--- a/src/HOL/Inductive.thy Sat Dec 17 12:10:37 2011 +0100
+++ b/src/HOL/Inductive.thy Sat Dec 17 12:42:10 2011 +0100
@@ -11,7 +11,6 @@
("Tools/inductive.ML")
("Tools/Datatype/datatype_aux.ML")
("Tools/Datatype/datatype_prop.ML")
- ("Tools/Datatype/datatype_abs_proofs.ML")
("Tools/Datatype/datatype_data.ML")
("Tools/Datatype/datatype_case.ML")
("Tools/Datatype/rep_datatype.ML")
@@ -277,7 +276,6 @@
use "Tools/Datatype/datatype_aux.ML"
use "Tools/Datatype/datatype_prop.ML"
-use "Tools/Datatype/datatype_abs_proofs.ML"
use "Tools/Datatype/datatype_data.ML" setup Datatype_Data.setup
use "Tools/Datatype/datatype_case.ML" setup Datatype_Case.setup
use "Tools/Datatype/rep_datatype.ML"
--- a/src/HOL/IsaMakefile Sat Dec 17 12:10:37 2011 +0100
+++ b/src/HOL/IsaMakefile Sat Dec 17 12:42:10 2011 +0100
@@ -211,7 +211,6 @@
Tools/ATP/atp_translate.ML \
Tools/ATP/atp_util.ML \
Tools/Datatype/datatype.ML \
- Tools/Datatype/datatype_abs_proofs.ML \
Tools/Datatype/datatype_aux.ML \
Tools/Datatype/datatype_case.ML \
Tools/Datatype/datatype_codegen.ML \
--- a/src/HOL/Tools/Datatype/datatype_abs_proofs.ML Sat Dec 17 12:10:37 2011 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,457 +0,0 @@
-(* Title: HOL/Tools/Datatype/datatype_abs_proofs.ML
- Author: Stefan Berghofer, TU Muenchen
-
-Datatype package: proofs and definitions independent of concrete
-representation of datatypes (i.e. requiring only abstract
-properties: injectivity / distinctness of constructors and induction).
-*)
-
-signature DATATYPE_ABS_PROOFS =
-sig
- type config = Datatype_Aux.config
- type descr = Datatype_Aux.descr
- val prove_casedist_thms : config -> string list -> descr list -> thm ->
- attribute list -> theory -> thm list * theory
- val prove_primrec_thms : config -> string list -> descr list ->
- (string -> thm list) -> thm list list -> thm list list * thm list list ->
- thm -> theory -> (string list * thm list) * theory
- val prove_case_thms : config -> string list -> descr list ->
- string list -> thm list -> theory -> (thm list list * string list) * theory
- val prove_split_thms : config -> string list -> string list -> descr list ->
- thm list list -> thm list list -> thm list -> thm list list -> theory ->
- (thm * thm) list * theory
- val prove_nchotomys : config -> string list -> descr list ->
- thm list -> theory -> thm list * theory
- val prove_weak_case_congs : string list -> string list -> descr list -> theory -> thm list * theory
- val prove_case_congs : string list -> string list -> descr list ->
- thm list -> thm list list -> theory -> thm list * theory
-end;
-
-structure Datatype_Abs_Proofs: DATATYPE_ABS_PROOFS =
-struct
-
-type config = Datatype_Aux.config;
-type descr = Datatype_Aux.descr;
-
-
-(************************ case distinction theorems ***************************)
-
-fun prove_casedist_thms (config : config) new_type_names descr induct case_names_exhausts thy =
- let
- val _ = Datatype_Aux.message config "Proving case distinction theorems ...";
-
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val newTs = take (length (hd descr)) recTs;
-
- val maxidx = Thm.maxidx_of induct;
- val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
-
- fun prove_casedist_thm (i, (T, t)) =
- let
- val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
- Abs ("z", T', Const (@{const_name True}, T''))) induct_Ps;
- val P =
- Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx + 1), T), Bound 0) $
- Var (("P", 0), HOLogic.boolT));
- val insts = take i dummyPs @ (P :: drop (i + 1) dummyPs);
- val cert = cterm_of thy;
- val insts' = map cert induct_Ps ~~ map cert insts;
- val induct' =
- refl RS
- (nth (Datatype_Aux.split_conj_thm (cterm_instantiate insts' induct)) i RSN (2, rev_mp));
- in
- Skip_Proof.prove_global thy []
- (Logic.strip_imp_prems t)
- (Logic.strip_imp_concl t)
- (fn {prems, ...} =>
- EVERY
- [rtac induct' 1,
- REPEAT (rtac TrueI 1),
- REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
- REPEAT (rtac TrueI 1)])
- end;
-
- val casedist_thms =
- map_index prove_casedist_thm (newTs ~~ Datatype_Prop.make_casedists descr);
- in
- thy
- |> Datatype_Aux.store_thms_atts "exhaust" new_type_names
- (map single case_names_exhausts) casedist_thms
- end;
-
-
-(*************************** primrec combinators ******************************)
-
-fun prove_primrec_thms (config : config) new_type_names descr
- injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy =
- let
- val _ = Datatype_Aux.message config "Constructing primrec combinators ...";
-
