Primitives

Overview

The following primitive types have been identified.

All other types can be composed from them by using those and the operators.

Primitives

The Any type (upper boundary)

The Any type is often used to explicitly allow arbitrary values. However, the Any type is complex and doesn't add much value to a type system. Instead, we should use type variables whenever possible.

Interestingly there are two different Any types:

e.g. If we look at CUE-lang (which is also inspired by nix)

CUE defines the values bottom, or error, (denoted |) that is an instance of all types and top, or any, (denoted _) of which all types are an instance.

• TOP any all types are an instance of that. You can imagine it as the TOP-most set, that includes every type. But no value has that type.

• Bottom any which is an instance of all types. This is kind of the imaginary value that has the any type. Still, doesn't contain any value. Which could also be denoted: Never or Empty Type it is a type that is the subtype of any type.

The following is a nice quote from the Typescript world

The any type is so dangerous because it exists outside of the type tree. It is both a top and bottom type. Everything can be assigned to it and it can be assigned to everything else. ...

I think it might make most sense to define Any as TOP in our type system. This means it is the upper boundary of our type system. All types within the system are a subtype of Any.

Never (lower boundary)

I think it makes most sense to have a distinct Bottom type. Other type systems call this: Bottom any or Empty Type. This is the lower boundary of our type system. All types are a supertype of Never and that is true for all types that may eventualy exist in this type system.

The easiest way of thinking about Never is this example:

let
 # a -> Never
 f = x: abort "now";
 # Never <- f 42
 result = f 42;
in
 # result :: Never
 result

A function f that takes Any argument and since it aborts the evaluation it returns Never.

Never might need its own chapter since it requires understanding lazyness in the language to determine which expression returns never during evaluation.

The Bool type

As the Bool type can only have two values (true/false)

The following is the definition of the Bool type

Bool :: true | false