--- a/src/HOL/Tools/datatype_prop.ML Sat Jun 13 07:03:51 2009 -0700
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,435 +0,0 @@
-(* Title: HOL/Tools/datatype_prop.ML
- Author: Stefan Berghofer, TU Muenchen
-
-Characteristic properties of datatypes.
-*)
-
-signature DATATYPE_PROP =
-sig
- val indexify_names: string list -> string list
- val make_tnames: typ list -> string list
- val make_injs : DatatypeAux.descr list -> (string * sort) list -> term list list
- val make_distincts : DatatypeAux.descr list ->
- (string * sort) list -> (int * term list) list (*no symmetric inequalities*)
- val make_ind : DatatypeAux.descr list -> (string * sort) list -> term
- val make_casedists : DatatypeAux.descr list -> (string * sort) list -> term list
- val make_primrec_Ts : DatatypeAux.descr list -> (string * sort) list ->
- string list -> typ list * typ list
- val make_primrecs : string list -> DatatypeAux.descr list ->
- (string * sort) list -> theory -> term list
- val make_cases : string list -> DatatypeAux.descr list ->
- (string * sort) list -> theory -> term list list
- val make_splits : string list -> DatatypeAux.descr list ->
- (string * sort) list -> theory -> (term * term) list
- val make_weak_case_congs : string list -> DatatypeAux.descr list ->
- (string * sort) list -> theory -> term list
- val make_case_congs : string list -> DatatypeAux.descr list ->
- (string * sort) list -> theory -> term list
- val make_nchotomys : DatatypeAux.descr list ->
- (string * sort) list -> term list
-end;
-
-structure DatatypeProp : DATATYPE_PROP =
-struct
-
-open DatatypeAux;
-
-fun indexify_names names =
- let
- fun index (x :: xs) tab =
- (case AList.lookup (op =) tab x of
- NONE => if member (op =) xs x then (x ^ "1") :: index xs ((x, 2) :: tab) else x :: index xs tab
- | SOME i => (x ^ string_of_int i) :: index xs ((x, i + 1) :: tab))
- | index [] _ = [];
- in index names [] end;
-
-fun make_tnames Ts =
- let
- fun type_name (TFree (name, _)) = implode (tl (explode name))
- | type_name (Type (name, _)) =
- let val name' = Long_Name.base_name name
- in if Syntax.is_identifier name' then name' else "x" end;
- in indexify_names (map type_name Ts) end;
-
-
-(************************* injectivity of constructors ************************)
-
-fun make_injs descr sorts =
- let
- val descr' = flat descr;
- fun make_inj T (cname, cargs) =
- if null cargs then I else
- let
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val constr_t = Const (cname, Ts ---> T);
- val tnames = make_tnames Ts;
- val frees = map Free (tnames ~~ Ts);
- val frees' = map Free ((map ((op ^) o (rpair "'")) tnames) ~~ Ts);
- in cons (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (HOLogic.mk_eq (list_comb (constr_t, frees), list_comb (constr_t, frees')),
- foldr1 (HOLogic.mk_binop "op &")
- (map HOLogic.mk_eq (frees ~~ frees')))))
- end;
- in
- map2 (fn d => fn T => fold_rev (make_inj T) (#3 (snd d)) [])
- (hd descr) (Library.take (length (hd descr), get_rec_types descr' sorts))
- end;
-
-
-(************************* distinctness of constructors ***********************)
-
-fun make_distincts descr sorts =
- let
- val descr' = flat descr;
- val recTs = get_rec_types descr' sorts;
- val newTs = Library.take (length (hd descr), recTs);
-
- fun prep_constr (cname, cargs) = (cname, map (typ_of_dtyp descr' sorts) cargs);
-
- fun make_distincts' _ [] = []
- | make_distincts' T ((cname, cargs)::constrs) =
- let
- val frees = map Free ((make_tnames cargs) ~~ cargs);
- val t = list_comb (Const (cname, cargs ---> T), frees);
-
- fun make_distincts'' (cname', cargs') =
- let
- val frees' = map Free ((map ((op ^) o (rpair "'"))
- (make_tnames cargs')) ~~ cargs');
- val t' = list_comb (Const (cname', cargs' ---> T), frees')
- in
- HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t, t'))
