Chapter 4. Values and Types

Goal

By the end of this chapter you will know the kinds of value Keleusma works with, and the name of the type that each kind belongs to.

A type is a set of values that make sense together

A frequency, such as 261.6 hertz, is a fractional number. A count of beats is a whole number. Whether a note is sounding right now is a plain yes or no. These are different kinds of value, and a kind of value is called a type. The type is how the language knows what makes sense for a value and what does not.

This chapter uses the interactive prompt. Start it with keleusma repl and type along.

Word, a whole number

A Word is a whole number. Counts are words: a number of beats, a number of semitones, a MIDI note number.

> 12
12
> 7 + 5
12

One result will surprise you. Dividing one Word by another throws away any remainder:

> 7 / 2
3

Seven divided by two is three, with one left over, and the leftover is discarded. Whole-number division always rounds toward zero. When a fraction is needed, the next type is the one to reach for.

Float, a fractional number

A Float is a number that can have a fractional part. Frequencies are floats. A float is written with a decimal point, and the point is what tells the language the value is a float and not a word.

> 3.5
3.5
> 7.0 / 2.0
3.5

Note the .0 in 7.0 and 2.0. Dividing two floats keeps the fractional part, so 7.0 / 2.0 is 3.5, not 3.

bool, true or false

A bool is the answer to a yes-or-no question. It has exactly two values, true and false. A comparison produces a bool:

> 3 < 5
true

Text, written words

A Text value is a piece of writing. It is written between double quotes.

> "middle C"
middle C

Unit, no value at all

Unit is the type of (), which is read aloud as “unit.” It means there is no meaningful value. A function that does something useful but has nothing to hand back returns ().

> ()
()

A few more number types, met later

Keleusma has three further number types. None is needed in Part II, so they are only named here.

• Byte is an eight-bit whole number, used for byte-level work. It appears in Chapter 23.
• Fixed is a fractional number with fully deterministic, repeatable arithmetic, used where audio code must produce the exact same result every time. The piano roll uses it.
• Multiword<N, F> is a fixed-width multi-word number, N words wide with F fractional bits, for values too large for a single Word. It appears in Chapter 23.

Why types matter

Every value in a Keleusma program has a type, and the language checks, before the program runs, that values are only used where their type makes sense. Handing a frequency to a function that expects a count of beats is caught at that check, not discovered later as a wrong note. The types are a safety net stretched under the whole program.

What you now know

• Word is a whole number, and whole-number division drops the remainder.
• Float is a fractional number, written with a decimal point.
• bool is true or false.
• Text is writing in double quotes.
• Unit, written (), means no value.
• Byte, Fixed, and Multiword<N, F> are further number types, met later.

The next chapter gives values names.