--- a/src/HOL/Tools/Datatype/datatype_prop.ML Mon Sep 01 16:17:46 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,427 +0,0 @@
-(* Title: HOL/Tools/Datatype/datatype_prop.ML
- Author: Stefan Berghofer, TU Muenchen
-
-Datatype package: characteristic properties of datatypes.
-*)
-
-signature DATATYPE_PROP =
-sig
- type descr = Datatype_Aux.descr
- val indexify_names: string list -> string list
- val make_tnames: typ list -> string list
- val make_injs : descr list -> term list list
- val make_distincts : descr list -> term list list (*no symmetric inequalities*)
- val make_ind : descr list -> term
- val make_casedists : descr list -> term list
- val make_primrec_Ts : descr list -> string list -> typ list * typ list
- val make_primrecs : string list -> descr list -> theory -> term list
- val make_cases : string list -> descr list -> theory -> term list list
- val make_splits : string list -> descr list -> theory -> (term * term) list
- val make_case_combs : string list -> descr list -> theory -> string -> term list
- val make_case_cong_weaks : string list -> descr list -> theory -> term list
- val make_case_congs : string list -> descr list -> theory -> term list
- val make_nchotomys : descr list -> term list
-end;
-
-structure Datatype_Prop : DATATYPE_PROP =
-struct
-
-type descr = Datatype_Aux.descr;
-
-
-val indexify_names = Case_Translation.indexify_names;
-val make_tnames = Case_Translation.make_tnames;
-
-fun make_tnames Ts =
- let
- fun type_name (TFree (name, _)) = unprefix "'" name
- | type_name (Type (name, _)) =
- let val name' = Long_Name.base_name name
- in if Symbol_Pos.is_identifier name' then name' else "x" end;
- in indexify_names (map type_name Ts) end;
-
-
-(************************* injectivity of constructors ************************)
-
-fun make_injs descr =
- let
- val descr' = flat descr;
- fun make_inj T (cname, cargs) =
- if null cargs then I
- else
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val constr_t = Const (cname, Ts ---> T);
- val tnames = make_tnames Ts;
- val frees = map Free (tnames ~~ Ts);
- val frees' = map Free (map (suffix "'") 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 @{const_name HOL.conj})
- (map HOLogic.mk_eq (frees ~~ frees')))))
- end;
- in
- map2 (fn d => fn T => fold_rev (make_inj T) (#3 (snd d)) [])
- (hd descr) (take (length (hd descr)) (Datatype_Aux.get_rec_types descr'))
- end;
-
-
-(************************* distinctness of constructors ***********************)
-
-fun make_distincts descr =
- let
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val newTs = take (length (hd descr)) recTs;
-
- fun prep_constr (cname, cargs) = (cname, map (Datatype_Aux.typ_of_dtyp descr') 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 (suffix "'") (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 =>
- make_distincts' T (map prep_constr constrs)) (hd descr) newTs
- end;
-
-
-(********************************* induction **********************************)
-
-fun make_ind descr =
- let
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- 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 (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
- Logic.list_all (map (pair "x") Us,
- HOLogic.mk_Trueprop
- (make_pred (Datatype_Aux.body_index dt) U $
- Datatype_Aux.app_bnds (Free (s, T)) (length Us)))
- end;
-
- val recs = filter Datatype_Aux.is_rec_type cargs;
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val recTs' = map (Datatype_Aux.typ_of_dtyp descr') recs;
- val tnames = Name.variant_list pnames (make_tnames Ts);
- val rec_tnames = map fst (filter (Datatype_Aux.is_rec_type o snd) (tnames ~~ cargs));
- val frees = tnames ~~ Ts;
- val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
- in
- fold_rev (Logic.all o 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 =
- maps (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 @{const_name HOL.conj})
- (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 =
- let
- val descr' = flat descr;
-
- fun make_casedist_prem T (cname, cargs) =
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val frees = Name.variant_list ["P", "y"] (make_tnames Ts) ~~ Ts;
- val free_ts = map Free frees;
- in
- fold_rev (Logic.all o 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
- map2 make_casedist (hd descr)
- (take (length (hd descr)) (Datatype_Aux.get_rec_types descr'))
- end;
-
-(*************** characteristic equations for primrec combinator **************)
-
-fun make_primrec_Ts descr used =
- let
- val descr' = flat descr;
-
- val rec_result_Ts =
- map TFree
- (Name.variant_list used (replicate (length descr') "'t") ~~
- replicate (length descr') @{sort type});
-
- val reccomb_fn_Ts = maps (fn (i, (_, _, constrs)) =>
