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Lists
and list operators are usually
"built in"
with programming languages based on Lambda Calculus
but they can be defined in Lambda Calculus.
The following example shows a way to
define CONS, NIL, HD (head), TL (tail), NULL.
(PRINT is a cheat because it is defined using the
system's built-in lists (::),
but it too could be defined in Lambda Calculus.)
let rec
CONS = lambda h. lambda t. lambda f. f h t,
NIL = lambda f. true,
NULL = lambda L. L (lambda h. lambda t. false),
HD = lambda L. L (lambda h. lambda t. h),
TL = lambda L. L (lambda h. lambda t. t),
PRINT = lambda L.
if NULL L then '/' else (HD L)::(PRINT (TL L))
in let L = CONS 1 (CONS 2 (CONS 3 NIL)) {an e.g.}
in PRINT( CONS (NULL NIL) {T}
( CONS (NULL L) {F}
( CONS (HD L) {1}
( CONS (HD (TL L)) {2}
( CONS (HD (TL (TL L))) {3}
NIL))))) {/}
{\fB Define (Flat) Lists From Scratch. \fP}
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Also see
[Boolean]
and
[Ints].
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λ ...
| :: | list cons |
| nil | the [ ] list |
| null | predicate |
| hd | head (1st) |
| tl | tail (rest) |
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