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Back to FP, Continued. On to Introduction to Logic Programming.
Held Friday, March 12
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Def fact = eq0 -> one ; recurse
one
Def one = constant 1
%
in
our implementation of fp.
{one %1}
eq0
id
Def eq0 = = @ [id,%0]
@
is function composition
[...]
if function construction
{eq0 = @ [id,%0]}
sub1
Def sub1 = - @ [id,%1]
{sub1 - @ [id,%1]}
* @ [id, fact@sub1]
{fact (eq0 -> %1 ; * @ [id, fact@sub1])}
[%1, %1, id]
+ @ [id,%1] @ 1
1
is a selector, which extracts the first
part of the tuple.
+ @ [1,%1]
* @ [1,2]
3
[+ @ [id,%1], * @ [1,2], 3]
< @ [1,3]
Def itfact = 2 @ (while (<= @ [1,3]) ([+ @ [1,%1], * @ [1,2], 3])) @ [%1, %1, id]
{itfact 2 @ (while (<= @ [1,3]) ([+ @ [1,%1], * @ [1,2], 3])) @ [%1, %1, id]}
iota
.
iota:n
gives all the numbers from 1 to n,
we just want to insert multiplication between them.
{newfact !*@iota}
fact 0 = 1 fact n = n * fact n-1
car (cons x xs) = x cdr (cons x xs) = xs
if True x y = x if False x y = y
square (plus 2 3)
,
(given the defintion of square
as
square x = times x x
square (plus 2 3) => times (plus 2 3) (plus 2 3) => times 5 (plus 2 3) => times 5 5 => 25
square (plus 2 3) => square 5 => times 5 5 25
fact n = iif (n == 0) 1 (n * (fact (n - 1)))
fact 1 => iif (1 == 0) 1 (1 * (fact (1 - 1))) => iif false 1 (n * (fact (1 - 1))) => iif false 1 (n * (fact 0)) => iif false 1 (iif (0 == 0) 1 (0 * (fact (0-1)))) => iif false 1 (iif false 1 (0 * (fact (0-1)))) => iif false 1 (iif false 1 (0 * (fact (-1)))) => iif false 1 (iif false 1 (0 * (iif (-1 == 0) 1 (-1 * fact(-1-1))))) => ...
History
Back to FP, Continued. On to Introduction to Logic Programming.
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