- val big_name = space_implode "_" new_type_names;
- val thy0 = Sign.add_path big_name thy;
-
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val used = fold Term.add_tfree_namesT recTs [];
- val newTs = take (length (hd descr)) recTs;
-
- val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
-
- val big_rec_name' = big_name ^ "_rec_set";
- val rec_set_names' =
- if length descr' = 1 then [big_rec_name']
- else map (prefix (big_rec_name' ^ "_") o string_of_int) (1 upto length descr');
- val rec_set_names = map (Sign.full_bname thy0) rec_set_names';
-
- val (rec_result_Ts, reccomb_fn_Ts) = Datatype_Prop.make_primrec_Ts descr used;
-
- val rec_set_Ts =
- map (fn (T1, T2) => (reccomb_fn_Ts @ [T1, T2]) ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
-
- val rec_fns =
- map (uncurry (Datatype_Aux.mk_Free "f")) (reccomb_fn_Ts ~~ (1 upto length reccomb_fn_Ts));
- val rec_sets' =
- map (fn c => list_comb (Free c, rec_fns)) (rec_set_names' ~~ rec_set_Ts);
- val rec_sets =
- map (fn c => list_comb (Const c, rec_fns)) (rec_set_names ~~ rec_set_Ts);
-
- (* introduction rules for graph of primrec function *)
-
- fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) =
- let
- fun mk_prem (dt, U) (j, k, prems, t1s, t2s) =
- let val free1 = Datatype_Aux.mk_Free "x" U j in
- (case (Datatype_Aux.strip_dtyp dt, strip_type U) of
- ((_, Datatype_Aux.DtRec m), (Us, _)) =>
- let
- val free2 = Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k;
- val i = length Us;
- in
- (j + 1, k + 1,
- HOLogic.mk_Trueprop (HOLogic.list_all
- (map (pair "x") Us, nth rec_sets' m $
- Datatype_Aux.app_bnds free1 i $ Datatype_Aux.app_bnds free2 i)) :: prems,
- free1 :: t1s, free2 :: t2s)
- end
- | _ => (j + 1, k, prems, free1 :: t1s, t2s))
- end;
-
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []);
-
- in
- (rec_intr_ts @
- [Logic.list_implies (prems, HOLogic.mk_Trueprop
- (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
- list_comb (nth rec_fns l, t1s @ t2s)))], l + 1)
- end;
-
- val (rec_intr_ts, _) =
- fold (fn ((d, T), set_name) =>
- fold (make_rec_intr T set_name) (#3 (snd d))) (descr' ~~ recTs ~~ rec_sets') ([], 0);
-
- val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
- thy0
- |> Sign.map_naming Name_Space.conceal
- |> Inductive.add_inductive_global
- {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name',
- coind = false, no_elim = false, no_ind = true, skip_mono = true, fork_mono = false}
- (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
- (map dest_Free rec_fns)
- (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) []
- ||> Sign.restore_naming thy0
- ||> Theory.checkpoint;
-
- (* prove uniqueness and termination of primrec combinators *)
-
- val _ = Datatype_Aux.message config "Proving termination and uniqueness of primrec functions ...";
-
- fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) =
- let
- val distinct_tac =
- if i < length newTs then
- full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1
- else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1;
-
- val inject =
- map (fn r => r RS iffD1)
- (if i < length newTs then nth constr_inject i else injects_of tname);
-
- fun mk_unique_constr_tac n (cname, cargs) (tac, intr :: intrs, j) =
- let
- val k = length (filter Datatype_Aux.is_rec_type cargs);
- in
- (EVERY
- [DETERM tac,
- REPEAT (etac ex1E 1), rtac ex1I 1,
- DEPTH_SOLVE_1 (ares_tac [intr] 1),
- REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
- etac elim 1,
- REPEAT_DETERM_N j distinct_tac,
- TRY (dresolve_tac inject 1),
- REPEAT (etac conjE 1), hyp_subst_tac 1,
- REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
- TRY (hyp_subst_tac 1),
- rtac refl 1,
- REPEAT_DETERM_N (n - j - 1) distinct_tac],
- intrs, j + 1)
- end;
-
- val (tac', intrs', _) =
- fold (mk_unique_constr_tac (length constrs)) constrs (tac, intrs, 0);
- in (tac', intrs') end;
-
- val rec_unique_thms =
- let
- val rec_unique_ts =
- map (fn (((set_t, T1), T2), i) =>
- Const (@{const_name Ex1}, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
- absfree ("y", T2) (set_t $ Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2)))
- (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
- val cert = cterm_of thy1;
- val insts =
- map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t)
- ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
- val induct' = cterm_instantiate (map cert induct_Ps ~~ map cert insts) induct;
- val (tac, _) =
- fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
- (((rtac induct' THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1 THEN
