1 Type Reference
Hash Table
2 Special Form Reference
2.1 Binding Forms
let/ cc:
let/ ec:
2.2 Anonymous Functions
2.3 Loops
2.4 Definitions
2.5 Structure Definitions
2.6 Type Aliases
2.7 Type Annotation and Instantiation
2.8 Require
require/ typed
3 Libraries Provided With Typed Scheme
4 Typed Scheme Syntax Without Type Checking
Version: 4.2.1

The Typed Scheme Reference

Sam Tobin-Hochstadt

 #lang typed-scheme

1 Type Reference

Base Types
These types represent primitive Scheme data. Note that Integer represents exact integers.

Any Scheme value. All other types are subtypes of Any.

The following base types are parameteric in their type arguments.

(Listof t)
Homogenous lists of t
(Boxof t)
A box of t
A syntax object containing a t
Homogenous vectors of t
(Option t)
Either t of #f
(Parameter t)
(Parameter s t)
A parameter of t. If two type arguments are supplied, the first is the type the parameter accepts, and the second is the type returned.
(Pair s t)
is the pair containing s as the car and t as the cdr
(HashTable k v)
is the type of a hash table with key type k and value type v.

Type Constructors

(dom ... -> rng)
(dom ... rest * -> rng)
(dom ... rest ... bound -> rng)
(dom -> rng : pred)
is the type of functions from the (possibly-empty) sequence dom ... to the rng type. The second form specifies a uniform rest argument of type rest, and the third form specifies a non-uniform rest argument of type rest with bound bound. In the third form, the second occurrence of ... is literal, and bound must be an identifier denoting a type variable. In the fourth form, there must be only one dom and pred is the type checked by the predicate.
(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 ...
(All (v ...) t)
is a parameterization of type t, with type variables v ...
(List t ...)
is the type of the list with one element, in order, for each type provided to the List type constructor.
(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.
where v is a number, boolean or string, is the singleton type containing only that value
where val is a Scheme value, is the singleton type containing only that value
where i is an identifier can be a reference to a type name or a type variable
(Rec n t)
is a recursive type where n is bound to the recursive type in the body t

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.
is the printed representation of a reference to the type variable n

2 Special Form Reference

Typed Scheme provides a variety of special forms above and beyond those in PLT Scheme. They are used for annotating variables with types, creating new types, and annotating expressions.

2.1 Binding Forms

loop, f, a, and v are names, t is a type. e is an expression and body is a block.

(let: ([v : t e] ...) . body)
(let: loop : t0 ([v : t e] ...) . body)
Local bindings, like let, each with associated types. In the second form, t0 is the type of the result of loop (and thus the result of the entire expression as well as the final expression in body).
(letrec: ([v : t e] ...) . body)
(let*: ([v : t e] ...) . body)
Type-annotated versions of letrec and let*.

(let/cc: v : t . body)
(let/ec: v : t . body)
Type-annotated versions of let/cc and let/ec.

2.2 Anonymous Functions

(lambda: formals . body)
formals = ([v : t] ...)
  | ([v : t] ...    v : t)
A function of the formal arguments v, where each formal argument has the associated type. If a rest argument is present, then it has type (Listof t).
(λ: formals . body)
An alias for the same form using lambda:.
(plambda: (a ...) formals . body)
A polymorphic function, abstracted over the type variables a. The type variables a are bound in both the types of the formal, and in any type expressions in the body.
(case-lambda: [formals body] ...)
A function of multiple arities. Note that each formals must have a different arity.
(pcase-lambda: (a ...) [formals body] ...)
A polymorphic function of multiple arities.

2.3 Loops

(do: : u ([id : t init-expr step-expr-maybe] ...)
         (stop?-expr finish-expr ...)
  expr ...+)
step-expr-maybe = 
  | step-expr
Like do, but each id having the associated type t, and the final body expr having the type u.

