--- a/src/HOL/Tools/list_to_set_comprehension.ML Wed Mar 30 20:19:21 2011 +0200
+++ b/src/HOL/Tools/list_to_set_comprehension.ML Wed Mar 30 20:21:40 2011 +0200
@@ -8,7 +8,7 @@
signature LIST_TO_SET_COMPREHENSION =
sig
val simproc : simpset -> cterm -> thm option
-end;
+end
structure List_to_Set_Comprehension : LIST_TO_SET_COMPREHENSION =
struct
@@ -16,66 +16,69 @@
(* conversion *)
fun all_exists_conv cv ctxt ct =
- case Thm.term_of ct of
- Const(@{const_name HOL.Ex}, _) $ Abs(_, _, _) =>
+ (case Thm.term_of ct of
+ Const (@{const_name HOL.Ex}, _) $ Abs _ =>
Conv.arg_conv (Conv.abs_conv (all_exists_conv cv o #2) ctxt) ct
- | _ => cv ctxt ct
+ | _ => cv ctxt ct)
fun all_but_last_exists_conv cv ctxt ct =
- case Thm.term_of ct of
+ (case Thm.term_of ct of
Const (@{const_name HOL.Ex}, _) $ Abs (_, _, Const (@{const_name HOL.Ex}, _) $ _) =>
Conv.arg_conv (Conv.abs_conv (all_but_last_exists_conv cv o #2) ctxt) ct
- | _ => cv ctxt ct
+ | _ => cv ctxt ct)
fun Collect_conv cv ctxt ct =
(case Thm.term_of ct of
Const (@{const_name Set.Collect}, _) $ Abs _ => Conv.arg_conv (Conv.abs_conv cv ctxt) ct
- | _ => raise CTERM ("Collect_conv", [ct]));
+ | _ => raise CTERM ("Collect_conv", [ct]))
fun Trueprop_conv cv ct =
(case Thm.term_of ct of
Const (@{const_name Trueprop}, _) $ _ => Conv.arg_conv cv ct
- | _ => raise CTERM ("Trueprop_conv", [ct]));
+ | _ => raise CTERM ("Trueprop_conv", [ct]))
fun eq_conv cv1 cv2 ct =
(case Thm.term_of ct of
Const (@{const_name HOL.eq}, _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv1) cv2 ct
- | _ => raise CTERM ("eq_conv", [ct]));
+ | _ => raise CTERM ("eq_conv", [ct]))
fun conj_conv cv1 cv2 ct =
(case Thm.term_of ct of
Const (@{const_name HOL.conj}, _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv1) cv2 ct
- | _ => raise CTERM ("conj_conv", [ct]));
+ | _ => raise CTERM ("conj_conv", [ct]))
fun rewr_conv' th = Conv.rewr_conv (mk_meta_eq th)
-
-fun conjunct_assoc_conv ct = Conv.try_conv
+
+fun conjunct_assoc_conv ct =
+ Conv.try_conv
((rewr_conv' @{thm conj_assoc}) then_conv conj_conv Conv.all_conv conjunct_assoc_conv) ct
-
-fun right_hand_set_comprehension_conv conv ctxt = Trueprop_conv (eq_conv Conv.all_conv
- (Collect_conv (all_exists_conv conv o #2) ctxt))
+
+fun right_hand_set_comprehension_conv conv ctxt =
+ Trueprop_conv (eq_conv Conv.all_conv
+ (Collect_conv (all_exists_conv conv o #2) ctxt))
+
(* term abstraction of list comprehension patterns *)
-
+
datatype termlets = If | Case of (typ * int)
fun simproc ss redex =
let
val ctxt = Simplifier.the_context ss
- val thy = ProofContext.theory_of ctxt
+ val thy = ProofContext.theory_of ctxt
val set_Nil_I = @{thm trans} OF [@{thm set.simps(1)}, @{thm empty_def}]
val set_singleton = @{lemma "set [a] = {x. x = a}" by simp}
val inst_Collect_mem_eq = @{lemma "set A = {x. x : set A}" by simp}
- val del_refl_eq = @{lemma "(t = t & P) == P" by simp}
+ val del_refl_eq = @{lemma "(t = t & P) == P" by simp}
fun mk_set T = Const (@{const_name List.set}, HOLogic.listT T --> HOLogic.mk_setT T)
fun dest_set (Const (@{const_name List.set}, _) $ xs) = xs
fun dest_singleton_list (Const (@{const_name List.Cons}, _)
