author | kleing |
Mon, 21 Jun 2004 10:25:57 +0200 | |
changeset 14981 | e73f8140af78 |
parent 14799 | a405aadff16c |
child 15459 | 16dd63c78049 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/datatype_prop.ML |
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ID: $Id$ |
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Author: Stefan Berghofer, TU Muenchen |
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Characteristic properties of datatypes. |
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*) |
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signature DATATYPE_PROP = |
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sig |
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val dtK : int ref |
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val indexify_names: string list -> string list |
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val make_tnames: typ list -> string list |
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val make_injs : DatatypeAux.descr list -> (string * sort) list -> term list list |
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val make_ind : DatatypeAux.descr list -> (string * sort) list -> term |
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val make_casedists : DatatypeAux.descr list -> (string * sort) list -> term list |
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val make_primrecs : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> term list |
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val make_cases : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> term list list |
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val make_distincts : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> term list list |
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val make_splits : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> (term * term) list |
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val make_size : DatatypeAux.descr list -> (string * sort) list -> |
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theory -> term list |
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val make_weak_case_congs : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> term list |
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val make_case_congs : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> term list |
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val make_nchotomys : DatatypeAux.descr list -> |
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(string * sort) list -> term list |
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end; |
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structure DatatypeProp : DATATYPE_PROP = |
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struct |
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open DatatypeAux; |
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(*the kind of distinctiveness axioms depends on number of constructors*) |
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val dtK = ref 7; |
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fun indexify_names names = |
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let |
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fun index (x :: xs) tab = |
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(case assoc (tab, x) of |
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None => if x mem xs then (x ^ "1") :: index xs ((x, 2) :: tab) else x :: index xs tab |
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| Some i => (x ^ Library.string_of_int i) :: index xs ((x, i + 1) :: tab)) |
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| index [] _ = []; |
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in index names [] end; |
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||
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fun make_tnames Ts = |
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let |
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fun type_name (TFree (name, _)) = implode (tl (explode name)) |
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| type_name (Type (name, _)) = |
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let val name' = Sign.base_name name |
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in if Syntax.is_identifier name' then name' else "x" end; |
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in indexify_names (map type_name Ts) end; |
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(************************* injectivity of constructors ************************) |
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fun make_injs descr sorts = |
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let |
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val descr' = flat descr; |
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fun make_inj T ((cname, cargs), injs) = |
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if null cargs then injs else |
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let |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val constr_t = Const (cname, Ts ---> T); |
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val tnames = make_tnames Ts; |
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val frees = map Free (tnames ~~ Ts); |
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val frees' = map Free ((map ((op ^) o (rpair "'")) tnames) ~~ Ts); |
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in (HOLogic.mk_Trueprop (HOLogic.mk_eq |