- rewrite_goals_tac [mk_meta_eq @{thm choice_eq}], rec_intrs));
- in
- Datatype_Aux.split_conj_thm (Skip_Proof.prove_global thy1 [] []
- (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj rec_unique_ts)) (K tac))
- end;
-
- val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms;
-
- (* define primrec combinators *)
-
- val big_reccomb_name = space_implode "_" new_type_names ^ "_rec";
- val reccomb_names =
- map (Sign.full_bname thy1)
- (if length descr' = 1 then [big_reccomb_name]
- else map (prefix (big_reccomb_name ^ "_") o string_of_int) (1 upto length descr'));
- val reccombs =
- map (fn ((name, T), T') => Const (name, reccomb_fn_Ts @ [T] ---> T'))
- (reccomb_names ~~ recTs ~~ rec_result_Ts);
-
- val (reccomb_defs, thy2) =
- thy1
- |> Sign.add_consts_i (map (fn ((name, T), T') =>
- (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn))
- (reccomb_names ~~ recTs ~~ rec_result_Ts))
- |> (Global_Theory.add_defs false o map Thm.no_attributes)
- (map
- (fn ((((name, comb), set), T), T') =>
- (Binding.name (Long_Name.base_name name ^ "_def"),
- Logic.mk_equals (comb, fold_rev lambda rec_fns (absfree ("x", T)
- (Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T')
- (set $ Free ("x", T) $ Free ("y", T')))))))
- (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
- ||> Sign.parent_path
- ||> Theory.checkpoint;
-
-
- (* prove characteristic equations for primrec combinators *)
-
- val _ = Datatype_Aux.message config "Proving characteristic theorems for primrec combinators ...";
-
- val rec_thms =
- map (fn t =>
- Skip_Proof.prove_global thy2 [] [] t
- (fn _ => EVERY
- [rewrite_goals_tac reccomb_defs,
- rtac @{thm the1_equality} 1,
- resolve_tac rec_unique_thms 1,
- resolve_tac rec_intrs 1,
- REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
- (Datatype_Prop.make_primrecs reccomb_names descr thy2);
- in
- thy2
- |> Sign.add_path (space_implode "_" new_type_names)
- |> Global_Theory.note_thmss ""
- [((Binding.name "recs", [Nitpick_Simps.add]), [(rec_thms, [])])]
- ||> Sign.parent_path
- ||> Theory.checkpoint
- |-> (fn thms => pair (reccomb_names, maps #2 thms))
- end;
-
-
-(***************************** case combinators *******************************)
-
-fun prove_case_thms (config : config) new_type_names descr reccomb_names primrec_thms thy =
- let
- val _ = Datatype_Aux.message config "Proving characteristic theorems for case combinators ...";
-
- val thy1 = Sign.add_path (space_implode "_" new_type_names) thy;
-
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val used = fold Term.add_tfree_namesT recTs [];
- val newTs = take (length (hd descr)) recTs;
- val T' = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS);
-
- fun mk_dummyT dt = binder_types (Datatype_Aux.typ_of_dtyp descr' dt) ---> T';
-
- val case_dummy_fns =
- map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val Ts' = map mk_dummyT (filter Datatype_Aux.is_rec_type cargs)
- in Const (@{const_name undefined}, Ts @ Ts' ---> T') end) constrs) descr';
-
- val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names;
-
- (* define case combinators via primrec combinators *)
-
- val (case_defs, thy2) =
- fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) =>
- let
- val (fns1, fns2) = split_list (map (fn ((_, cargs), j) =>
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val Ts' = Ts @ map mk_dummyT (filter Datatype_Aux.is_rec_type cargs);
- val frees' = map2 (Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts');
- val frees = take (length cargs) frees';
- val free = Datatype_Aux.mk_Free "f" (Ts ---> T') j;
- in
- (free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees)))
- end) (constrs ~~ (1 upto length constrs)));
-
- val caseT = map (snd o dest_Free) fns1 @ [T] ---> T';
- val fns = flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns);
- val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
- val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn);
- val def =
- (Binding.name (Long_Name.base_name name ^ "_def"),
- Logic.mk_equals (Const (name, caseT),
- fold_rev lambda fns1
- (list_comb (reccomb,
- flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns)))));
- val ([def_thm], thy') =
- thy
- |> Sign.declare_const_global decl |> snd
- |> (Global_Theory.add_defs false o map Thm.no_attributes) [def];
-
- in (defs @ [def_thm], thy') end)
- (hd descr ~~ newTs ~~ case_names ~~ take (length newTs) reccomb_names) ([], thy1)
- ||> Theory.checkpoint;
-
- val case_thms =
- (map o map) (fn t =>
