--- a/src/HOL/Tools/Datatype/datatype.ML Wed Nov 30 19:18:17 2011 +0100
+++ b/src/HOL/Tools/Datatype/datatype.ML Wed Nov 30 21:14:01 2011 +0100
@@ -65,7 +65,8 @@
val thy1 = Sign.add_path big_name thy;
val big_rec_name = big_name ^ "_rep_set";
val rep_set_names' =
- (if length descr' = 1 then [big_rec_name] else
+ (if length descr' = 1 then [big_rec_name]
+ else
(map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int)
(1 upto (length descr'))));
val rep_set_names = map (Sign.full_bname thy1) rep_set_names';
@@ -73,15 +74,19 @@
val tyvars = map (fn (_, (_, Ts, _)) => map Datatype_Aux.dest_DtTFree Ts) (hd descr);
val leafTs' = Datatype_Aux.get_nonrec_types descr' sorts;
val branchTs = Datatype_Aux.get_branching_types descr' sorts;
- val branchT = if null branchTs then HOLogic.unitT
+ val branchT =
+ if null branchTs then HOLogic.unitT
else Balanced_Tree.make (fn (T, U) => Type (@{type_name Sum_Type.sum}, [T, U])) branchTs;
val arities = remove (op =) 0 (Datatype_Aux.get_arities descr');
val unneeded_vars =
- subtract (op =) (List.foldr Misc_Legacy.add_typ_tfree_names [] (leafTs' @ branchTs)) (hd tyvars);
- val leafTs = leafTs' @ map (fn n => TFree (n, (the o AList.lookup (op =) sorts) n)) unneeded_vars;
+ subtract (op =)
+ (List.foldr Misc_Legacy.add_typ_tfree_names [] (leafTs' @ branchTs)) (hd tyvars);
+ val leafTs =
+ leafTs' @ map (fn n => TFree (n, (the o AList.lookup (op =) sorts) n)) unneeded_vars;
val recTs = Datatype_Aux.get_rec_types descr' sorts;
val (newTs, oldTs) = chop (length (hd descr)) recTs;
- val sumT = if null leafTs then HOLogic.unitT
+ val sumT =
+ if null leafTs then HOLogic.unitT
else Balanced_Tree.make (fn (T, U) => Type (@{type_name Sum_Type.sum}, [T, U])) leafTs;
val Univ_elT = HOLogic.mk_setT (Type (node_name, [sumT, branchT]));
val UnivT = HOLogic.mk_setT Univ_elT;
@@ -98,17 +103,17 @@
fun mk_inj T' x =
let
fun mk_inj' T n i =
- if n = 1 then x else
- let val n2 = n div 2;
- val Type (_, [T1, T2]) = T
- in
- if i <= n2 then
- Const (@{const_name Inl}, T1 --> T) $ (mk_inj' T1 n2 i)
- else
- Const (@{const_name Inr}, T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
- end
- in mk_inj' sumT (length leafTs) (1 + find_index (fn T'' => T'' = T') leafTs)
- end;
+ if n = 1 then x
+ else
+ let
+ val n2 = n div 2;
+ val Type (_, [T1, T2]) = T;
+ in
+ if i <= n2
+ then Const (@{const_name Inl}, T1 --> T) $ (mk_inj' T1 n2 i)
+ else Const (@{const_name Inr}, T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
+ end;
+ in mk_inj' sumT (length leafTs) (1 + find_index (fn T'' => T'' = T') leafTs) end;
(* make injections for constructors *)
@@ -124,17 +129,17 @@
fun mk_fun_inj T' x =
let
fun mk_inj T n i =
- if n = 1 then x else
- let
- val n2 = n div 2;
- val Type (_, [T1, T2]) = T;
- fun mkT U = (U --> Univ_elT) --> T --> Univ_elT
- in
- if i <= n2 then Const (Suml_name, mkT T1) $ mk_inj T1 n2 i
- else Const (Sumr_name, mkT T2) $ mk_inj T2 (n - n2) (i - n2)
- end
- in mk_inj branchT (length branchTs) (1 + find_index (fn T'' => T'' = T') branchTs)
- end;
+ if n = 1 then x
+ else
+ let
+ val n2 = n div 2;
+ val Type (_, [T1, T2]) = T;
+ fun mkT U = (U --> Univ_elT) --> T --> Univ_elT;
+ in
+ if i <= n2 then Const (Suml_name, mkT T1) $ mk_inj T1 n2 i