- end
-
- in map make_distincts'' constrs @ make_distincts' T constrs end;
-
- in
- map2 (fn ((_, (_, _, constrs))) => fn T =>
- (length constrs, make_distincts' T (map prep_constr constrs))) (hd descr) newTs
- end;
-
-
-(********************************* induction **********************************)
-
-fun make_ind descr sorts =
- let
- val descr' = List.concat descr;
- val recTs = get_rec_types descr' sorts;
- val pnames = if length descr' = 1 then ["P"]
- else map (fn i => "P" ^ string_of_int i) (1 upto length descr');
-
- fun make_pred i T =
- let val T' = T --> HOLogic.boolT
- in Free (List.nth (pnames, i), T') end;
-
- fun make_ind_prem k T (cname, cargs) =
- let
- fun mk_prem ((dt, s), T) =
- let val (Us, U) = strip_type T
- in list_all (map (pair "x") Us, HOLogic.mk_Trueprop
- (make_pred (body_index dt) U $ app_bnds (Free (s, T)) (length Us)))
- end;
-
- val recs = List.filter is_rec_type cargs;
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val recTs' = map (typ_of_dtyp descr' sorts) recs;
- val tnames = Name.variant_list pnames (make_tnames Ts);
- val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
- val frees = tnames ~~ Ts;
- val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
-
- in list_all_free (frees, Logic.list_implies (prems,
- HOLogic.mk_Trueprop (make_pred k T $
- list_comb (Const (cname, Ts ---> T), map Free frees))))
- end;
-
- val prems = List.concat (map (fn ((i, (_, _, constrs)), T) =>
- map (make_ind_prem i T) constrs) (descr' ~~ recTs));
- val tnames = make_tnames recTs;
- val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
- (map (fn (((i, _), T), tname) => make_pred i T $ Free (tname, T))
- (descr' ~~ recTs ~~ tnames)))
-
- in Logic.list_implies (prems, concl) end;
-
-(******************************* case distinction *****************************)
-
-fun make_casedists descr sorts =
- let
- val descr' = List.concat descr;
-
- fun make_casedist_prem T (cname, cargs) =
- let
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val frees = Name.variant_list ["P", "y"] (make_tnames Ts) ~~ Ts;
- val free_ts = map Free frees
- in list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop
- (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))),
- HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))))
- end;
-
- fun make_casedist ((_, (_, _, constrs)), T) =
- let val prems = map (make_casedist_prem T) constrs
- in Logic.list_implies (prems, HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)))
- end
-
- in map make_casedist
- ((hd descr) ~~ Library.take (length (hd descr), get_rec_types descr' sorts))
- end;
-
-(*************** characteristic equations for primrec combinator **************)
-
-fun make_primrec_Ts descr sorts used =
- let
- val descr' = List.concat descr;
-
- val rec_result_Ts = map TFree (Name.variant_list used (replicate (length descr') "'t") ~~
- replicate (length descr') HOLogic.typeS);
-
- val reccomb_fn_Ts = List.concat (map (fn (i, (_, _, constrs)) =>
- map (fn (_, cargs) =>
- let
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val recs = List.filter (is_rec_type o fst) (cargs ~~ Ts);
-
- fun mk_argT (dt, T) =
- binder_types T ---> List.nth (rec_result_Ts, body_index dt);
-
- val argTs = Ts @ map mk_argT recs
- in argTs ---> List.nth (rec_result_Ts, i)
- end) constrs) descr');
-
- in (rec_result_Ts, reccomb_fn_Ts) end;
-
-fun make_primrecs new_type_names descr sorts thy =
- let
- val descr' = List.concat descr;
- val recTs = get_rec_types descr' sorts;
- val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
-
- val (rec_result_Ts, reccomb_fn_Ts) = make_primrec_Ts descr sorts used;
-
- val rec_fns = map (uncurry (mk_Free "f"))
- (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
-
- val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
