ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
domrange/image_subset,vimage_subset: deleted needless premise!
misc: This slightly simplifies two proofs in Schroeder-Bernstein Theorem
ind-syntax/rule_concl: recoded to avoid exceptions
intr-elim: now checks conclusions of introduction rules
func/fun_disjoint_Un: now uses ex_ex1I
list-fn/hd,tl,drop: new
simpdata/bquant_simps: new
list/list_case_type: restored!
bool.thy: changed 1 from a "def" to a translation
Removed occurreces of one_def in bool.ML, nat.ML, univ.ML, ex/integ.ML
nat/succ_less_induct: new induction principle
arith/add_mono: new results about monotonicity
simpdata/mem_simps: removed the ones for succ and cons; added succI1,
consI2 to ZF_ss
upair/succ_iff: new, for use with simp_tac (cons_iff already existed)
ordinal/Ord_0_in_succ: renamed from Ord_0_mem_succ
nat/nat_0_in_succ: new
ex/prop-log/hyps_thms_if: split up the fast_tac call for more speed
(* Title: ZF/list-fn
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Functions for Lists in Zermelo-Fraenkel Set Theory
map is a binding operator -- it applies to meta-level functions, not
object-level functions. This simplifies the final form of term_rec_conv,
although complicating its derivation.
*)
ListFn = List +
consts
"@" :: "[i,i]=>i" (infixr 60)
list_rec :: "[i, i, [i,i,i]=>i] => i"
map :: "[i=>i, i] => i"
length,rev :: "i=>i"
flat :: "i=>i"
list_add :: "i=>i"
hd,tl :: "i=>i"
drop :: "[i,i]=>i"
(* List Enumeration *)
"[]" :: "i" ("[]")
"@List" :: "args => i" ("[(_)]")
translations
"[x, xs]" == "Cons(x, [xs])"
"[x]" == "Cons(x, [])"
"[]" == "Nil"
rules
hd_def "hd(l) == list_case(0, %x xs.x, l)"
tl_def "tl(l) == list_case(Nil, %x xs.xs, l)"
drop_def "drop(i,l) == rec(i, l, %j r. tl(r))"
list_rec_def
"list_rec(l,c,h) == Vrec(l, %l g.list_case(c, %x xs. h(x, xs, g`xs), l))"
map_def "map(f,l) == list_rec(l, Nil, %x xs r. Cons(f(x), r))"
length_def "length(l) == list_rec(l, 0, %x xs r. succ(r))"
app_def "xs@ys == list_rec(xs, ys, %x xs r. Cons(x,r))"
rev_def "rev(l) == list_rec(l, Nil, %x xs r. r @ [x])"
flat_def "flat(ls) == list_rec(ls, Nil, %l ls r. l @ r)"
list_add_def "list_add(l) == list_rec(l, 0, %x xs r. x#+r)"
end