- $ t $ (Const (@{const_name List.Nil}, _))) = t
+ $ t $ (Const (@{const_name List.Nil}, _))) = t
| dest_singleton_list t = raise TERM ("dest_singleton_list", [t])
(* We check that one case returns a singleton list and all other cases
- return [], and return the index of the one singleton list case *)
+ return [], and return the index of the one singleton list case *)
fun possible_index_of_singleton_case cases =
- let
+ let
fun check (i, case_t) s =
(case strip_abs_body case_t of
(Const (@{const_name List.Nil}, _)) => s
@@ -88,112 +91,127 @@
let
val (case_const, args) = strip_comb case_term
in
- case try dest_Const case_const of
- SOME (c, T) => (case Datatype_Data.info_of_case thy c of
- SOME _ => (case possible_index_of_singleton_case (fst (split_last args)) of
- SOME i =>
- let
- val (Ts, _) = strip_type T
- val T' = List.last Ts
- in SOME (List.last args, T', i, nth args i) end
+ (case try dest_Const case_const of
+ SOME (c, T) =>
+ (case Datatype_Data.info_of_case thy c of
+ SOME _ =>
+ (case possible_index_of_singleton_case (fst (split_last args)) of
+ SOME i =>
+ let
+ val (Ts, _) = strip_type T
+ val T' = List.last Ts
+ in SOME (List.last args, T', i, nth args i) end
+ | NONE => NONE)
| NONE => NONE)
- | NONE => NONE)
- | NONE => NONE
+ | NONE => NONE)
end
(* returns condition continuing term option *)
fun dest_if (Const (@{const_name If}, _) $ cond $ then_t $ Const (@{const_name Nil}, _)) =
SOME (cond, then_t)
| dest_if _ = NONE
- fun tac _ [] =
- rtac set_singleton 1 ORELSE rtac inst_Collect_mem_eq 1
- | tac ctxt (If :: cont) =
- Splitter.split_tac [@{thm split_if}] 1
- THEN rtac @{thm conjI} 1
- THEN rtac @{thm impI} 1
- THEN Subgoal.FOCUS (fn {prems, context, ...} =>
- CONVERSION (right_hand_set_comprehension_conv (K
- (conj_conv (Conv.rewr_conv (List.last prems RS @{thm Eq_TrueI})) Conv.all_conv
- then_conv rewr_conv' @{thm simp_thms(22)})) context) 1) ctxt 1
- THEN tac ctxt cont
- THEN rtac @{thm impI} 1
- THEN Subgoal.FOCUS (fn {prems, context, ...} =>
- CONVERSION (right_hand_set_comprehension_conv (K
- (conj_conv (Conv.rewr_conv (List.last prems RS @{thm Eq_FalseI})) Conv.all_conv
- then_conv rewr_conv' @{thm simp_thms(24)})) context) 1) ctxt 1
- THEN rtac set_Nil_I 1
- | tac ctxt (Case (T, i) :: cont) =
- let
- val info = Datatype.the_info thy (fst (dest_Type T))
- in
- (* do case distinction *)
- Splitter.split_tac [#split info] 1
- THEN EVERY (map_index (fn (i', case_rewrite) =>
- (if i' < length (#case_rewrites info) - 1 then rtac @{thm conjI} 1 else all_tac)
- THEN REPEAT_DETERM (rtac @{thm allI} 1)
+ fun tac _ [] = rtac set_singleton 1 ORELSE rtac inst_Collect_mem_eq 1
+ | tac ctxt (If :: cont) =
+ Splitter.split_tac [@{thm split_if}] 1
+ THEN rtac @{thm conjI} 1
+ THEN rtac @{thm impI} 1
+ THEN Subgoal.FOCUS (fn {prems, context, ...} =>
+ CONVERSION (right_hand_set_comprehension_conv (K
+ (conj_conv (Conv.rewr_conv (List.last prems RS @{thm Eq_TrueI})) Conv.all_conv
+ then_conv rewr_conv' @{thm simp_thms(22)})) context) 1) ctxt 1
+ THEN tac ctxt cont
THEN rtac @{thm impI} 1
- THEN (if i' = i then
- (* continue recursively *)
