (C.Appl [(C.MutInd (uri, 0, [])); _; t; C.Rel i])
+ when LO.is_eq_URI uri -> `RightToLeft, i, t
+ | _ -> raise (PET.Fail msg1)
+ in
+ let rewrite pattern =
+ let tactic = lift_rewrite_tac ~context ~direction ~pattern what in
+ try_tactic ~tactic
+ in
+ let var = match PEH.get_name context i with
+ | Some name -> name
+ | None -> raise (PET.Fail msg0)
+ in
+ if DTI.does_not_occur i t then () else raise (PET.Fail msg2);
+ let map self = function
+ | Some (C.Name s, _) when s <> self ->
+ Some (rewrite (None, [(s, hole)], None))
+ | _ -> None
+ in
+ let rew_hips = HEL.list_rev_map_filter (map hyp) context in
+ let rew_concl = rewrite (None, [], Some hole) in
+ let clear = PESR.clear ~hyps:[hyp; var] in
+ let tactics = List.rev_append (rew_concl :: rew_hips) [clear] in
+ PET.apply_tactic (T.seq ~tactics) status
+ in
+ PET.mk_tactic subst_tac