+ else Const (Sumr_name, mkT T2) $ mk_inj T2 (n - n2) (i - n2)
+ end;
+ in mk_inj branchT (length branchTs) (1 + find_index (fn T'' => T'' = T') branchTs) end;
fun mk_lim t Ts = fold_rev (fn T => fn t => Lim $ mk_fun_inj T (Abs ("x", T, t))) Ts t;
@@ -153,21 +158,19 @@
val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) dts;
val free_t =
Datatype_Aux.app_bnds (Datatype_Aux.mk_Free "x" (Ts ---> Univ_elT) j) (length Ts)
- in (j + 1, list_all (map (pair "x") Ts,
+ in
+ (j + 1, list_all (map (pair "x") Ts,
HOLogic.mk_Trueprop
(Free (nth rep_set_names' k, UnivT') $ free_t)) :: prems,
mk_lim free_t Ts :: ts)
end
| _ =>
let val T = Datatype_Aux.typ_of_dtyp descr' sorts dt
- in (j + 1, prems, (Leaf $ mk_inj T (Datatype_Aux.mk_Free "x" T j))::ts)
- end);
+ in (j + 1, prems, (Leaf $ mk_inj T (Datatype_Aux.mk_Free "x" T j)) :: ts) end);
val (_, prems, ts) = fold_rev mk_prem cargs (1, [], []);
- val concl = HOLogic.mk_Trueprop
- (Free (s, UnivT') $ mk_univ_inj ts n i)
- in Logic.list_implies (prems, concl)
- end;
+ val concl = HOLogic.mk_Trueprop (Free (s, UnivT') $ mk_univ_inj ts n i);
+ in Logic.list_implies (prems, concl) end;
val intr_ts = maps (fn ((_, (_, _, constrs)), rep_set_name) =>
map (make_intr rep_set_name (length constrs))
@@ -221,10 +224,12 @@
let
val T = Datatype_Aux.typ_of_dtyp descr' sorts dt;
val free_t = Datatype_Aux.mk_Free "x" T j;
- in (case (Datatype_Aux.strip_dtyp dt, strip_type T) of
- ((_, Datatype_Aux.DtRec m), (Us, U)) => (j + 1, free_t :: l_args, mk_lim
- (Const (nth all_rep_names m, U --> Univ_elT) $
- Datatype_Aux.app_bnds free_t (length Us)) Us :: r_args)
+ in
+ (case (Datatype_Aux.strip_dtyp dt, strip_type T) of
+ ((_, Datatype_Aux.DtRec m), (Us, U)) =>
+ (j + 1, free_t :: l_args, mk_lim
+ (Const (nth all_rep_names m, U --> Univ_elT) $
+ Datatype_Aux.app_bnds free_t (length Us)) Us :: r_args)
| _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args))
end;
@@ -251,16 +256,17 @@
(thy, defs, eqns, rep_congs, dist_lemmas) =
let
val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong;
- val rep_const = cterm_of thy
- (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> Univ_elT));
+ val rep_const =
+ cterm_of thy (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> Univ_elT));
val cong' =
Drule.export_without_context
(cterm_instantiate [(cterm_of thy cong_f, rep_const)] arg_cong);
val dist =
Drule.export_without_context
(cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
- val (thy', defs', eqns', _) = fold ((make_constr_def tname T) (length constrs))
- (constrs ~~ constr_syntax) (Sign.add_path tname thy, defs, [], 1);
+ val (thy', defs', eqns', _) =
+ fold ((make_constr_def tname T) (length constrs))
+ (constrs ~~ constr_syntax) (Sign.add_path tname thy, defs, [], 1);
in
(Sign.parent_path thy', defs', eqns @ [eqns'],
rep_congs @ [cong'], dist_lemmas @ [dist])
@@ -308,8 +314,10 @@
let
val T' = Datatype_Aux.typ_of_dtyp descr' sorts dt;
val (Us, U) = strip_type T'
- in (case Datatype_Aux.strip_dtyp dt of
- (_, Datatype_Aux.DtRec j) => if member (op =) ks' j then
+ in
+ (case Datatype_Aux.strip_dtyp dt of
+ (_, Datatype_Aux.DtRec j) =>
+ if member (op =) ks' j then
(i2 + 1, i2' + 1, ts @ [mk_lim (Datatype_Aux.app_bnds