- Skip_Proof.prove_global thy2 [] [] t
- (fn _ =>
- EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))
- (Datatype_Prop.make_cases case_names descr thy2);
- in
- thy2
- |> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms)
- |> Sign.parent_path
- |> Datatype_Aux.store_thmss "cases" new_type_names case_thms
- |-> (fn thmss => pair (thmss, case_names))
- end;
-
-
-(******************************* case splitting *******************************)
-
-fun prove_split_thms (config : config)
- new_type_names case_names descr constr_inject dist_rewrites casedist_thms case_thms thy =
- let
- val _ = Datatype_Aux.message config "Proving equations for case splitting ...";
-
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val newTs = take (length (hd descr)) recTs;
-
- fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), exhaustion), case_thms'), T) =
- let
- val cert = cterm_of thy;
- val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
- val exhaustion' = cterm_instantiate [(cert lhs, cert (Free ("x", T)))] exhaustion;
- val tac =
- EVERY [rtac exhaustion' 1,
- ALLGOALS (asm_simp_tac (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))];
- in
- (Skip_Proof.prove_global thy [] [] t1 (K tac),
- Skip_Proof.prove_global thy [] [] t2 (K tac))
- end;
-
- val split_thm_pairs =
- map prove_split_thms
- (Datatype_Prop.make_splits case_names descr thy ~~ constr_inject ~~
- dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
-
- val (split_thms, split_asm_thms) = split_list split_thm_pairs
-
- in
- thy
- |> Datatype_Aux.store_thms "split" new_type_names split_thms
- ||>> Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms
- |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
- end;
-
-fun prove_weak_case_congs new_type_names case_names descr thy =
- let
- fun prove_weak_case_cong t =
- Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
- (fn {prems, ...} => EVERY [rtac (hd prems RS arg_cong) 1]);
-
- val weak_case_congs =
- map prove_weak_case_cong (Datatype_Prop.make_weak_case_congs case_names descr thy);
-
- in thy |> Datatype_Aux.store_thms "weak_case_cong" new_type_names weak_case_congs end;
-
-(************************* additional theorems for TFL ************************)
-
-fun prove_nchotomys (config : config) new_type_names descr casedist_thms thy =
- let
- val _ = Datatype_Aux.message config "Proving additional theorems for TFL ...";
-
- fun prove_nchotomy (t, exhaustion) =
- let
- (* For goal i, select the correct disjunct to attack, then prove it *)
- fun tac i 0 = EVERY [TRY (rtac disjI1 i), hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
- | tac i n = rtac disjI2 i THEN tac i (n - 1);
- in
- Skip_Proof.prove_global thy [] [] t
- (fn _ =>
- EVERY [rtac allI 1,
- Datatype_Aux.exh_tac (K exhaustion) 1,
- ALLGOALS (fn i => tac i (i - 1))])
- end;
-
- val nchotomys =
- map prove_nchotomy (Datatype_Prop.make_nchotomys descr ~~ casedist_thms);
-
- in thy |> Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end;
-
-fun prove_case_congs new_type_names case_names descr nchotomys case_thms thy =
- let
- fun prove_case_cong ((t, nchotomy), case_rewrites) =
- let
- val Const ("==>", _) $ tm $ _ = t;
- val Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ Ma) = tm;
- val cert = cterm_of thy;
- val nchotomy' = nchotomy RS spec;
- val [v] = Term.add_vars (concl_of nchotomy') [];
- val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy';
- in
- Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
- (fn {prems, ...} =>
- let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) in
- EVERY [
- simp_tac (HOL_ss addsimps [hd prems]) 1,
- cut_facts_tac [nchotomy''] 1,
- REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
- REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
- end)
- end;
-
- val case_congs =
- map prove_case_cong
- (Datatype_Prop.make_case_congs case_names descr thy ~~ nchotomys ~~ case_thms);
-
- in thy |> Datatype_Aux.store_thms "case_cong" new_type_names case_congs end;
-
-end;
--- a/src/HOL/Tools/Datatype/rep_datatype.ML Sat Dec 17 12:10:37 2011 +0100
+++ b/src/HOL/Tools/Datatype/rep_datatype.ML Sat Dec 17 12:42:10 2011 +0100
@@ -1,7 +1,10 @@
(* Title: HOL/Tools/Datatype/rep_datatype.ML
Author: Stefan Berghofer, TU Muenchen
-Representation of existing types as datatypes.
+Representation of existing types as datatypes: proofs and definitions
+independent of concrete representation of datatypes (i.e. requiring
+only abstract properties: injectivity / distinctness of constructors
+and induction).