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(HOLogic.mk_eq (list_comb (constr_t, frees), list_comb (constr_t, frees')), |
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foldr1 (HOLogic.mk_binop "op &") |
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(map HOLogic.mk_eq (frees ~~ frees')))))::injs |
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end; |
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in map (fn (d, T) => foldr (make_inj T) (#3 (snd d), [])) |
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((hd descr) ~~ take (length (hd descr), get_rec_types descr' sorts)) |
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end; |
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(********************************* induction **********************************) |
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fun make_ind descr sorts = |
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let |
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val descr' = flat descr; |
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val recTs = get_rec_types descr' sorts; |
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val pnames = if length descr' = 1 then ["P"] |
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else map (fn i => "P" ^ string_of_int i) (1 upto length descr'); |
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fun make_pred i T = |
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let val T' = T --> HOLogic.boolT |
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in Free (nth_elem (i, pnames), T') end; |
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fun make_ind_prem k T (cname, cargs) = |
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let |
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fun mk_prem ((dt, s), T) = |
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let val (Us, U) = strip_type T |
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in list_all (map (pair "x") Us, HOLogic.mk_Trueprop |
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(make_pred (body_index dt) U $ app_bnds (Free (s, T)) (length Us))) |
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end; |
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val recs = filter is_rec_type cargs; |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val recTs' = map (typ_of_dtyp descr' sorts) recs; |
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val tnames = variantlist (make_tnames Ts, pnames); |
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val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs)); |
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val frees = tnames ~~ Ts; |
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val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); |
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in list_all_free (frees, Logic.list_implies (prems, |
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HOLogic.mk_Trueprop (make_pred k T $ |
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list_comb (Const (cname, Ts ---> T), map Free frees)))) |
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end; |
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val prems = flat (map (fn ((i, (_, _, constrs)), T) => |
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map (make_ind_prem i T) constrs) (descr' ~~ recTs)); |
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val tnames = make_tnames recTs; |
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val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") |
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(map (fn (((i, _), T), tname) => make_pred i T $ Free (tname, T)) |
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(descr' ~~ recTs ~~ tnames))) |
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in Logic.list_implies (prems, concl) end; |
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(******************************* case distinction *****************************) |
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fun make_casedists descr sorts = |
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let |
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val descr' = flat descr; |
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fun make_casedist_prem T (cname, cargs) = |
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let |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val frees = variantlist (make_tnames Ts, ["P", "y"]) ~~ Ts; |
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val free_ts = map Free frees |
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in list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop |
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(HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))), |
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HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)))) |
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end; |
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fun make_casedist ((_, (_, _, constrs)), T) = |
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let val prems = map (make_casedist_prem T) constrs |
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in Logic.list_implies (prems, HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))) |
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end |
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in map make_casedist |