(Datatype_Aux.mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us],
Ts @ [Us ---> Univ_elT])
@@ -341,29 +349,31 @@
fun process_dt (k, (tname, _, constrs)) (fs, eqns, isos) =
let
- val (fs', eqns', _) =
- fold (make_iso_def k ks (length constrs)) constrs (fs, eqns, 1);
- val iso = (nth recTs k, nth all_rep_names k)
+ val (fs', eqns', _) = fold (make_iso_def k ks (length constrs)) constrs (fs, eqns, 1);
+ val iso = (nth recTs k, nth all_rep_names k);
in (fs', eqns', isos @ [iso]) end;
-
+
val (fs, eqns, isos) = fold process_dt ds ([], [], []);
val fTs = map fastype_of fs;
- val defs = map (fn (rec_name, (T, iso_name)) => (Binding.name (Long_Name.base_name iso_name ^ "_def"),
- Logic.mk_equals (Const (iso_name, T --> Univ_elT),
- list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos);
+ val defs =
+ map (fn (rec_name, (T, iso_name)) =>
+ (Binding.name (Long_Name.base_name iso_name ^ "_def"),
+ Logic.mk_equals (Const (iso_name, T --> Univ_elT),
+ list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos);
val (def_thms, thy') =
apsnd Theory.checkpoint ((Global_Theory.add_defs false o map Thm.no_attributes) defs thy);
(* prove characteristic equations *)
val rewrites = def_thms @ (map mk_meta_eq rec_rewrites);
- val char_thms' = map (fn eqn => Skip_Proof.prove_global thy' [] [] eqn
- (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
+ val char_thms' =
+ map (fn eqn => Skip_Proof.prove_global thy' [] [] eqn
+ (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
in (thy', char_thms' @ char_thms) end;
- val (thy5, iso_char_thms) = apfst Theory.checkpoint (fold_rev make_iso_defs
- (tl descr) (Sign.add_path big_name thy4, []));
+ val (thy5, iso_char_thms) =
+ apfst Theory.checkpoint (fold_rev make_iso_defs (tl descr) (Sign.add_path big_name thy4, []));
(* prove isomorphism properties *)
@@ -376,35 +386,37 @@
fun mk_thm i =
let
- val Ts = map (TFree o rpair HOLogic.typeS)
- (Name.variant_list used (replicate i "'t"));
- val f = Free ("f", Ts ---> U)
- in Skip_Proof.prove_global thy [] [] (Logic.mk_implies
- (HOLogic.mk_Trueprop (HOLogic.list_all
- (map (pair "x") Ts, S $ Datatype_Aux.app_bnds f i)),
- HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
- r $ (a $ Datatype_Aux.app_bnds f i)), f))))
- (fn _ => EVERY [REPEAT_DETERM_N i (rtac ext 1),
- REPEAT (etac allE 1), rtac thm 1, atac 1])
+ val Ts = map (TFree o rpair HOLogic.typeS) (Name.variant_list used (replicate i "'t"));
+ val f = Free ("f", Ts ---> U);
+ in
+ Skip_Proof.prove_global thy [] []
+ (Logic.mk_implies
+ (HOLogic.mk_Trueprop (HOLogic.list_all
+ (map (pair "x") Ts, S $ Datatype_Aux.app_bnds f i)),
+ HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
+ r $ (a $ Datatype_Aux.app_bnds f i)), f))))
+ (fn _ => EVERY [REPEAT_DETERM_N i (rtac ext 1),
+ REPEAT (etac allE 1), rtac thm 1, atac 1])
end
in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
(* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *)
- val fun_congs = map (fn T => make_elim (Drule.instantiate'
- [SOME (ctyp_of thy5 T)] [] fun_cong)) branchTs;
+ val fun_congs =
+ map (fn T => make_elim (Drule.instantiate' [SOME (ctyp_of thy5 T)] [] fun_cong)) branchTs;
fun prove_iso_thms ds (inj_thms, elem_thms) =
let
val (_, (tname, _, _)) = hd ds;
