Modifiers and Functions

Preamble

We'll be using reduce. If you're familiar with reduce from other languages, be careful about the specifics, especially with functions like sub and div. Their order of operation might go against your intuition from other programming languages.

With prior experience, your mental model of a reduce might be something like this

For an array, reduce <function> will apply the function on all elements of the array, pairwise left to right, while keeping a running score.

And is that right?

    reduce + [5 10 15]
    /+ [5 10 15]
30

# Huh, shouldn't this be -13?
    reduce sub [1 2 3 4 5]
    /- [1 2 3 4 5]
3

We can quickly examine the consequences of the order in which Uiua operates with functions such as sub and div with the following typescript example:

> [1,2,3,4,5].reduce((a,b) => a-b)
-13

> [1,2,3,4,5].reduce((a,b) => b-a)
3

If you really want the former you can simply use the back modifier

    reduce back sub [1 2 3 4 5]
    /˜- [1 2 3 4 5]

Challenge 1

Write a program that calculates the product of the first n positive integers.

C1 Solution

/×+1⇡

or the idiomatic solution

/×⇡₁

Why?

Let's take n=5 as an example and work through it step by step

# What is the product?
    mul mul mul mul 1 2 3 4 5
    × × × × 1 2 3 4 5
120

# We can't just write mul over and over
# We can use `reduce mul` instead
    reduce mul [1 2 3 4 5]
    /× [1 2 3 4 5]
120

# Ok, but let's not write out
# 1 2 3 4 5. Range to the rescue
    ⇡5
[0 1 2 3 4]

# Let's add 1 to the range
    +1 ⇡5
[1 2 3 4 5]

# Putting it all together
    reduce mul add 1 range 5
    /× + 1 ⇡ 5
120

But what about the idiomatic solution?

The Uiua docs page for subscripts is worth skimming through. Basically, using a comma, ,, after a function and then following it with a number, will create a subscript for that function. These have varying properties and it is good to read the documentation for a function to gauge it.

Try that now: The Uiua docs for range has a section in it that explains what happens.

# Why was six afraid of seven?
    range,7 9
    ⇡₇9
[7 8 9]

Challenge 2

Write a program that adds each column of a matrix to the next.

C2 Solution

≡/+

Why?

You might be comfortable with reduce by now but you can read the preamble and problem 1 for a refresher.

I think it is helpful to look at two examples with reverse to see visually what rows does.

# Reverses each row. 1_2_3 → 3_2_1
    rows reverse [1_2_3 4_5_6 7_8_9]
    ≡⇌ [1_2_3 4_5_6 7_8_9]
╭─       
╷ 3 2 1  
  6 5 4  
  9 8 7  
        ╯

# Reverse here is not modified to
# operate on rows. Therefore the 
# whole 2D array is reversed instead
    reverse [1_2_3 4_5_6 7_8_9]
    ⇌ [1_2_3 4_5_6 7_8_9]
╭─       
╷ 7 8 9  
  4 5 6  
  1 2 3  
        ╯

Exercise C2-1

What is the difference between reduce add [1_2 3_4 5_6] and rows reduce add [1_2 3_4 5_6]?