*)
signature REP_DATATYPE =
@@ -17,6 +20,440 @@
structure Rep_Datatype: REP_DATATYPE =
struct
+type config = Datatype_Aux.config;
+type descr = Datatype_Aux.descr;
+
+
+
+(** derived definitions and proofs **)
+
+(* case distinction theorems *)
+
+fun prove_casedist_thms (config : config) new_type_names descr induct case_names_exhausts thy =
+ let
+ val _ = Datatype_Aux.message config "Proving case distinction theorems ...";
+
+ val descr' = flat descr;
+ val recTs = Datatype_Aux.get_rec_types descr';
+ val newTs = take (length (hd descr)) recTs;
+
+ val maxidx = Thm.maxidx_of induct;
+ val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
+
+ fun prove_casedist_thm (i, (T, t)) =
+ let
+ val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
+ Abs ("z", T', Const (@{const_name True}, T''))) induct_Ps;
+ val P =
+ Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx + 1), T), Bound 0) $
+ Var (("P", 0), HOLogic.boolT));
+ val insts = take i dummyPs @ (P :: drop (i + 1) dummyPs);
+ val cert = cterm_of thy;
+ val insts' = map cert induct_Ps ~~ map cert insts;
+ val induct' =
+ refl RS
+ (nth (Datatype_Aux.split_conj_thm (cterm_instantiate insts' induct)) i RSN (2, rev_mp));
+ in
+ Skip_Proof.prove_global thy []
+ (Logic.strip_imp_prems t)
+ (Logic.strip_imp_concl t)
+ (fn {prems, ...} =>
+ EVERY
+ [rtac induct' 1,
+ REPEAT (rtac TrueI 1),
+ REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
+ REPEAT (rtac TrueI 1)])
+ end;
+
+ val casedist_thms =
+ map_index prove_casedist_thm (newTs ~~ Datatype_Prop.make_casedists descr);
+ in
+ thy
+ |> Datatype_Aux.store_thms_atts "exhaust" new_type_names
+ (map single case_names_exhausts) casedist_thms
+ end;
+
+
+(* primrec combinators *)
+
+fun prove_primrec_thms (config : config) new_type_names descr
+ injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy =
+ let
+ val _ = Datatype_Aux.message config "Constructing primrec combinators ...";
+
+ val big_name = space_implode "_" new_type_names;
+ val thy0 = Sign.add_path big_name thy;
+
+ val descr' = flat descr;
+ val recTs = Datatype_Aux.get_rec_types descr';
+ val used = fold Term.add_tfree_namesT recTs [];
+ val newTs = take (length (hd descr)) recTs;
+
+ val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
+
+ val big_rec_name' = big_name ^ "_rec_set";
+ val rec_set_names' =
+ if length descr' = 1 then [big_rec_name']
+ else map (prefix (big_rec_name' ^ "_") o string_of_int) (1 upto length descr');
+ val rec_set_names = map (Sign.full_bname thy0) rec_set_names';
+
+ val (rec_result_Ts, reccomb_fn_Ts) = Datatype_Prop.make_primrec_Ts descr used;
+
+ val rec_set_Ts =
+ map (fn (T1, T2) => (reccomb_fn_Ts @ [T1, T2]) ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
+
+ val rec_fns =
+ map (uncurry (Datatype_Aux.mk_Free "f")) (reccomb_fn_Ts ~~ (1 upto length reccomb_fn_Ts));
+ val rec_sets' =
+ map (fn c => list_comb (Free c, rec_fns)) (rec_set_names' ~~ rec_set_Ts);
+ val rec_sets =
+ map (fn c => list_comb (Const c, rec_fns)) (rec_set_names ~~ rec_set_Ts);
+
+ (* introduction rules for graph of primrec function *)
+
+ fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) =
+ let
+ fun mk_prem (dt, U) (j, k, prems, t1s, t2s) =
+ let val free1 = Datatype_Aux.mk_Free "x" U j in
+ (case (Datatype_Aux.strip_dtyp dt, strip_type U) of
+ ((_, Datatype_Aux.DtRec m), (Us, _)) =>
+ let
+ val free2 = Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k;
+ val i = length Us;
+ in
+ (j + 1, k + 1,
+ HOLogic.mk_Trueprop (HOLogic.list_all
+ (map (pair "x") Us, nth rec_sets' m $
+ Datatype_Aux.app_bnds free1 i $ Datatype_Aux.app_bnds free2 i)) :: prems,
+ free1 :: t1s, free2 :: t2s)
+ end
+ | _ => (j + 1, k, prems, free1 :: t1s, t2s))
+ end;
+
+ val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
+ val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []);
+
+ in
+ (rec_intr_ts @
+ [Logic.list_implies (prems, HOLogic.mk_Trueprop
+ (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
+ list_comb (nth rec_fns l, t1s @ t2s)))], l + 1)
+ end;
+
+ val (rec_intr_ts, _) =
+ fold (fn ((d, T), set_name) =>
+ fold (make_rec_intr T set_name) (#3 (snd d))) (descr' ~~ recTs ~~ rec_sets') ([], 0);
+
+ val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
+ thy0
+ |> Sign.map_naming Name_Space.conceal
+ |> Inductive.add_inductive_global
+ {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name',