- val induct = (#induct o the o Symtab.lookup dt_info) tname;
+ val induct = #induct (the (Symtab.lookup dt_info tname));
fun mk_ind_concl (i, _) =
let
val T = nth recTs i;
val Rep_t = Const (nth all_rep_names i, T --> Univ_elT);
- val rep_set_name = nth rep_set_names i
- in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $
+ val rep_set_name = nth rep_set_names i;
+ in
+ (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $
HOLogic.mk_eq (Rep_t $ Datatype_Aux.mk_Free "x" T i, Rep_t $ Bound 0) $
HOLogic.mk_eq (Datatype_Aux.mk_Free "x" T i, Bound 0)),
Const (rep_set_name, UnivT') $ (Rep_t $ Datatype_Aux.mk_Free "x" T i))
@@ -413,59 +425,60 @@
val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds);
val rewrites = map mk_meta_eq iso_char_thms;
- val inj_thms' = map snd newT_iso_inj_thms @
- map (fn r => r RS @{thm injD}) inj_thms;
+ val inj_thms' = map snd newT_iso_inj_thms @ map (fn r => r RS @{thm injD}) inj_thms;
- val inj_thm = Skip_Proof.prove_global thy5 [] []
- (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj ind_concl1)) (fn _ => EVERY
- [(Datatype_Aux.indtac induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
- REPEAT (EVERY
- [rtac allI 1, rtac impI 1,
- Datatype_Aux.exh_tac (exh_thm_of dt_info) 1,
- REPEAT (EVERY
- [hyp_subst_tac 1,
- rewrite_goals_tac rewrites,
- REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
- (eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1)
- ORELSE (EVERY
- [REPEAT (eresolve_tac (Scons_inject ::
- map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1),
- REPEAT (cong_tac 1), rtac refl 1,
- REPEAT (atac 1 ORELSE (EVERY
- [REPEAT (rtac ext 1),
- REPEAT (eresolve_tac (mp :: allE ::
- map make_elim (Suml_inject :: Sumr_inject ::
- Lim_inject :: inj_thms') @ fun_congs) 1),
- atac 1]))])])])]);
+ val inj_thm =
+ Skip_Proof.prove_global thy5 [] []
+ (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj ind_concl1))
+ (fn _ => EVERY
+ [(Datatype_Aux.indtac induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
+ REPEAT (EVERY
+ [rtac allI 1, rtac impI 1,
+ Datatype_Aux.exh_tac (exh_thm_of dt_info) 1,
+ REPEAT (EVERY
+ [hyp_subst_tac 1,
+ rewrite_goals_tac rewrites,
+ REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
+ (eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1)
+ ORELSE (EVERY
+ [REPEAT (eresolve_tac (Scons_inject ::
+ map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1),
+ REPEAT (cong_tac 1), rtac refl 1,
+ REPEAT (atac 1 ORELSE (EVERY
+ [REPEAT (rtac ext 1),
+ REPEAT (eresolve_tac (mp :: allE ::
+ map make_elim (Suml_inject :: Sumr_inject ::
+ Lim_inject :: inj_thms') @ fun_congs) 1),
+ atac 1]))])])])]);
val inj_thms'' = map (fn r => r RS datatype_injI) (Datatype_Aux.split_conj_thm inj_thm);
- val elem_thm =
- Skip_Proof.prove_global thy5 [] [] (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj ind_concl2))
+ val elem_thm =
+ Skip_Proof.prove_global thy5 [] []
+ (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj ind_concl2))
(fn _ =>
- EVERY [(Datatype_Aux.indtac induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
- rewrite_goals_tac rewrites,
- REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW
- ((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]);
