Macros

Preamble

These challenges are solved using index macros. There is another type of macro, the code macro, that generates Uiua code to be run. They are even so powerful that they can create bindings. It's fun reading about though personally I have not used them much.

Challenge 1

Write a program that creates a macro called F! which calls its function on each row of an array, reverses each row, and reverses the whole array.

C1 Solution

F! ← ⇌≡(⇌^)

Or explicitly

F! ← ⇌≡(⇌^0)

Why?

The program we're being asked to write is not that complicated, it's just about how we get there and understanding what a macro does. Let's start by choosing a function, say self add, that multiplies a number by two.

If we multiply each row of an array by two, reverse the row and then reverse the whole array it looks like this

    ⇌ ≡(⇌˙+) [1_2_3 4_5_6 7_8_9]
╭─
╷ 18 16 14
  12 10  8
   6  4  2
           ╯

If we deem the action of applying functions this way useful, we can generalize it with a macro. To make it an index macro we define the same operations, except, we substitute self add with ^. I think it's helpful to think of index macros as being text substitutions on code. Let's look at the function self mul, provide it to the macro and then run it again as if it were substituted

    F! ← ⇌≡(⇌^0)

    F!˙× [1_2_3 4_5_6 7_8_9]
╭─
╷ 81 64 49
  36 25 16
   9  4  1
           ╯

Invoking F! self mul is the same thing as substituting the F! definition with self mul where ^ appears.

    ⇌ ≡(⇌ ˙×) [1_2_3 4_5_6 7_8_9]
╭─
╷ 81 64 49
  36 25 16
   9  4  1
           ╯

Challenge 2

Write a program that creates a macro called F‼ which calls its first function, then its second, then its first again.

C2 Solution

    F‼ ← ^0^1^0

Why?

Let's say we want to create a function that multiplies a number by three, adds one and then multiplies by three again.

We might do it like this

    H ← +₁
    G ← ×₃
    F ← H G H

    F 5
19

In Fs body we have two functions, three function invocations. There is an easy way to convert this to an index macro by substituting the functions with ^n where n represents the argument position into the macro. The first function is n=0, the second n=1 and so on. Let's substitute H → ^0 and G →^1. Just remember that a macro needs to be defined with !s as many as there are ^s.

    F ← H G H
    F‼ ← ^0^1^0

and we can invoke it like so

    F‼+₁×₃ 5
19

At this point we do have what is asked for. A macro that calls its first function, then second, then again its first.

We can do whatever. Why not get a number's largest prime factor, square it and get the largest prime factor of the result

    F‼(⊣°/×)˙× 11
11
    F‼(⊣°/×)˙× 13
13
    F‼(⊣°/×)˙× 15
5
    F‼(⊣°/×)˙× 16
2