+ coind = false, no_elim = false, no_ind = true, skip_mono = true, fork_mono = false}
+ (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
+ (map dest_Free rec_fns)
+ (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) []
+ ||> Sign.restore_naming thy0
+ ||> Theory.checkpoint;
+
+ (* prove uniqueness and termination of primrec combinators *)
+
+ val _ = Datatype_Aux.message config "Proving termination and uniqueness of primrec functions ...";
+
+ fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) =
+ let
+ val distinct_tac =
+ if i < length newTs then
+ full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1
+ else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1;
+
+ val inject =
+ map (fn r => r RS iffD1)
+ (if i < length newTs then nth constr_inject i else injects_of tname);
+
+ fun mk_unique_constr_tac n (cname, cargs) (tac, intr :: intrs, j) =
+ let
+ val k = length (filter Datatype_Aux.is_rec_type cargs);
+ in
+ (EVERY
+ [DETERM tac,
+ REPEAT (etac ex1E 1), rtac ex1I 1,
+ DEPTH_SOLVE_1 (ares_tac [intr] 1),
+ REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
+ etac elim 1,
+ REPEAT_DETERM_N j distinct_tac,
+ TRY (dresolve_tac inject 1),
+ REPEAT (etac conjE 1), hyp_subst_tac 1,
+ REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
+ TRY (hyp_subst_tac 1),
+ rtac refl 1,
+ REPEAT_DETERM_N (n - j - 1) distinct_tac],
+ intrs, j + 1)
+ end;
+
+ val (tac', intrs', _) =
+ fold (mk_unique_constr_tac (length constrs)) constrs (tac, intrs, 0);
+ in (tac', intrs') end;
+
+ val rec_unique_thms =
+ let
+ val rec_unique_ts =
+ map (fn (((set_t, T1), T2), i) =>
+ Const (@{const_name Ex1}, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
+ absfree ("y", T2) (set_t $ Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2)))
+ (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
+ val cert = cterm_of thy1;
+ val insts =
+ map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t)
+ ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
+ val induct' = cterm_instantiate (map cert induct_Ps ~~ map cert insts) induct;
+ val (tac, _) =
+ fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
+ (((rtac induct' THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1 THEN
+ rewrite_goals_tac [mk_meta_eq @{thm choice_eq}], rec_intrs));
+ in
+ Datatype_Aux.split_conj_thm (Skip_Proof.prove_global thy1 [] []
+ (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj rec_unique_ts)) (K tac))
+ end;
+
+ val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms;
+
+ (* define primrec combinators *)
+
+ val big_reccomb_name = space_implode "_" new_type_names ^ "_rec";
+ val reccomb_names =
+ map (Sign.full_bname thy1)
+ (if length descr' = 1 then [big_reccomb_name]
+ else map (prefix (big_reccomb_name ^ "_") o string_of_int) (1 upto length descr'));
+ val reccombs =
+ map (fn ((name, T), T') => Const (name, reccomb_fn_Ts @ [T] ---> T'))
+ (reccomb_names ~~ recTs ~~ rec_result_Ts);
+
+ val (reccomb_defs, thy2) =
+ thy1
+ |> Sign.add_consts_i (map (fn ((name, T), T') =>
+ (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn))
+ (reccomb_names ~~ recTs ~~ rec_result_Ts))
+ |> (Global_Theory.add_defs false o map Thm.no_attributes)
+ (map
+ (fn ((((name, comb), set), T), T') =>
+ (Binding.name (Long_Name.base_name name ^ "_def"),
+ Logic.mk_equals (comb, fold_rev lambda rec_fns (absfree ("x", T)
+ (Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T')
+ (set $ Free ("x", T) $ Free ("y", T')))))))
+ (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
+ ||> Sign.parent_path
+ ||> Theory.checkpoint;
+
+
+ (* prove characteristic equations for primrec combinators *)
+
+ val _ = Datatype_Aux.message config "Proving characteristic theorems for primrec combinators ...";
+
+ val rec_thms =
+ map (fn t =>
+ Skip_Proof.prove_global thy2 [] [] t
+ (fn _ => EVERY
+ [rewrite_goals_tac reccomb_defs,
+ rtac @{thm the1_equality} 1,
+ resolve_tac rec_unique_thms 1,
+ resolve_tac rec_intrs 1,
+ REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
+ (Datatype_Prop.make_primrecs reccomb_names descr thy2);
+ in
+ thy2
+ |> Sign.add_path (space_implode "_" new_type_names)
+ |> Global_Theory.note_thmss ""
+ [((Binding.name "recs", [Nitpick_Simps.add]), [(rec_thms, [])])]
+ ||> Sign.parent_path
+ ||> Theory.checkpoint
+ |-> (fn thms => pair (reccomb_names, maps #2 thms))
+ end;
+
+
+(* case combinators *)
+
