Version: 5.0
The Typed Racket Reference
1 Type Reference
Base Types
These types represent primitive Racket data. Note that
Integer represents exact integers.
Any Racket value. All other types are subtypes of
Any.
The empty type. No values inhabit this type, and
any expression of this type will not evaluate to a value.
The following base types are parameteric in their type arguments.
Either t of #f
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.
is the pair containing
s as the
car
and
t as the
cdr
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.
is the union of the types
t ...
is a function that behaves like all of
the
fun-tys. The
fun-tys must all be function
types constructed with
->.
is the instantiation of the parametric type
t at types
t1 t2 ...
is a parameterization of type
t, with
type variables
v ...
is the type of the list with one element, in order,
for each type provided to the
List type constructor.
is the type of the list with one element, in order,
for each type provided to the
Vector type constructor.
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 Racket 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
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.
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 Racket provides a variety of special forms above and beyond
those in Racket. 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).
|
| (let*: ([v : t e] ...) . body) |
|
|
|
|
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).
An alias for the same form using
lambda:.
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.
A function of multiple arities. Note that each formals must have a
different arity.
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
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.
Like
define-struct:, but defines an procedural structure.
The procdure
e is used as the value for
prop:procedure, and must have type
proc-t.
2.6 Names for Types
The first form defines
name as type, with the same meaning as
t. The second form is equivalent to
(define-type name (All (v ...) t)). Type names may
refer to other types defined in the same module, but
cycles among them are prohibited.
2.7 Generating Predicates Automatically
Defines
name as a predicate for the type
t.
name has the type
(Any -> Boolean : t).
t may not contain function types.
2.8 Type Annotation and Instantiation
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.
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.
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).
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 ...).
2.9 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
Racket, either built-in or via require/typed. The
structure predicate has the appropriate Typed Racket filter type so
that it may be used as a predicate in if expressions in Typed
Racket.
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).
Opaque types must be required lexically before they are used.
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 Racket
The typed/racket language corresponds to the
racket language – that is, any identifier provided
by racket, such as modulo is available by default in
typed/racket.
The typed/racket/base language corresponds to the
racket/base language.
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.
To participate in making more libraries available, please visit
here.
Other libraries can be used with Typed Racket via
require/typed.
4 Typed Racket Syntax Without Type Checking
On occasions where the Typed Racket 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
Racket, but does no type checking.
Examples:
5 Typed Regions
The with-type for allows for localized Typed Racket regions in otherwise untyped code.
| (with-type result-spec fv-clause body ...+) |
| (with-type export-spec fv-clause body ...+) |
| |
| fv-clause | | = | | | | | | | | | #:freevars ([id fv-type] ...) | | | | | | | | result-spec | | = | | #:result type | | | | | | | | export-spec | | = | | ([export-id export-type] ...) |
|
The first form, an expression, checks that
body ...+ has the type
type.
If the last expression in
body ...+ returns multiple values,
type must
be a type of the form
(values t ...).
Uses of the result values are appropriately checked by contracts generated from
type.
The second form, which can be used as a definition, checks that each of the export-ids
has the specified type. These types are also enforced in the surrounding code with contracts.
The ids are assumed to
have the types ascribed to them; these types are converted to contracts and checked dynamically.
Examples: |
| > (with-type #:result Number 3) |
3 |
|
top-level broke the contract (-> Number Number) given to |
(region typed-region); expected <Number>, given: #f |
|
"hello, world" |
|
eval:5.0: top-level broke the contract String on x; |
expected <String>, given: 'hello |
|
| > (fun val) |
17 |