+ EVERY [(Datatype_Aux.indtac induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
+ rewrite_goals_tac rewrites,
+ REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW
+ ((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]);
- in (inj_thms'' @ inj_thms, elem_thms @ (Datatype_Aux.split_conj_thm elem_thm))
- end;
+ in (inj_thms'' @ inj_thms, elem_thms @ (Datatype_Aux.split_conj_thm elem_thm)) end;
val (iso_inj_thms_unfolded, iso_elem_thms) =
fold_rev prove_iso_thms (tl descr) ([], map #3 newT_iso_axms);
- val iso_inj_thms = map snd newT_iso_inj_thms @
- map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded;
+ val iso_inj_thms =
+ map snd newT_iso_inj_thms @ map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded;
(* prove dt_rep_set_i x --> x : range dt_Rep_i *)
fun mk_iso_t (((set_name, iso_name), i), T) =
- let val isoT = T --> Univ_elT
- in HOLogic.imp $
- (Const (set_name, UnivT') $ Datatype_Aux.mk_Free "x" Univ_elT i) $
- (if i < length newTs then HOLogic.true_const
- else HOLogic.mk_mem (Datatype_Aux.mk_Free "x" Univ_elT i,
- Const (@{const_name image}, isoT --> HOLogic.mk_setT T --> UnivT) $
- Const (iso_name, isoT) $ Const (@{const_abbrev UNIV}, HOLogic.mk_setT T)))
+ let val isoT = T --> Univ_elT in
+ HOLogic.imp $
+ (Const (set_name, UnivT') $ Datatype_Aux.mk_Free "x" Univ_elT i) $
+ (if i < length newTs then HOLogic.true_const
+ else HOLogic.mk_mem (Datatype_Aux.mk_Free "x" Univ_elT i,
+ Const (@{const_name image}, isoT --> HOLogic.mk_setT T --> UnivT) $
+ Const (iso_name, isoT) $ Const (@{const_abbrev UNIV}, HOLogic.mk_setT T)))
end;
val iso_t = HOLogic.mk_Trueprop (Datatype_Aux.mk_conj (map mk_iso_t
@@ -473,23 +486,24 @@
(* all the theorems are proved by one single simultaneous induction *)
- val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq}))
- iso_inj_thms_unfolded;
+ val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq})) iso_inj_thms_unfolded;
- val iso_thms = if length descr = 1 then [] else
- drop (length newTs) (Datatype_Aux.split_conj_thm
- (Skip_Proof.prove_global thy5 [] [] iso_t (fn _ => EVERY
- [(Datatype_Aux.indtac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
- REPEAT (rtac TrueI 1),
- rewrite_goals_tac (mk_meta_eq @{thm choice_eq} ::
- Thm.symmetric (mk_meta_eq @{thm fun_eq_iff}) :: range_eqs),
- rewrite_goals_tac (map Thm.symmetric range_eqs),
- REPEAT (EVERY
- [REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @
- maps (mk_funs_inv thy5 o #1) newT_iso_axms) 1),
- TRY (hyp_subst_tac 1),
- rtac (sym RS range_eqI) 1,
- resolve_tac iso_char_thms 1])])));
+ val iso_thms =
+ if length descr = 1 then []
+ else
+ drop (length newTs) (Datatype_Aux.split_conj_thm
+ (Skip_Proof.prove_global thy5 [] [] iso_t (fn _ => EVERY
+ [(Datatype_Aux.indtac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
+ REPEAT (rtac TrueI 1),
+ rewrite_goals_tac (mk_meta_eq @{thm choice_eq} ::
+ Thm.symmetric (mk_meta_eq @{thm fun_eq_iff}) :: range_eqs),
+ rewrite_goals_tac (map Thm.symmetric range_eqs),
+ REPEAT (EVERY
+ [REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @
+ maps (mk_funs_inv thy5 o #1) newT_iso_axms) 1),
+ TRY (hyp_subst_tac 1),
+ rtac (sym RS range_eqI) 1,
+ resolve_tac iso_char_thms 1])])));
val Abs_inverse_thms' =
map #1 newT_iso_axms @
