Version: 4.1.5
The Typed Scheme Reference
Sam Tobin-Hochstadt
1 Type Reference
Base Types
These types represent primitive Scheme data.
Any Scheme value. All other types are subtypes of Any.
The following base types are parameteric in their type arguments.
Homogenous lists of t
A box of t
Homogenous vectors of t
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 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 sym is a symbol, is the singleton type containing only that symbol
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 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).
|
| (let*: ([v : t e] ...) . body) |
|
Type-annotated versions of
letrec and let*.
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 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:.
2.4 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.
2.5 Type Aliases
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.
2.6 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 ...).
2.7 Require
Here, m is a module spec, pred is an identifier
naming a predicate, and r is an optionally-renamed identifier.
The first form requires r from module m, giving
it type t. The second form generalizes this to multiple
identifiers.
In both cases, the identifiers are protected with contracts which
enforce the type t. 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.
This 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).
Requires all the functions associated with the structure name from the module m,
with the appropriate types. 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.
In the second form, parent must already be a structure type
known to Typed Scheme, either via define-struct: or
require-typed-struct.
| (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.
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.
Any value provided by scheme is available by simply
requireing it; use of require/typed is not
neccessary.
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 Scheme via
require/typed.