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((hd descr) ~~ take (length (hd descr), get_rec_types descr' sorts)) |
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end; |
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(*************** characteristic equations for primrec combinator **************) |
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fun make_primrecs new_type_names descr sorts thy = |
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let |
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val sign = Theory.sign_of thy; |
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val descr' = flat descr; |
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val recTs = get_rec_types descr' sorts; |
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val used = foldr add_typ_tfree_names (recTs, []); |
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val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~ |
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replicate (length descr') HOLogic.typeS); |
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val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) => |
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map (fn (_, cargs) => |
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let |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val recs = filter (is_rec_type o fst) (cargs ~~ Ts); |
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fun mk_argT (dt, T) = |
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binder_types T ---> nth_elem (body_index dt, rec_result_Ts); |
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val argTs = Ts @ map mk_argT recs |
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in argTs ---> nth_elem (i, rec_result_Ts) |
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end) constrs) descr'); |
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val rec_fns = map (uncurry (mk_Free "f")) |
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(reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts))); |
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val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; |
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val reccomb_names = map (Sign.intern_const sign) |
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(if length descr' = 1 then [big_reccomb_name] else |
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(map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) |
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(1 upto (length descr')))); |
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val reccombs = map (fn ((name, T), T') => list_comb |
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(Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) |
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(reccomb_names ~~ recTs ~~ rec_result_Ts); |
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fun make_primrec T comb_t ((ts, f::fs), (cname, cargs)) = |
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let |
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val recs = filter is_rec_type cargs; |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val recTs' = map (typ_of_dtyp descr' sorts) recs; |
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val tnames = make_tnames Ts; |
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val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs)); |
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val frees = map Free (tnames ~~ Ts); |
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val frees' = map Free (rec_tnames ~~ recTs'); |
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fun mk_reccomb ((dt, T), t) = |
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let val (Us, U) = strip_type T |
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in list_abs (map (pair "x") Us, |
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nth_elem (body_index dt, reccombs) $ app_bnds t (length Us)) |
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end; |
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val reccombs' = map mk_reccomb (recs ~~ recTs' ~~ frees') |
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|
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in (ts @ [HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
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(comb_t $ list_comb (Const (cname, Ts ---> T), frees), |
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list_comb (f, frees @ reccombs')))], fs) |
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end |
213 |
||
214 |
in fst (foldl (fn (x, ((dt, T), comb_t)) => |
|
215 |
foldl (make_primrec T comb_t) (x, #3 (snd dt))) |
|
216 |
(([], rec_fns), descr' ~~ recTs ~~ reccombs)) |
|
217 |
end; |
|
218 |
||
219 |
(****************** make terms of form t_case f1 ... fn *********************) |
|
220 |
||
221 |
fun make_case_combs new_type_names descr sorts thy fname = |
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222 |
let |
|
223 |
val descr' = flat descr; |
|
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val recTs = get_rec_types descr' sorts; |
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val used = foldr add_typ_tfree_names (recTs, []); |
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val newTs = take (length (hd descr), recTs); |
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val T' = TFree (variant used "'t", HOLogic.typeS); |