+fun prove_case_thms (config : config) new_type_names descr reccomb_names primrec_thms thy =
+ let
+ val _ = Datatype_Aux.message config "Proving characteristic theorems for case combinators ...";
+
+ val thy1 = Sign.add_path (space_implode "_" new_type_names) thy;
+
+ val descr' = flat descr;
+ val recTs = Datatype_Aux.get_rec_types descr';
+ val used = fold Term.add_tfree_namesT recTs [];
+ val newTs = take (length (hd descr)) recTs;
+ val T' = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS);
+
+ fun mk_dummyT dt = binder_types (Datatype_Aux.typ_of_dtyp descr' dt) ---> T';
+
+ val case_dummy_fns =
+ map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
+ let
+ val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
+ val Ts' = map mk_dummyT (filter Datatype_Aux.is_rec_type cargs)
+ in Const (@{const_name undefined}, Ts @ Ts' ---> T') end) constrs) descr';
+
+ val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names;
+
+ (* define case combinators via primrec combinators *)
+
+ val (case_defs, thy2) =
+ fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) =>
+ let
+ val (fns1, fns2) = split_list (map (fn ((_, cargs), j) =>
+ let
+ val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
+ val Ts' = Ts @ map mk_dummyT (filter Datatype_Aux.is_rec_type cargs);
+ val frees' = map2 (Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts');
+ val frees = take (length cargs) frees';
+ val free = Datatype_Aux.mk_Free "f" (Ts ---> T') j;
+ in
+ (free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees)))
+ end) (constrs ~~ (1 upto length constrs)));
+
+ val caseT = map (snd o dest_Free) fns1 @ [T] ---> T';
+ val fns = flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns);
+ val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
+ val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn);
+ val def =
+ (Binding.name (Long_Name.base_name name ^ "_def"),
+ Logic.mk_equals (Const (name, caseT),
+ fold_rev lambda fns1
+ (list_comb (reccomb,
+ flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns)))));
+ val ([def_thm], thy') =
+ thy
+ |> Sign.declare_const_global decl |> snd
+ |> (Global_Theory.add_defs false o map Thm.no_attributes) [def];
+
+ in (defs @ [def_thm], thy') end)
+ (hd descr ~~ newTs ~~ case_names ~~ take (length newTs) reccomb_names) ([], thy1)
+ ||> Theory.checkpoint;
+
+ val case_thms =
+ (map o map) (fn t =>
+ Skip_Proof.prove_global thy2 [] [] t
+ (fn _ =>
+ EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))
+ (Datatype_Prop.make_cases case_names descr thy2);
+ in
+ thy2
+ |> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms)
+ |> Sign.parent_path
+ |> Datatype_Aux.store_thmss "cases" new_type_names case_thms
+ |-> (fn thmss => pair (thmss, case_names))
+ end;
+
+
+(* case splitting *)
+
+fun prove_split_thms (config : config)
+ new_type_names case_names descr constr_inject dist_rewrites casedist_thms case_thms thy =
+ let
+ val _ = Datatype_Aux.message config "Proving equations for case splitting ...";
+
+ val descr' = flat descr;
+ val recTs = Datatype_Aux.get_rec_types descr';
+ val newTs = take (length (hd descr)) recTs;
+
+ fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), exhaustion), case_thms'), T) =
+ let
+ val cert = cterm_of thy;
+ val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
+ val exhaustion' = cterm_instantiate [(cert lhs, cert (Free ("x", T)))] exhaustion;
+ val tac =
+ EVERY [rtac exhaustion' 1,
+ ALLGOALS (asm_simp_tac (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))];
+ in
+ (Skip_Proof.prove_global thy [] [] t1 (K tac),
+ Skip_Proof.prove_global thy [] [] t2 (K tac))
+ end;
+
+ val split_thm_pairs =
+ map prove_split_thms
+ (Datatype_Prop.make_splits case_names descr thy ~~ constr_inject ~~
+ dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
+
+ val (split_thms, split_asm_thms) = split_list split_thm_pairs
+
+ in
+ thy
+ |> Datatype_Aux.store_thms "split" new_type_names split_thms
+ ||>> Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms
+ |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
+ end;
+
+fun prove_weak_case_congs new_type_names case_names descr thy =
+ let
+ fun prove_weak_case_cong t =
+ Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
+ (fn {prems, ...} => EVERY [rtac (hd prems RS arg_cong) 1]);
+
+ val weak_case_congs =
+ map prove_weak_case_cong (Datatype_Prop.make_weak_case_congs case_names descr thy);