- map (fn (_, cargs) =>
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val recs = filter (Datatype_Aux.is_rec_type o fst) (cargs ~~ Ts);
-
- fun mk_argT (dt, T) =
- binder_types T ---> nth rec_result_Ts (Datatype_Aux.body_index dt);
-
- val argTs = Ts @ map mk_argT recs
- in argTs ---> nth rec_result_Ts i end) constrs) descr';
-
- in (rec_result_Ts, reccomb_fn_Ts) end;
-
-fun make_primrecs reccomb_names descr thy =
- let
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val used = fold Term.add_tfree_namesT recTs [];
-
- val (rec_result_Ts, reccomb_fn_Ts) = make_primrec_Ts descr used;
-
- val rec_fns =
- map (uncurry (Datatype_Aux.mk_Free "f"))
- (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
-
- 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 (cname, cargs) (ts, f :: fs) =
- let
- val recs = filter Datatype_Aux.is_rec_type cargs;
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val recTs' = map (Datatype_Aux.typ_of_dtyp descr') recs;
- val tnames = make_tnames Ts;
- val rec_tnames = map fst (filter (Datatype_Aux.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
- fold_rev (Term.abs o pair "x") Us
- (nth reccombs (Datatype_Aux.body_index dt) $ Datatype_Aux.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
- fold (fn ((dt, T), comb_t) => fold (make_primrec T comb_t) (#3 (snd dt)))
- (descr' ~~ recTs ~~ reccombs) ([], rec_fns)
- |> fst
- end;
-
-(****************** make terms of form t_case f1 ... fn *********************)
-
-fun make_case_combs case_names descr thy fname =
- let
- 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", @{sort type});
-
- val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
- map (fn (_, cargs) =>
- let val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs
- in Ts ---> T' end) constrs) (hd descr);
- in
- map (fn ((name, Ts), T) => list_comb
- (Const (name, Ts @ [T] ---> T'),
- map (uncurry (Datatype_Aux.mk_Free fname)) (Ts ~~ (1 upto length Ts))))
- (case_names ~~ case_fn_Ts ~~ newTs)
- end;
-
-(**************** characteristic equations for case combinator ****************)
-
-fun make_cases case_names descr thy =
- let
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val newTs = take (length (hd descr)) recTs;
-
- fun make_case T comb_t ((cname, cargs), f) =
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') 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 case_names descr thy "f")
- end;
-
-
-(*************************** the "split" - equations **************************)
-
-fun make_splits case_names descr thy =
- let
- 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", @{sort type});
- 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 (Datatype_Aux.typ_of_dtyp descr') 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
- (fold_rev (fn Free (s, T) => fn t => HOLogic.mk_all (s, T, t)) frees
- (HOLogic.imp $ eqn $ P') :: t1s,
- fold_rev (fn Free (s, T) => fn t => HOLogic.mk_exists (s, T, t)) frees
- (HOLogic.conj $ eqn $ (HOLogic.Not $ P')) :: t2s)
- end;
-
- val (t1s, t2s) = fold_rev process_constr (constrs ~~ fs) ([], []);
- val lhs = P $ (comb_t $ Free ("x", T));
- in
- (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, Datatype_Aux.mk_conj t1s)),
- HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, HOLogic.Not $ Datatype_Aux.mk_disj t2s)))
- end
-
- in
- map make_split (hd descr ~~ newTs ~~ make_case_combs case_names descr thy "f")
- end;
-
-(************************* additional rules for TFL ***************************)
-
-fun make_case_cong_weaks case_names descr thy =
- let
- val case_combs = make_case_combs case_names descr 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 case_names descr thy =
- let
- val case_combs = make_case_combs case_names descr thy "f";
- val case_combs' = make_case_combs case_names descr 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 = binder_types (fastype_of f);
- val tnames = Name.variant_list used (make_tnames Ts);
- val frees = map Free (tnames ~~ Ts);
- in
- fold_rev Logic.all frees
- (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 =
- let
- val descr' = flat descr;
- val recTs = Datatype_Aux.get_rec_types descr';
- val newTs = take (length (hd descr)) recTs;
-
- fun mk_eqn T (cname, cargs) =
- let
- val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
- val tnames = Name.variant_list ["v"] (make_tnames Ts);
- val frees = tnames ~~ Ts;
- in
- fold_rev (fn (s, T') => fn t => HOLogic.mk_exists (s, T', t)) frees
- (HOLogic.mk_eq (Free ("v", T),
- list_comb (Const (cname, Ts ---> T), map Free frees)))
- end;
- in
- map (fn ((_, (_, _, constrs)), T) =>
- HOLogic.mk_Trueprop
- (HOLogic.mk_all ("v", T, Datatype_Aux.mk_disj (map (mk_eqn T) constrs))))
- (hd descr ~~ newTs)
- end;
-
-end;