@@ -503,17 +517,19 @@
val _ = Datatype_Aux.message config "Proving freeness of constructors ...";
(* prove theorem Rep_i (Constr_j ...) = Inj_j ... *)
-
+
fun prove_constr_rep_thm eqn =
let
val inj_thms = map fst newT_iso_inj_thms;
- val rewrites = @{thm o_def} :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms)
- in Skip_Proof.prove_global thy5 [] [] eqn (fn _ => EVERY
- [resolve_tac inj_thms 1,
- rewrite_goals_tac rewrites,
- rtac refl 3,
- resolve_tac rep_intrs 2,
- REPEAT (resolve_tac iso_elem_thms 1)])
+ val rewrites = @{thm o_def} :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms);
+ in
+ Skip_Proof.prove_global thy5 [] [] eqn
+ (fn _ => EVERY
+ [resolve_tac inj_thms 1,
+ rewrite_goals_tac rewrites,
+ rtac refl 3,
+ resolve_tac rep_intrs 2,
+ REPEAT (resolve_tac iso_elem_thms 1)])
end;
(*--------------------------------------------------------------*)
@@ -523,9 +539,10 @@
val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns;
- val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
- dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
- (constr_rep_thms ~~ dist_lemmas);
+ val dist_rewrites =
+ map (fn (rep_thms, dist_lemma) =>
+ dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
+ (constr_rep_thms ~~ dist_lemmas);
fun prove_distinct_thms dist_rewrites' (k, ts) =
let
@@ -537,29 +554,34 @@
in dist_thm :: Drule.export_without_context (dist_thm RS not_sym) :: prove ts end;
in prove ts end;
- val distinct_thms = map2 (prove_distinct_thms)
- dist_rewrites (Datatype_Prop.make_distincts descr sorts);
+ val distinct_thms =
+ map2 (prove_distinct_thms) dist_rewrites (Datatype_Prop.make_distincts descr sorts);
(* prove injectivity of constructors *)
fun prove_constr_inj_thm rep_thms t =
- let val inj_thms = Scons_inject :: (map make_elim
- (iso_inj_thms @
- [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject,
- Lim_inject, Suml_inject, Sumr_inject]))
- in Skip_Proof.prove_global thy5 [] [] t (fn _ => EVERY
- [rtac iffI 1,
- REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2,
- dresolve_tac rep_congs 1, dtac box_equals 1,
- REPEAT (resolve_tac rep_thms 1),
- REPEAT (eresolve_tac inj_thms 1),
- REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1),
- REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1),
- atac 1]))])
+ let
+ val inj_thms = Scons_inject ::
+ map make_elim
+ (iso_inj_thms @
+ [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject,
+ Lim_inject, Suml_inject, Sumr_inject])
+ in
+ Skip_Proof.prove_global thy5 [] [] t
+ (fn _ => EVERY
+ [rtac iffI 1,
+ REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2,
+ dresolve_tac rep_congs 1, dtac box_equals 1,
+ REPEAT (resolve_tac rep_thms 1),
+ REPEAT (eresolve_tac inj_thms 1),
+ REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1),
+ REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1),
+ atac 1]))])
end;
- val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts)
- ((Datatype_Prop.make_injs descr sorts) ~~ constr_rep_thms);
+ val constr_inject =
+ map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts)
+ ((Datatype_Prop.make_injs descr sorts) ~~ constr_rep_thms);
val ((constr_inject', distinct_thms'), thy6) =
thy5
@@ -571,22 +593,22 @@