+
+ in thy |> Datatype_Aux.store_thms "weak_case_cong" new_type_names weak_case_congs end;
+
+
+(* additional theorems for TFL *)
+
+fun prove_nchotomys (config : config) new_type_names descr casedist_thms thy =
+ let
+ val _ = Datatype_Aux.message config "Proving additional theorems for TFL ...";
+
+ fun prove_nchotomy (t, exhaustion) =
+ let
+ (* For goal i, select the correct disjunct to attack, then prove it *)
+ fun tac i 0 = EVERY [TRY (rtac disjI1 i), hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
+ | tac i n = rtac disjI2 i THEN tac i (n - 1);
+ in
+ Skip_Proof.prove_global thy [] [] t
+ (fn _ =>
+ EVERY [rtac allI 1,
+ Datatype_Aux.exh_tac (K exhaustion) 1,
+ ALLGOALS (fn i => tac i (i - 1))])
+ end;
+
+ val nchotomys =
+ map prove_nchotomy (Datatype_Prop.make_nchotomys descr ~~ casedist_thms);
+
+ in thy |> Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end;
+
+fun prove_case_congs new_type_names case_names descr nchotomys case_thms thy =
+ let
+ fun prove_case_cong ((t, nchotomy), case_rewrites) =
+ let
+ val Const ("==>", _) $ tm $ _ = t;
+ val Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ Ma) = tm;
+ val cert = cterm_of thy;
+ val nchotomy' = nchotomy RS spec;
+ val [v] = Term.add_vars (concl_of nchotomy') [];
+ val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy';
+ in
+ Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
+ (fn {prems, ...} =>
+ let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) in
+ EVERY [
+ simp_tac (HOL_ss addsimps [hd prems]) 1,
+ cut_facts_tac [nchotomy''] 1,
+ REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
+ REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
+ end)
+ end;
+
+ val case_congs =
+ map prove_case_cong
+ (Datatype_Prop.make_case_congs case_names descr thy ~~ nchotomys ~~ case_thms);
+
+ in thy |> Datatype_Aux.store_thms "case_cong" new_type_names case_congs end;
+
+
+
+(** derive datatype props **)
+
+local
+
fun make_dt_info descr induct inducts rec_names rec_rewrites
(index, (((((((((((_, (tname, _, _))), inject), distinct),
exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong),
@@ -39,6 +476,8 @@
split = split,
split_asm = split_asm});
+in
+
fun derive_datatype_props config dt_names descr induct inject distinct thy1 =
let
val thy2 = thy1 |> Theory.checkpoint;
@@ -49,25 +488,23 @@
("Deriving properties for datatype(s) " ^ commas_quote new_type_names);
val (exhaust, thy3) = thy2
- |> Datatype_Abs_Proofs.prove_casedist_thms config new_type_names
- descr induct (Datatype_Data.mk_case_names_exhausts flat_descr dt_names);
+ |> prove_casedist_thms config new_type_names descr induct
+ (Datatype_Data.mk_case_names_exhausts flat_descr dt_names);
val (nchotomys, thy4) = thy3
- |> Datatype_Abs_Proofs.prove_nchotomys config new_type_names descr exhaust;
+ |> prove_nchotomys config new_type_names descr exhaust;
val ((rec_names, rec_rewrites), thy5) = thy4
- |> Datatype_Abs_Proofs.prove_primrec_thms
- config new_type_names descr (#inject o the o Symtab.lookup (Datatype_Data.get_all thy4))
- inject (distinct, Datatype_Data.all_distincts thy2 (Datatype_Aux.get_rec_types flat_descr))
- induct;
+ |> prove_primrec_thms config new_type_names descr
+ (#inject o the o Symtab.lookup (Datatype_Data.get_all thy4)) inject
+ (distinct, Datatype_Data.all_distincts thy2 (Datatype_Aux.get_rec_types flat_descr)) induct;
val ((case_rewrites, case_names), thy6) = thy5
- |> Datatype_Abs_Proofs.prove_case_thms config new_type_names descr rec_names rec_rewrites;
+ |> prove_case_thms config new_type_names descr rec_names rec_rewrites;
val (case_congs, thy7) = thy6
- |> Datatype_Abs_Proofs.prove_case_congs new_type_names case_names descr
- nchotomys case_rewrites;
+ |> prove_case_congs new_type_names case_names descr nchotomys case_rewrites;
val (weak_case_congs, thy8) = thy7
- |> Datatype_Abs_Proofs.prove_weak_case_congs new_type_names case_names descr;
+ |> prove_weak_case_congs new_type_names case_names descr;
val (splits, thy9) = thy8
- |> Datatype_Abs_Proofs.prove_split_thms
- config new_type_names case_names descr inject distinct exhaust case_rewrites;
+ |> prove_split_thms config new_type_names case_names descr
+ inject distinct exhaust case_rewrites;
val inducts = Project_Rule.projections (Proof_Context.init_global thy2) induct;
val dt_infos =
@@ -106,6 +543,8 @@
|> pair dt_names
end;
+end;
+
(** declare existing type as datatype **)