- val reccomb_names = map (Sign.intern_const thy)
- (if length descr' = 1 then [big_reccomb_name] else
- (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
- (1 upto (length descr'))));
- val reccombs = map (fn ((name, T), T') => list_comb
- (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
- (reccomb_names ~~ recTs ~~ rec_result_Ts);
-
- fun make_primrec T comb_t ((ts, f::fs), (cname, cargs)) =
- let
- val recs = List.filter is_rec_type cargs;
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val recTs' = map (typ_of_dtyp descr' sorts) recs;
- val tnames = make_tnames Ts;
- val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
- val frees = map Free (tnames ~~ Ts);
- val frees' = map Free (rec_tnames ~~ recTs');
-
- fun mk_reccomb ((dt, T), t) =
- let val (Us, U) = strip_type T
- in list_abs (map (pair "x") Us,
- List.nth (reccombs, body_index dt) $ app_bnds t (length Us))
- end;
-
- val reccombs' = map mk_reccomb (recs ~~ recTs' ~~ frees')
-
- in (ts @ [HOLogic.mk_Trueprop (HOLogic.mk_eq
- (comb_t $ list_comb (Const (cname, Ts ---> T), frees),
- list_comb (f, frees @ reccombs')))], fs)
- end
-
- in fst (Library.foldl (fn (x, ((dt, T), comb_t)) =>
- Library.foldl (make_primrec T comb_t) (x, #3 (snd dt)))
- (([], rec_fns), descr' ~~ recTs ~~ reccombs))
- end;
-
-(****************** make terms of form t_case f1 ... fn *********************)
-
-fun make_case_combs new_type_names descr sorts thy fname =
- let
- val descr' = List.concat descr;
- val recTs = get_rec_types descr' sorts;
- val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
- val newTs = Library.take (length (hd descr), recTs);
- val T' = TFree (Name.variant used "'t", HOLogic.typeS);
-
- val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
- map (fn (_, cargs) =>
- let val Ts = map (typ_of_dtyp descr' sorts) cargs
- in Ts ---> T' end) constrs) (hd descr);
-
- val case_names = map (fn s =>
- Sign.intern_const thy (s ^ "_case")) new_type_names
- in
- map (fn ((name, Ts), T) => list_comb
- (Const (name, Ts @ [T] ---> T'),
- map (uncurry (mk_Free fname)) (Ts ~~ (1 upto length Ts))))
- (case_names ~~ case_fn_Ts ~~ newTs)
- end;
-
-(**************** characteristic equations for case combinator ****************)
-
-fun make_cases new_type_names descr sorts thy =
- let
- val descr' = List.concat descr;
- val recTs = get_rec_types descr' sorts;
- val newTs = Library.take (length (hd descr), recTs);
-
- fun make_case T comb_t ((cname, cargs), f) =
- let
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val frees = map Free ((make_tnames Ts) ~~ Ts)
- in HOLogic.mk_Trueprop (HOLogic.mk_eq
- (comb_t $ list_comb (Const (cname, Ts ---> T), frees),
- list_comb (f, frees)))
- end
-
- in map (fn (((_, (_, _, constrs)), T), comb_t) =>
- map (make_case T comb_t) (constrs ~~ (snd (strip_comb comb_t))))
- ((hd descr) ~~ newTs ~~ (make_case_combs new_type_names descr sorts thy "f"))
- end;
-
-
-(*************************** the "split" - equations **************************)
-
-fun make_splits new_type_names descr sorts thy =
- let
- val descr' = List.concat descr;
- val recTs = get_rec_types descr' sorts;
- val used' = List.foldr OldTerm.add_typ_tfree_names [] recTs;
- val newTs = Library.take (length (hd descr), recTs);
- val T' = TFree (Name.variant used' "'t", HOLogic.typeS);
- val P = Free ("P", T' --> HOLogic.boolT);
-
- fun make_split (((_, (_, _, constrs)), T), comb_t) =
- let
- val (_, fs) = strip_comb comb_t;
- val used = ["P", "x"] @ (map (fst o dest_Free) fs);
-
- fun process_constr (((cname, cargs), f), (t1s, t2s)) =
- let
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val frees = map Free (Name.variant_list used (make_tnames Ts) ~~ Ts);
- val eqn = HOLogic.mk_eq (Free ("x", T),
- list_comb (Const (cname, Ts ---> T), frees));
