--- a/src/HOL/Tools/list_to_set_comprehension.ML Fri Dec 07 16:38:25 2012 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,224 +0,0 @@
-(* Title: HOL/Tools/list_to_set_comprehension.ML
- Author: Lukas Bulwahn, TU Muenchen
-
-Simproc for rewriting list comprehensions applied to List.set to set
-comprehension.
-*)
-
-signature LIST_TO_SET_COMPREHENSION =
-sig
- val simproc : simpset -> cterm -> thm option
-end
-
-structure List_to_Set_Comprehension : LIST_TO_SET_COMPREHENSION =
-struct
-
-(* conversion *)
-
-fun all_exists_conv cv ctxt ct =
- (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)
-
-fun all_but_last_exists_conv cv ctxt ct =
- (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)
-
-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]))
-
-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]))
-
-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]))
-
-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]))
-
-fun rewr_conv' th = Conv.rewr_conv (mk_meta_eq th)
-
-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))
-
-
-(* 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 = Proof_Context.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}
- 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
- | 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 *)
- fun possible_index_of_singleton_case cases =
- let
- fun check (i, case_t) s =
- (case strip_abs_body case_t of
- (Const (@{const_name List.Nil}, _)) => s
- | _ => (case s of NONE => SOME i | SOME _ => NONE))
- in
- fold_index check cases NONE
- end
- (* returns (case_expr type index chosen_case) option *)
- fun dest_case case_term =
- let
- val (case_const, args) = strip_comb case_term
- in
- (case try dest_Const case_const of
- SOME (c, T) =>
- (case Datatype.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)
- 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' @{lemma "(True & P) = P" by simp})) 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' @{lemma "(False & P) = False" by simp})) 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', _) =>
- (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'
- @{lemma "(EX x. x = t & P x) = P t" by simp})) 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' @{lemma "(False & P) = False" by simp}))) context then_conv
- Trueprop_conv
- (eq_conv Conv.all_conv
- (Collect_conv (fn (_, ctxt) =>
- Conv.repeat_conv
- (Conv.bottom_conv
- (K (rewr_conv'
- @{lemma "(EX x. P) = P" by simp})) 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
- 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.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_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 (_, 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
-
-end