- Subgoal.FOCUS (fn {prems, context, ...} =>
- CONVERSION (Thm.eta_conversion then_conv right_hand_set_comprehension_conv (K
- ((conj_conv
- (eq_conv Conv.all_conv (rewr_conv' (List.last prems))
- then_conv (Conv.try_conv (Conv.rewrs_conv (map mk_meta_eq (#inject info))))) Conv.all_conv)
- then_conv (Conv.try_conv (Conv.rewr_conv del_refl_eq))
- then_conv conjunct_assoc_conv)) context
- then_conv (Trueprop_conv (eq_conv Conv.all_conv (Collect_conv (fn (_, ctxt) =>
- Conv.repeat_conv (all_but_last_exists_conv (K (rewr_conv' @{thm simp_thms(39)})) ctxt)) context)))) 1) ctxt 1
- THEN tac ctxt cont
- else
- Subgoal.FOCUS (fn {prems, context, ...} =>
- CONVERSION ((right_hand_set_comprehension_conv (K
- (conj_conv
- ((eq_conv Conv.all_conv
- (rewr_conv' (List.last prems)))
- then_conv (Conv.rewrs_conv (map (fn th => th RS @{thm Eq_FalseI}) (#distinct info)))) Conv.all_conv
- then_conv (rewr_conv' @{thm simp_thms(24)}))) context)
- then_conv (Trueprop_conv (eq_conv Conv.all_conv (Collect_conv (fn (_, ctxt) =>
- Conv.repeat_conv (Conv.bottom_conv (K (rewr_conv' @{thm simp_thms(36)})) ctxt)) context)))) 1) ctxt 1
- THEN rtac set_Nil_I 1)) (#case_rewrites info))
- end
+ THEN Subgoal.FOCUS (fn {prems, context, ...} =>
+ CONVERSION (right_hand_set_comprehension_conv (K
+ (conj_conv (Conv.rewr_conv (List.last prems RS @{thm Eq_FalseI})) Conv.all_conv
+ then_conv rewr_conv' @{thm simp_thms(24)})) context) 1) ctxt 1
+ THEN rtac set_Nil_I 1
+ | tac ctxt (Case (T, i) :: cont) =
+ let
+ val info = Datatype.the_info thy (fst (dest_Type T))
+ in
+ (* do case distinction *)
+ Splitter.split_tac [#split info] 1
+ THEN EVERY (map_index (fn (i', case_rewrite) =>
+ (if i' < length (#case_rewrites info) - 1 then rtac @{thm conjI} 1 else all_tac)
+ THEN REPEAT_DETERM (rtac @{thm allI} 1)
+ THEN rtac @{thm impI} 1
+ THEN (if i' = i then
+ (* continue recursively *)
+ Subgoal.FOCUS (fn {prems, context, ...} =>
+ CONVERSION (Thm.eta_conversion then_conv right_hand_set_comprehension_conv (K
+ ((conj_conv
+ (eq_conv Conv.all_conv (rewr_conv' (List.last prems)) then_conv
+ (Conv.try_conv (Conv.rewrs_conv (map mk_meta_eq (#inject info)))))
+ Conv.all_conv)
+ then_conv (Conv.try_conv (Conv.rewr_conv del_refl_eq))
+ then_conv conjunct_assoc_conv)) context
+ then_conv (Trueprop_conv (eq_conv Conv.all_conv (Collect_conv (fn (_, ctxt) =>
+ Conv.repeat_conv
+ (all_but_last_exists_conv
+ (K (rewr_conv' @{thm simp_thms(39)})) ctxt)) context)))) 1) ctxt 1
+ THEN tac ctxt cont
+ else
+ Subgoal.FOCUS (fn {prems, context, ...} =>
+ CONVERSION ((right_hand_set_comprehension_conv (K
+ (conj_conv
+ ((eq_conv Conv.all_conv
+ (rewr_conv' (List.last prems))) then_conv
+ (Conv.rewrs_conv (map (fn th => th RS @{thm Eq_FalseI}) (#distinct info))))
+ Conv.all_conv then_conv
+ (rewr_conv' @{thm simp_thms(24)}))) context) then_conv
+ (Trueprop_conv
+ (eq_conv Conv.all_conv (Collect_conv (fn (_, ctxt) =>
+ Conv.repeat_conv
+ (Conv.bottom_conv
+ (K (rewr_conv' @{thm simp_thms(36)})) ctxt)) context)))) 1) ctxt 1
+ THEN rtac set_Nil_I 1)) (#case_rewrites info))
+ end
fun make_inner_eqs bound_vs Tis eqs t =
- case dest_case t of