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|
229 |
val case_fn_Ts = map (fn (i, (_, _, constrs)) => |
|
230 |
map (fn (_, cargs) => |
|
231 |
let val Ts = map (typ_of_dtyp descr' sorts) cargs |
|
232 |
in Ts ---> T' end) constrs) (hd descr); |
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233 |
||
234 |
val case_names = map (fn s => |
|
6394 | 235 |
Sign.intern_const (Theory.sign_of thy) (s ^ "_case")) new_type_names |
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in |
237 |
map (fn ((name, Ts), T) => list_comb |
|
238 |
(Const (name, Ts @ [T] ---> T'), |
|
239 |
map (uncurry (mk_Free fname)) (Ts ~~ (1 upto length Ts)))) |
|
240 |
(case_names ~~ case_fn_Ts ~~ newTs) |
|
241 |
end; |
|
242 |
||
243 |
(**************** characteristic equations for case combinator ****************) |
|
244 |
||
245 |
fun make_cases new_type_names descr sorts thy = |
|
246 |
let |
|
247 |
val descr' = flat descr; |
|
248 |
val recTs = get_rec_types descr' sorts; |
|
249 |
val newTs = take (length (hd descr), recTs); |
|
250 |
||
251 |
fun make_case T comb_t ((cname, cargs), f) = |
|
252 |
let |
|
253 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
254 |
val frees = map Free ((make_tnames Ts) ~~ Ts) |
|
255 |
in HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
256 |
(comb_t $ list_comb (Const (cname, Ts ---> T), frees), |
|
257 |
list_comb (f, frees))) |
|
258 |
end |
|
259 |
||
260 |
in map (fn (((_, (_, _, constrs)), T), comb_t) => |
|
261 |
map (make_case T comb_t) (constrs ~~ (snd (strip_comb comb_t)))) |
|
262 |
((hd descr) ~~ newTs ~~ (make_case_combs new_type_names descr sorts thy "f")) |
|
263 |
end; |
|
264 |
||
265 |
(************************* distinctness of constructors ***********************) |
|
266 |
||
267 |
fun make_distincts new_type_names descr sorts thy = |
|
268 |
let |
|
269 |
val descr' = flat descr; |
|
270 |
val recTs = get_rec_types descr' sorts; |
|
271 |
val newTs = take (length (hd descr), recTs); |
|
272 |
||
273 |
(**** number of constructors < dtK : C_i ... ~= C_j ... ****) |
|
274 |
||
275 |
fun make_distincts_1 _ [] = [] |
|
276 |
| make_distincts_1 T ((cname, cargs)::constrs) = |
|
277 |
let |
|
278 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
279 |
val frees = map Free ((make_tnames Ts) ~~ Ts); |
|
280 |
val t = list_comb (Const (cname, Ts ---> T), frees); |
|
281 |
||
282 |
fun make_distincts' [] = [] |
|
283 |
| make_distincts' ((cname', cargs')::constrs') = |
|
284 |
let |
|
285 |
val Ts' = map (typ_of_dtyp descr' sorts) cargs'; |
|
286 |
val frees' = map Free ((map ((op ^) o (rpair "'")) |
|
287 |
(make_tnames Ts')) ~~ Ts'); |
|
288 |
val t' = list_comb (Const (cname', Ts' ---> T), frees') |
|
289 |
in |
|
8434 | 290 |
(HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t, t'))):: |
291 |
(HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t', t))):: |
|
5177 | 292 |
(make_distincts' constrs') |
293 |
end |
|
294 |
||
295 |
in (make_distincts' constrs) @ (make_distincts_1 T constrs) |
|
296 |
end; |
|
297 |
||
298 |
in map (fn (((_, (_, _, constrs)), T), tname) => |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6394
diff
changeset
|
299 |
if length constrs < !dtK then make_distincts_1 T constrs else []) |
5177 | 300 |
((hd descr) ~~ newTs ~~ new_type_names) |
301 |
end; |
|
302 |
||
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6394
diff
changeset
|
303 |
|
5177 | 304 |
(*************************** the "split" - equations **************************) |
305 |
||
306 |
fun make_splits new_type_names descr sorts thy = |
|
307 |
let |
|
308 |
val descr' = flat descr; |
|
309 |
val recTs = get_rec_types descr' sorts; |
|
5578
7de426cf179c
Package now chooses type variable names more carefully to
berghofe
parents:
5177
diff
changeset
|
310 |
val used' = foldr add_typ_tfree_names (recTs, []); |
5177 | 311 |
val newTs = take (length (hd descr), recTs); |
12338
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
wenzelm
parents:
11957
diff
changeset
|
312 |
val T' = TFree (variant used' "'t", HOLogic.typeS); |
5177 | 313 |
val P = Free ("P", T' --> HOLogic.boolT); |
314 |
||
315 |
fun make_split (((_, (_, _, constrs)), T), comb_t) = |
|
316 |
let |
|
317 |
val (_, fs) = strip_comb comb_t; |
|
318 |
val used = ["P", "x"] @ (map (fst o dest_Free) fs); |
|
319 |
||
320 |
fun process_constr (((cname, cargs), f), (t1s, t2s)) = |
|
321 |
let |
|
322 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
323 |
val frees = map Free (variantlist (make_tnames Ts, used) ~~ Ts); |
|
324 |
val eqn = HOLogic.mk_eq (Free ("x", T), |
|
325 |
list_comb (Const (cname, Ts ---> T), frees)); |
|
326 |
val P' = P $ list_comb (f, frees) |
|
327 |
in ((foldr (fn (Free (s, T), t) => HOLogic.mk_all (s, T, t)) |
|
328 |
(frees, HOLogic.imp $ eqn $ P'))::t1s, |
|
329 |
(foldr (fn (Free (s, T), t) => HOLogic.mk_exists (s, T, t)) |
|
8434 | 330 |
(frees, HOLogic.conj $ eqn $ (HOLogic.Not $ P')))::t2s) |
5177 | 331 |
end; |
332 |
||
333 |
val (t1s, t2s) = foldr process_constr (constrs ~~ fs, ([], [])); |
|
334 |
val lhs = P $ (comb_t $ Free ("x", T)) |
|
335 |
in |
|
336 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, mk_conj t1s)), |
|
8434 | 337 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, HOLogic.Not $ mk_disj t2s))) |
5177 | 338 |
end |
339 |
||
340 |
in map make_split ((hd descr) ~~ newTs ~~ |
|
341 |
(make_case_combs new_type_names descr sorts thy "f")) |
|
342 |
end; |
|
343 |
||
344 |
||
345 |
