Compose

>> << Usr Pri JfC LJ Phr Dic Voc !: Help Dictionary

Compose

u&v mv mv mv

u&v y ↔ u v y . Thus +:&- 7 is _14 (double the negation). Moreover, the monads u&v and u@v are equivalent. x u&v y ↔ (v x) u (v y) . For example, 3 +&! 4 is 30, the sum of factorials.

The monadic case is equivalent to the composition used in mathematics, but the dyadic case opens up other possibilities. For example:

   3 +&^. 4                    NB. Sum of natural logarithms
2.48491

   ^ 3 +&^. 4                  NB. Multiplication using natural logs
12

   3 +&(10&^.) 4               NB. Sum of base ten logarithms
1.07918

   10 ^ 3 +&(10&^.) 4          NB. Multiplication using base ten logs
12

   3 +&.^. 4                   NB. See the related conjunction Under (&.)
12

   3 +&.(10&^.) 4
12

Compare the behaviour of & with that of &: . They differ only in the ranks of the verbs that they produce.

>> << Usr Pri JfC LJ Phr Dic Voc !: Help Dictionary