src/ZF/List.thy
 author paulson Fri, 16 Feb 1996 18:00:47 +0100 changeset 1512 ce37c64244c0 parent 1478 2b8c2a7547ab child 1806 12708740f58d permissions -rw-r--r--
Elimination of fully-functorial style. Type tactic changed to a type abbrevation (from a datatype). Constructor tactic and function apply deleted.
```
(*  Title:      ZF/List
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright   1994  University of Cambridge

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.
*)

List = Datatype +

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
hd,tl      :: i=>i
drop       :: [i,i]=>i

(* List Enumeration *)
"[]"        :: i                                       ("[]")
"@List"     :: is => i                                 ("[(_)]")

list       :: i=>i

datatype
"list(A)" = Nil | Cons ("a:A", "l: list(A)")

translations
"[x, xs]"     == "Cons(x, [xs])"
"[x]"         == "Cons(x, [])"
"[]"          == "Nil"

defs

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
```