(******************************* size functions *******************************) |
|
346 |
||
9739 | 347 |
fun make_size descr sorts thy = |
5177 | 348 |
let |
349 |
val descr' = flat descr; |
|
350 |
val recTs = get_rec_types descr' sorts; |
|
351 |
||
11957 | 352 |
val size_name = "Nat.size"; |
5177 | 353 |
val size_names = replicate (length (hd descr)) size_name @ |
9739 | 354 |
map (Sign.intern_const (Theory.sign_of thy)) (indexify_names |
355 |
(map (fn T => name_of_typ T ^ "_size") (drop (length (hd descr), recTs)))); |
|
5177 | 356 |
val size_consts = map (fn (s, T) => |
357 |
Const (s, T --> HOLogic.natT)) (size_names ~~ recTs); |
|
358 |
||
7704 | 359 |
fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2; |
5177 | 360 |
|
361 |
fun make_size_eqn size_const T (cname, cargs) = |
|
362 |
let |
|
363 |
val recs = filter is_rec_type cargs; |
|
364 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
365 |
val recTs = map (typ_of_dtyp descr' sorts) recs; |
|
366 |
val tnames = make_tnames Ts; |
|
367 |
val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs)); |
|
368 |
val ts = map (fn ((r, s), T) => nth_elem (dest_DtRec r, size_consts) $ |
|
369 |
Free (s, T)) (recs ~~ rec_tnames ~~ recTs); |
|
370 |
val t = if ts = [] then HOLogic.zero else |
|
7704 | 371 |
foldl1 plus (ts @ [HOLogic.mk_nat 1]) |
5177 | 372 |
in |
373 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (size_const $ |
|
374 |
list_comb (Const (cname, Ts ---> T), map Free (tnames ~~ Ts)), t)) |
|
375 |
end |
|
376 |
||
377 |
in |
|
378 |
flat (map (fn (((_, (_, _, constrs)), size_const), T) => |
|
379 |
map (make_size_eqn size_const T) constrs) (descr' ~~ size_consts ~~ recTs)) |
|
380 |
end; |
|
381 |
||
382 |
(************************* additional rules for TFL ***************************) |
|
383 |
||
8601 | 384 |
fun make_weak_case_congs new_type_names descr sorts thy = |
385 |
let |
|
386 |
val case_combs = make_case_combs new_type_names descr sorts thy "f"; |
|
387 |
||
388 |
fun mk_case_cong comb = |
|
389 |
let |
|
390 |
val Type ("fun", [T, _]) = fastype_of comb; |
|
391 |
val M = Free ("M", T); |
|
392 |
val M' = Free ("M'", T); |
|
393 |
in |
|
394 |
Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')), |
|
395 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb $ M'))) |
|
396 |
end |
|
397 |
in |
|
398 |
map mk_case_cong case_combs |
|
399 |
end; |
|
400 |
||
401 |
||
5177 | 402 |
(*--------------------------------------------------------------------------- |
403 |
* Structure of case congruence theorem looks like this: |
|
404 |
* |
|
405 |
* (M = M') |
|
406 |
* ==> (!!x1,...,xk. (M' = C1 x1..xk) ==> (f1 x1..xk = g1 x1..xk)) |
|
407 |
* ==> ... |
|
408 |
* ==> (!!x1,...,xj. (M' = Cn x1..xj) ==> (fn x1..xj = gn x1..xj)) |
|
409 |
* ==> |
|
410 |
* (ty_case f1..fn M = ty_case g1..gn M') |
|
411 |
*---------------------------------------------------------------------------*) |
|
412 |
||
413 |
fun make_case_congs new_type_names descr sorts thy = |
|
414 |
let |
|
415 |
val case_combs = make_case_combs new_type_names descr sorts thy "f"; |
|
416 |
val case_combs' = make_case_combs new_type_names descr sorts thy "g"; |
|
417 |
||
418 |
fun mk_case_cong ((comb, comb'), (_, (_, _, constrs))) = |
|
419 |
let |
|
420 |
val Type ("fun", [T, _]) = fastype_of comb; |
|
421 |
val (_, fs) = strip_comb comb; |
|
422 |
val (_, gs) = strip_comb comb'; |
|
423 |
val used = ["M", "M'"] @ map (fst o dest_Free) (fs @ gs); |
|
424 |
val M = Free ("M", T); |
|
425 |
val M' = Free ("M'", T); |
|
426 |
||
427 |
fun mk_clause ((f, g), (cname, _)) = |
|
428 |
let |
|
429 |
val (Ts, _) = strip_type (fastype_of f); |
|
430 |
val tnames = variantlist (make_tnames Ts, used); |
|
431 |
val frees = map Free (tnames ~~ Ts) |
|
432 |
in |
|
433 |
list_all_free (tnames ~~ Ts, Logic.mk_implies |
|
434 |
(HOLogic.mk_Trueprop |
|
435 |
(HOLogic.mk_eq (M', list_comb (Const (cname, Ts ---> T), frees))), |
|
436 |
HOLogic.mk_Trueprop |
|
437 |
(HOLogic.mk_eq (list_comb (f, frees), list_comb (g, frees))))) |
|
438 |
end |
|
439 |
||
440 |
in |
|
441 |
Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')) :: |
|
442 |
map mk_clause (fs ~~ gs ~~ constrs), |
|
443 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb' $ M'))) |
|
444 |
end |
|
445 |
||
446 |
in |
|
447 |
map mk_case_cong (case_combs ~~ case_combs' ~~ hd descr) |
|
448 |
end; |
|
449 |
||
450 |
(*--------------------------------------------------------------------------- |
|
451 |
* Structure of exhaustion theorem looks like this: |
|
452 |
* |
|
453 |
* !v. (? y1..yi. v = C1 y1..yi) | ... | (? y1..yj. v = Cn y1..yj) |
|
454 |
*---------------------------------------------------------------------------*) |
|
455 |
||
456 |
fun make_nchotomys descr sorts = |
|
457 |
let |
|
458 |
val descr' = flat descr; |
|
459 |
val recTs = get_rec_types descr' sorts; |
|
460 |
val newTs = take (length (hd descr), recTs); |
|
461 |
||
462 |
fun mk_eqn T (cname, cargs) = |
|
463 |
let |
|
464 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
465 |
val tnames = variantlist (make_tnames Ts, ["v"]); |
|
466 |
val frees = tnames ~~ Ts |
|
467 |
in |
|
468 |
foldr (fn ((s, T'), t) => HOLogic.mk_exists (s, T', t)) |
|
469 |
(frees, HOLogic.mk_eq (Free ("v", T), |
|
470 |
list_comb (Const (cname, Ts ---> T), map Free frees))) |
|
471 |
end |
|
472 |
||
473 |
in map (fn ((_, (_, _, constrs)), T) => |
|
474 |
HOLogic.mk_Trueprop (HOLogic.mk_all ("v", T, mk_disj (map (mk_eqn T) constrs)))) |
|
475 |
(hd descr ~~ newTs) |
|
476 |
end; |
|
477 |
||
478 |
end; |