2.4 Definitions

(define: v : t e)
(define: (f . formals) : t . body)
(define: (a ...) (f . formals) : t . body)
These forms define variables, with annotated types. The first form defines v with type t and value e. The second and third forms defines a function f with appropriate types. In most cases, use of : is preferred to use of define:.

2.5 Structure Definitions

(define-struct: maybe-type-vars name-spec ([f : t] ...))
maybe-type-vars = 
  | (v ...)
name-spec = name
  | (name parent)
Defines a structure with the name name, where the fields f have types t. When parent, the structure is a substructure of parent. When maybe-type-vars is present, the structure is polymorphic in the type variables v.

2.6 Type Aliases

(define-type-alias name t)
(define-type-alias (name v ...) t)
The first form defines name as type, with the same meaning as t. The second form is equivalent to (define-type-alias name (All (v ...) t)). Type aliases may refer to other type aliases or types defined in the same module, but cycles among type aliases are prohibited.

2.7 Type Annotation and Instantiation

(: v t)
This declares that v has type t. The definition of v must appear after this declaration. This can be used anywhere a definition form may be used.

(provide: [v t] ...)
This declares that the vs have the types t, and also provides all of the vs.

#{v : t} This declares that the variable v has type t. This is legal only for binding occurences of v.

(ann e t)
Ensure that e has type t, or some subtype. The entire expression has type t. This is legal only in expression contexts.

#{e :: t} This is identical to (ann e t).

(inst e t ...)
Instantiate the type of e with types t .... e must have a polymorphic type with the appropriate number of type variables. This is legal only in expression contexts.

#{e @ t ...} This is identical to (inst e t ...).

2.8 Require

Here, m is a module spec, pred is an identifier naming a predicate, and r is an optionally-renamed identifier.

(require/typed m rt-clause ...)
rt-clause = [r t]
  | [struct name ([f : t] ...)]
  | [struct (name parent) ([f : t] ...)]
  | [opaque t pred]
This form requires identifiers from the module m, giving them the specified types.

The first form requires r, giving it type t.

The second and third forms require the struct with name name with fields f ..., where each field has type t. The third form allows a parent structure type to be specified. The parent type must already be a structure type known to Typed Scheme, either built-in or via require/typed. The structure predicate has the appropriate Typed Scheme filter type so that it may be used as a predicate in if expressions in Typed Scheme.

The fourth case defines a new type t. pred, imported from module m, is a predicate for this type. The type is defined as precisely those values to which pred produces #t. pred must have type (Any -> Boolean).

In all cases, the identifiers are protected with contracts which enforce the specified types. If this contract fails, the module m is blamed.

Some types, notably polymorphic types constructed with All, cannot be converted to contracts and raise a static error when used in a require/typed form.

3 Libraries Provided With Typed Scheme

The typed-scheme language corresponds to the scheme/base language – that is, any identifier provided by scheme/base, such as mod is available by default in typed-scheme.

  #lang typed-scheme
  (modulo 12 2)

Any value provided by scheme is available by simply requireing it; use of require/typed is not neccessary.

  #lang typed-scheme
  (require scheme/list)
  (display (first (list 1 2 3)))

Some libraries have counterparts in the typed collection, which provide the same exports as the untyped versions. Such libraries include srfi/14, net/url, and many others.

  #lang typed-scheme
  (require typed/srfi/14)
  (char-set= (string->char-set "hello")
             (string->char-set "olleh"))

To participate in making more libraries available, please visit here.

Other libraries can be used with Typed Scheme via require/typed.

  #lang typed-scheme
  (require/typed version/check
                 [check-version (-> (U Symbol (Listof Any)))])

4 Typed Scheme Syntax Without Type Checking

 #lang typed-scheme/no-check

On occasions where the Typed Scheme syntax is useful, but actual typechecking is not desired, the typed-scheme/no-check language is useful. It provides the same bindings and syntax as Typed Scheme, but does no type checking.


  #lang typed-scheme/no-check
  (: x Number)
  (define x "not-a-number")