- val P' = P $ list_comb (f, frees)
- in ((List.foldr (fn (Free (s, T), t) => HOLogic.mk_all (s, T, t))
- (HOLogic.imp $ eqn $ P') frees)::t1s,
- (List.foldr (fn (Free (s, T), t) => HOLogic.mk_exists (s, T, t))
- (HOLogic.conj $ eqn $ (HOLogic.Not $ P')) frees)::t2s)
- end;
-
- val (t1s, t2s) = List.foldr process_constr ([], []) (constrs ~~ fs);
- val lhs = P $ (comb_t $ Free ("x", T))
- in
- (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, mk_conj t1s)),
- HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, HOLogic.Not $ mk_disj t2s)))
- end
-
- in map make_split ((hd descr) ~~ newTs ~~
- (make_case_combs new_type_names descr sorts thy "f"))
- end;
-
-(************************* additional rules for TFL ***************************)
-
-fun make_weak_case_congs new_type_names descr sorts thy =
- let
- val case_combs = make_case_combs new_type_names descr sorts thy "f";
-
- fun mk_case_cong comb =
- let
- val Type ("fun", [T, _]) = fastype_of comb;
- val M = Free ("M", T);
- val M' = Free ("M'", T);
- in
- Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')),
- HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb $ M')))
- end
- in
- map mk_case_cong case_combs
- end;
-
-
-(*---------------------------------------------------------------------------
- * Structure of case congruence theorem looks like this:
- *
- * (M = M')
- * ==> (!!x1,...,xk. (M' = C1 x1..xk) ==> (f1 x1..xk = g1 x1..xk))
- * ==> ...
- * ==> (!!x1,...,xj. (M' = Cn x1..xj) ==> (fn x1..xj = gn x1..xj))
- * ==>
- * (ty_case f1..fn M = ty_case g1..gn M')
- *---------------------------------------------------------------------------*)
-
-fun make_case_congs new_type_names descr sorts thy =
- let
- val case_combs = make_case_combs new_type_names descr sorts thy "f";
- val case_combs' = make_case_combs new_type_names descr sorts thy "g";
-
- fun mk_case_cong ((comb, comb'), (_, (_, _, constrs))) =
- let
- val Type ("fun", [T, _]) = fastype_of comb;
- val (_, fs) = strip_comb comb;
- val (_, gs) = strip_comb comb';
- val used = ["M", "M'"] @ map (fst o dest_Free) (fs @ gs);
- val M = Free ("M", T);
- val M' = Free ("M'", T);
-
- fun mk_clause ((f, g), (cname, _)) =
- let
- val (Ts, _) = strip_type (fastype_of f);
- val tnames = Name.variant_list used (make_tnames Ts);
- val frees = map Free (tnames ~~ Ts)
- in
- list_all_free (tnames ~~ Ts, Logic.mk_implies
- (HOLogic.mk_Trueprop
- (HOLogic.mk_eq (M', list_comb (Const (cname, Ts ---> T), frees))),
- HOLogic.mk_Trueprop
- (HOLogic.mk_eq (list_comb (f, frees), list_comb (g, frees)))))
- end
-
- in
- Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')) ::
- map mk_clause (fs ~~ gs ~~ constrs),
- HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb' $ M')))
- end
-
- in
- map mk_case_cong (case_combs ~~ case_combs' ~~ hd descr)
- end;
-
-(*---------------------------------------------------------------------------
- * Structure of exhaustion theorem looks like this:
- *
- * !v. (? y1..yi. v = C1 y1..yi) | ... | (? y1..yj. v = Cn y1..yj)
- *---------------------------------------------------------------------------*)
-
-fun make_nchotomys descr sorts =
- let
- val descr' = List.concat descr;
- val recTs = get_rec_types descr' sorts;
- val newTs = Library.take (length (hd descr), recTs);
-
- fun mk_eqn T (cname, cargs) =
- let
- val Ts = map (typ_of_dtyp descr' sorts) cargs;
- val tnames = Name.variant_list ["v"] (make_tnames Ts);
- val frees = tnames ~~ Ts
- in
- List.foldr (fn ((s, T'), t) => HOLogic.mk_exists (s, T', t))
- (HOLogic.mk_eq (Free ("v", T),
- list_comb (Const (cname, Ts ---> T), map Free frees))) frees
- end
-
- in map (fn ((_, (_, _, constrs)), T) =>
- HOLogic.mk_Trueprop (HOLogic.mk_all ("v", T, mk_disj (map (mk_eqn T) constrs))))
- (hd descr ~~ newTs)
- end;
-
-end;