+ (case dest_case t of
SOME (x, T, i, cont) =>
let
val (vs, body) = strip_abs (Pattern.eta_long (map snd bound_vs) cont)
val x' = incr_boundvars (length vs) x
val eqs' = map (incr_boundvars (length vs)) eqs
val (constr_name, _) = nth (the (Datatype_Data.get_constrs thy (fst (dest_Type T)))) i
- val constr_t = list_comb (Const (constr_name, map snd vs ---> T), map Bound (((length vs) - 1) downto 0))
+ val constr_t =
+ list_comb
+ (Const (constr_name, map snd vs ---> T), map Bound (((length vs) - 1) downto 0))
val constr_eq = Const (@{const_name HOL.eq}, T --> T --> @{typ bool}) $ constr_t $ x'
in
make_inner_eqs (rev vs @ bound_vs) (Case (T, i) :: Tis) (constr_eq :: eqs') body
end
| NONE =>
- case dest_if t of
- SOME (condition, cont) => make_inner_eqs bound_vs (If :: Tis) (condition :: eqs) cont
- | NONE =>
- if eqs = [] then NONE (* no rewriting, nothing to be done *)
- else
- let
- val Type (@{type_name List.list}, [rT]) = fastype_of1 (map snd bound_vs, t)
- val pat_eq =
- case try dest_singleton_list t of
- SOME t' => Const (@{const_name HOL.eq}, rT --> rT --> @{typ bool})
- $ Bound (length bound_vs) $ t'
- | NONE => Const (@{const_name Set.member}, rT --> HOLogic.mk_setT rT --> @{typ bool})
- $ Bound (length bound_vs) $ (mk_set rT $ t)
- val reverse_bounds = curry subst_bounds
- ((map Bound ((length bound_vs - 1) downto 0)) @ [Bound (length bound_vs)])
- val eqs' = map reverse_bounds eqs
- val pat_eq' = reverse_bounds pat_eq
- val inner_t = fold (fn (v, T) => fn t => HOLogic.exists_const T $ absdummy (T, t))
- (rev bound_vs) (fold (curry HOLogic.mk_conj) eqs' pat_eq')
- val lhs = term_of redex
- val rhs = HOLogic.mk_Collect ("x", rT, inner_t)
- val rewrite_rule_t = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs))
- in
- SOME ((Goal.prove ctxt [] [] rewrite_rule_t (fn {context, ...} => tac context (rev Tis))) RS @{thm eq_reflection})
- end
+ (case dest_if t of
+ SOME (condition, cont) => make_inner_eqs bound_vs (If :: Tis) (condition :: eqs) cont
+ | NONE =>
+ if eqs = [] then NONE (* no rewriting, nothing to be done *)
+ else
+ let
+ val Type (@{type_name List.list}, [rT]) = fastype_of1 (map snd bound_vs, t)
+ val pat_eq =
+ (case try dest_singleton_list t of
+ SOME t' =>
+ Const (@{const_name HOL.eq}, rT --> rT --> @{typ bool}) $
+ Bound (length bound_vs) $ t'
+ | NONE =>
+ Const (@{const_name Set.member}, rT --> HOLogic.mk_setT rT --> @{typ bool}) $
+ Bound (length bound_vs) $ (mk_set rT $ t))
+ val reverse_bounds = curry subst_bounds
+ ((map Bound ((length bound_vs - 1) downto 0)) @ [Bound (length bound_vs)])
+ val eqs' = map reverse_bounds eqs
+ val pat_eq' = reverse_bounds pat_eq
+ val inner_t =
+ fold (fn (v, T) => fn t => HOLogic.exists_const T $ absdummy (T, t))
+ (rev bound_vs) (fold (curry HOLogic.mk_conj) eqs' pat_eq')
+ val lhs = term_of redex
+ val rhs = HOLogic.mk_Collect ("x", rT, inner_t)
+ val rewrite_rule_t = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs))
+ in
+ SOME
+ ((Goal.prove ctxt [] [] rewrite_rule_t
+ (fn {context, ...} => tac context (rev Tis))) RS @{thm eq_reflection})
+ end))
in
make_inner_eqs [] [] [] (dest_set (term_of redex))
end