val _ = Datatype_Aux.message config "Proving induction rule for datatypes ...";
- val Rep_inverse_thms = (map (fn (_, iso, _) => iso RS subst) newT_iso_axms) @
- (map (fn r => r RS @{thm the_inv_f_f} RS subst) iso_inj_thms_unfolded);
+ val Rep_inverse_thms =
+ map (fn (_, iso, _) => iso RS subst) newT_iso_axms @
+ map (fn r => r RS @{thm the_inv_f_f} RS subst) iso_inj_thms_unfolded;
val Rep_inverse_thms' = map (fn r => r RS @{thm the_inv_f_f}) iso_inj_thms_unfolded;
fun mk_indrule_lemma ((i, _), T) (prems, concls) =
let
- val Rep_t = Const (nth all_rep_names i, T --> Univ_elT) $
- Datatype_Aux.mk_Free "x" T i;
+ val Rep_t =
+ Const (nth all_rep_names i, T --> Univ_elT) $ Datatype_Aux.mk_Free "x" T i;
- val Abs_t = if i < length newTs then
- Const (Sign.intern_const thy6
- ("Abs_" ^ (nth new_type_names i)), Univ_elT --> T)
+ val Abs_t =
+ if i < length newTs then
+ Const (Sign.intern_const thy6 ("Abs_" ^ nth new_type_names i), Univ_elT --> T)
else Const (@{const_name the_inv_into},
[HOLogic.mk_setT T, T --> Univ_elT, Univ_elT] ---> T) $
- HOLogic.mk_UNIV T $ Const (nth all_rep_names i, T --> Univ_elT)
-
+ HOLogic.mk_UNIV T $ Const (nth all_rep_names i, T --> Univ_elT);
in
(prems @
[HOLogic.imp $
@@ -601,31 +623,38 @@
val cert = cterm_of thy6;
- val indrule_lemma = Skip_Proof.prove_global thy6 [] []
- (Logic.mk_implies
- (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems),
- HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls))) (fn _ => EVERY
+ val indrule_lemma =
+ Skip_Proof.prove_global thy6 [] []
+ (Logic.mk_implies
+ (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems),
+ HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls)))
+ (fn _ =>
+ EVERY
[REPEAT (etac conjE 1),
REPEAT (EVERY
[TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1,
etac mp 1, resolve_tac iso_elem_thms 1])]);
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
- val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
- map (Free o apfst fst o dest_Var) Ps;
+ val frees =
+ if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))]
+ else map (Free o apfst fst o dest_Var) Ps;
val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma;
val dt_induct_prop = Datatype_Prop.make_ind descr sorts;
- val dt_induct = Skip_Proof.prove_global thy6 []
- (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
- (fn {prems, ...} => EVERY
- [rtac indrule_lemma' 1,
- (Datatype_Aux.indtac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
- EVERY (map (fn (prem, r) => (EVERY
- [REPEAT (eresolve_tac Abs_inverse_thms 1),
- simp_tac (HOL_basic_ss addsimps (Thm.symmetric r :: Rep_inverse_thms')) 1,
- DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
- (prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]);
+ val dt_induct =
+ Skip_Proof.prove_global thy6 []
+ (Logic.strip_imp_prems dt_induct_prop)
+ (Logic.strip_imp_concl dt_induct_prop)
+ (fn {prems, ...} =>
+ EVERY
+ [rtac indrule_lemma' 1,
+ (Datatype_Aux.indtac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
+ EVERY (map (fn (prem, r) => (EVERY
+ [REPEAT (eresolve_tac Abs_inverse_thms 1),
+ simp_tac (HOL_basic_ss addsimps (Thm.symmetric r :: Rep_inverse_thms')) 1,
+ DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
+ (prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]);
