Pass function as an argument in APL

Question

How do I pass a function as an argument?

The basic idea is something like this (which doesn't work):

∇R ← double a
R ← 2 × a
∇

∇R ← a applytwice f
R ← f f a
∇

5 applytwice double

Is there something like \fun in erlang or function-pointers in C?

Answer 1

In APL, functions may not be passed as arguments to functions. However, APL has operators, which are higher order functions, that can take functions as arguments. There are primitive operators like / (reduction) used for example to sum up a vector +/v. The function + is the left operand and is passed into the operator /.

In Dyalog APL, there is a primitive operator using the (named "power") for apply a function n times so we can write:

      double←{2×⍵}
      (double ⍣ 2) 7
28
      (double ⍣ 10) 7
7168

You can also write your own operators (in most APLs). In Dyalog APL we can write your applytwice operator as:

     applytwice←{⍺⍺ ⍺⍺ ⍵}
     double applytwice 7
28

Finally, you can pass functions around by putting them in a namespace and passing the namespace around instead. This is like a very light weight instance of class with a method. For example:

       s←⎕NS ''
       s.f←{2×⍵}
       ApplyFTwice←{⍺.f ⍺.f ⍵}
       s ApplyFTwice 7
28

In this case, the function has to be named f, but we could many different functions named f, each in its own namespace.