# Glossary

#### Arithmetic

Addition `(x + y)`, multiplication `(x * y)`, etc.

#### Dependent Type

A type that depends on another value. For example, a variable `n`‘s type might be “the length of `s`”, for some other slice-typed variable `s`. Dependent types are a way to implement bounds checking, but they’re not the only way. Wuffs does not use them.

#### Interval Arithmetic

See the interval arithmetic note.

#### Modular Arithmetic

Arithmetic that wraps around at a certain modulus, such as `256` for the `base.u8` type. For example, if `x` is a `base.u8` with value `200`, then `(x + 70)` has value `270` and would overflow, but `(x ~mod+ 70)` has value `14`.

#### Refinement Type

A basic type further constrained to a subset of its natural range. For example, if `x` has type `base.u8[0 ..= 99]` then it is an unsigned 8-bit integer whose value must be less than `100`. Without the refinement, `x` could be as high as `255`.

`base.u8[0 ..= 99]` and `base.u32[0 ..= 99]` are two different types. They can have different run-time representations.

Non-nullable pointer types can be thought of as a refinement of regular pointer types, where the refined range excludes the `nullptr` value.

#### Saturating Arithmetic

Arithmetic that stops at certain bounds, such as `0` and `255` for the `base.u8` type. For example, if `x` is a `base.u8` with value `200`, then `(x + 70)` has value `270` and would overflow, but `(x ~sat+ 70)` has value `255`.