val ([dt_induct'], thy7) =
thy6
@@ -647,21 +676,20 @@
val _ = Theory.requires thy "Datatype" "datatype definitions";
(* this theory is used just for parsing *)
- val tmp_thy = thy |>
- Theory.copy |>
- Sign.add_types_global (map (fn (tvs, tname, mx, _) =>
- (tname, length tvs, mx)) dts);
+ val tmp_thy = thy
+ |> Theory.copy
+ |> Sign.add_types_global (map (fn (tvs, tname, mx, _) => (tname, length tvs, mx)) dts);
- val (tyvars, _, _, _)::_ = dts;
+ val (tyvars, _, _, _) ::_ = dts;
val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
- let val full_tname = Sign.full_name tmp_thy tname
- in
+ let val full_tname = Sign.full_name tmp_thy tname in
(case duplicates (op =) tvs of
[] =>
if eq_set (op =) (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
else error ("Mutually recursive datatypes must have same type parameters")
- | dups => error ("Duplicate parameter(s) for datatype " ^ Binding.print tname ^
- " : " ^ commas dups))
+ | dups =>
+ error ("Duplicate parameter(s) for datatype " ^ Binding.print tname ^
+ " : " ^ commas dups))
end) dts);
val dt_names = map fst new_dts;
@@ -683,24 +711,23 @@
in
(constrs @ [(c, map (Datatype_Aux.dtyp_of_typ new_dts) cargs')],
constr_syntax' @ [(cname, mx')], sorts'')
- end handle ERROR msg => cat_error msg
- ("The error above occurred in constructor " ^ Binding.print cname ^
- " of datatype " ^ Binding.print tname);
+ end handle ERROR msg =>
+ cat_error msg ("The error above occurred in constructor " ^ Binding.print cname ^
+ " of datatype " ^ Binding.print tname);
- val (constrs', constr_syntax', sorts') =
- fold prep_constr constrs ([], [], sorts)
+ val (constrs', constr_syntax', sorts') = fold prep_constr constrs ([], [], sorts);
in
- case duplicates (op =) (map fst constrs') of
+ (case duplicates (op =) (map fst constrs') of
[] =>
(dts' @ [(i, (Sign.full_name tmp_thy tname, map Datatype_Aux.DtTFree tvs, constrs'))],
constr_syntax @ [constr_syntax'], sorts', i + 1)
| dups =>
- error ("Duplicate constructors " ^ commas dups ^ " in datatype " ^ Binding.print tname)
+ error ("Duplicate constructors " ^ commas dups ^ " in datatype " ^ Binding.print tname))
end;
- val (dts', constr_syntax, sorts', i) =
- fold2 prep_dt_spec dts new_type_names ([], [], [], 0);
- val sorts = sorts' @ map (rpair (Sign.defaultS tmp_thy)) (subtract (op =) (map fst sorts') tyvars);
+ val (dts', constr_syntax, sorts', i) = fold2 prep_dt_spec dts new_type_names ([], [], [], 0);
+ val sorts =
+ sorts' @ map (rpair (Sign.defaultS tmp_thy)) (subtract (op =) (map fst sorts') tyvars);
val dt_info = Datatype_Data.get_all thy;
val (descr, _) = Datatype_Aux.unfold_datatypes tmp_thy dts' sorts dt_info dts' i;
val _ =
@@ -715,9 +742,10 @@
thy
|> representation_proofs config dt_info new_type_names descr sorts
types_syntax constr_syntax (Datatype_Data.mk_case_names_induct (flat descr))
- |-> (fn (inject, distinct, induct) => Datatype_Data.derive_datatype_props
- config dt_names (SOME new_type_names) descr sorts
- induct inject distinct)
+ |-> (fn (inject, distinct, induct) =>
+ Datatype_Data.derive_datatype_props
+ config dt_names (SOME new_type_names) descr sorts
+ induct inject distinct)
end;
val add_datatype = gen_add_datatype Datatype_Data.cert_typ;