Chapter 3

More Built-In Types

Typed Scheme comes with a number of other types and type constructors, corresponding (mostly) to primitive types provided by PLT Scheme.

• The base types represent primitive data

  • number Any number

  • str A string

  • symbol A symbol

  • boolean Either #t or #f

  • keyword A PLT Scheme literal keyword

  • top Any value

• The following constructors are parameteric in a single type argument

  • (Listof t) Homogenous lists of t

  • (Vectorof t) Homogenous vectors of t

  • (Option t) Either t or #f

• (cons s t) is the pair containing s as the car and t as the cdr

• (dom ... -> rng) is the type of functions from the (possibly-empty) sequence dom ... to the rng type.

• (dom ... rst .. -> rng) is the type of functions from the (possibly-empty) sequence dom ... with an optional trailing sequence of rst to the rng type. Note: .. is a part of the syntax of these types.

• (U t ...) is the union of the types t ...

• (case-lambda fun-ty ...) is a function that behaves like all of the fun-tys. The fun-tys must all be function types constructed with ->.

• (t t1 t2 ...) is the instantiation of the parametric type t at types t1 t2 ...

• (pred t) is a predicate for type t

• (All (v ...) t) is a parameterization of type t, with type variables v ...

• (values t ...) is the type of a sequence of multiple values, with types t .... This can only appear as the return type of a function.

• v where v is a number, boolean or string, is the singleton type containing only that value

• i where i is an identifier can be a reference to a type name or a type variable

Other types cannot be written by the programmer, but are used internally and may appear in error messages.

• #<struct:n (t ...)> is the type of structures named n with field types t. There may be multiple such types with the same printed representation.

• (mu n t) is a recursive type where n is bound to the recursive type in the body t

• <n> is the printed representation of a reference to the type variable n