Every expression in disco has a type, which tells us what kind of value will result when we evaluate the expression. For example, if an expression has type N, it means we are guaranteed to get a natural number as a result once the expression is done being evaluated.

The type of an expression thus represents a promise or guarantee about the behavior of a program. Checking that all the types in a program match up can also be seen as a way of predicting or analyzing the behavior of a program without actually running it.

Each type can be thought of as a collection of values which all have a similar “shape”.

The type of each variable in Disco must be declared with a type signature. We can also give Disco hints about the intended type of an expression using a type annotation. We can define our own new types using a type definition.

In some situations, Disco may be willing to accept something of one type when it was expecting another: specifically, when the given type is a subtype of the one it was expecting.