2F. Hooks

A pair of functions in isolation form a hook whose monadic case is defined as in:

hence the function h=: =<. compares its argument with its integer part, and therefore provides a test for integers. Hooks occur frequently in most sections.

m0=: It=: =<.

Integer test

m1=: Rt=: =+

Real test

d2=: $,:

x copies of y

d3=: $,

Reshape as in APL

m4=: cf=: (+%)/

Continued fraction

m5=: cfc=: (+%)/\

Continued fraction convergents

m6=: ifb=: # i.@#

Integers from boolean list

m7=: [m

([m)y invokes m y , then returns y 

For example: 

   cf 3 7 15 1          NB. Approximation to pi
3.14159

   cfc 3 7 15 1         NB. Convergents to pi
3 3.14286 3.14151 3.14159        

   cfc 1 1 1 1 1 1 1    NB. Convergents to golden mean
1 2 1.5 1.66667 1.6 1.625 1.61538       

   cfc 10$1x            NB. As above in extended precision
1 2 3r2 5r3 8r5 13r8 21r13 34r21 55r34 89r55