248 lines
10 KiB
Racket
248 lines
10 KiB
Racket
#lang scribble/doc
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@begin[(require scribble/manual)
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(require (for-label typed-scheme))]
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@begin[
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(define (item* header . args) (apply item @bold[header]{: } args))
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(define-syntax-rule (tmod forms ...) (schememod typed-scheme forms ...))
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(define (gtech . x) (apply tech x #:doc '(lib "scribblings/guide/guide.scrbl")))
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(define (rtech . x) (apply tech x #:doc '(lib "scribblings/reference/reference.scrbl")))
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]
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@title[#:tag "top"]{The Typed Scheme Reference}
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@author["Sam Tobin-Hochstadt"]
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@(defmodulelang typed-scheme)
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@section[#:tag "type-ref"]{Type Reference}
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@subsubsub*section{Base Types}
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@deftogether[(
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@defidform[Number]
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@defidform[Integer]
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@defidform[Boolean]
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@defidform[String]
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@defidform[Keyword]
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@defidform[Symbol]
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@defidform[Void]
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@defidform[Input-Port]
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@defidform[Output-Port]
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@defidform[Path]
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@defidform[Regexp]
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@defidform[PRegexp]
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@defidform[Syntax]
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@defidform[Bytes]
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@defidform[Namespace]
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@defidform[EOF]
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@defidform[Char])]{
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These types represent primitive Scheme data.}
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@defidform[Any]{Any Scheme value. All other types are subtypes of @scheme[Any].}
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The following base types are parameteric in their type arguments.
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@defform[(Listof t)]{Homogenous @rtech{lists} of @scheme[t]}
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@defform[(Boxof t)]{A @rtech{box} of @scheme[t]}
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@defform[(Vectorof t)]{Homogenous @rtech{vectors} of @scheme[t]}
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@defform[(Option t)]{Either @scheme[t] of @scheme[#f]}
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@defform*[[(Parameter t)
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(Parameter s t)]]{A @rtech{parameter} of @scheme[t]. If two type arguments are supplied,
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the first is the type the parameter accepts, and the second is the type returned.}
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@defform[(Pair s t)]{is the pair containing @scheme[s] as the @scheme[car]
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and @scheme[t] as the @scheme[cdr]}
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@subsubsub*section{Type Constructors}
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@defform*[#:id -> #:literals (* ...)
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[(dom ... -> rng)
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(dom ... rest * -> rng)
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(dom ... rest ... bound -> rng)
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(dom -> rng : pred)]]{is the type of functions from the (possibly-empty)
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sequence @scheme[dom ...] to the @scheme[rng] type. The second form
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specifies a uniform rest argument of type @scheme[rest], and the
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third form specifies a non-uniform rest argument of type
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@scheme[rest] with bound @scheme[bound]. In the third form, the
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second occurrence of @scheme[...] is literal, and @scheme[bound]
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must be an identifier denoting a type variable. In the fourth form,
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there must be only one @scheme[dom] and @scheme[pred] is the type
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checked by the predicate.}
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@defform[(U t ...)]{is the union of the types @scheme[t ...]}
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@defform[(case-lambda fun-ty ...)]{is a function that behaves like all of
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the @scheme[fun-ty]s. The @scheme[fun-ty]s must all be function
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types constructed with @scheme[->].}
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@defform/none[(t t1 t2 ...)]{is the instantiation of the parametric type
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@scheme[t] at types @scheme[t1 t2 ...]}
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@defform[(All (v ...) t)]{is a parameterization of type @scheme[t], with
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type variables @scheme[v ...]}
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@defform[(List t ...)]{is the type of the list with one element, in order,
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for each type provided to the @scheme[List] type constructor.}
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@defform[(values t ...)]{is the type of a sequence of multiple values, with
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types @scheme[t ...]. This can only appear as the return type of a
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function.}
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@defform/none[v]{where @scheme[v] is a number, boolean or string, is the singleton type containing only that value}
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@defform/none['sym]{where @scheme[sym] is a symbol, is the singleton type containing only that symbol}
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@defform/none[i]{where @scheme[i] is an identifier can be a reference to a type
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name or a type variable}
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@defform[(Rec n t)]{is a recursive type where @scheme[n] is bound to the
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recursive type in the body @scheme[t]}
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Other types cannot be written by the programmer, but are used
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internally and may appear in error messages.
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@defform/none[(struct:n (t ...))]{is the type of structures named
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@scheme[n] with field types @scheme[t]. There may be multiple such
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types with the same printed representation.}
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@defform/none[<n>]{is the printed representation of a reference to the
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type variable @scheme[n]}
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@section[#:tag "special-forms"]{Special Form Reference}
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Typed Scheme provides a variety of special forms above and beyond
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those in PLT Scheme. They are used for annotating variables with types,
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creating new types, and annotating expressions.
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@subsection{Binding Forms}
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@scheme[_loop], @scheme[_f], @scheme[_a], and @scheme[_v] are names, @scheme[_t] is a type.
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@scheme[_e] is an expression and @scheme[_body] is a block.
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@defform*[[
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(let: ([v : t e] ...) . body)
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(let: loop : t0 ([v : t e] ...) . body)]]{
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Local bindings, like @scheme[let], each with
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associated types. In the second form, @scheme[_t0] is the type of the
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result of @scheme[_loop] (and thus the result of the entire
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expression as well as the final
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expression in @scheme[body]).}
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@deftogether[[
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@defform[(letrec: ([v : t e] ...) . body)]
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@defform[(let*: ([v : t e] ...) . body)]]]{Type-annotated versions of
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@scheme[letrec] and @scheme[let*].}
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@subsection{Anonymous Functions}
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@defform/subs[(lambda: formals . body)
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([formals ([v : t] ...)
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([v : t] ... . [v : t])])]{
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A function of the formal arguments @scheme[v], where each formal
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argument has the associated type. If a rest argument is present, then
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it has type @scheme[(Listof t)].}
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@defform[(λ: formals . body)]{
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An alias for the same form using @scheme[lambda:].}
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@defform[(plambda: (a ...) formals . body)]{
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A polymorphic function, abstracted over the type variables
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@scheme[a]. The type variables @scheme[a] are bound in both the types
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of the formal, and in any type expressions in the @scheme[body].}
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@defform[(case-lambda: [formals body] ...)]{
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A function of multiple arities. Note that each @scheme[formals] must have a
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different arity.}
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@defform[(pcase-lambda: (a ...) [formals body] ...)]{
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A polymorphic function of multiple arities.}
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@subsection{Definitions}
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@defform*[[(define: v : t e)
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(define: (f . formals) : t . body)
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(define: (a ...) (f . formals) : t . body)]]{
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These forms define variables, with annotated types. The first form
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defines @scheme[v] with type @scheme[t] and value @scheme[e]. The
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second and third forms defines a function @scheme[f] with appropriate
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types. In most cases, use of @scheme[:] is preferred to use of @scheme[define:].}
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@subsection{Structure Definitions}
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@defform/subs[
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(define-struct: maybe-type-vars name-spec ([f : t] ...))
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([maybe-type-vars code:blank (v ...)]
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[name-spec name (name parent)])]{
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Defines a @rtech{structure} with the name @scheme[name], where the
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fields @scheme[f] have types @scheme[t]. When @scheme[parent], the
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structure is a substructure of @scheme[parent]. When
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@scheme[maybe-type-vars] is present, the structure is polymorphic in the type
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variables @scheme[v].}
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@subsection{Type Aliases}
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@defform*[[(define-type-alias name t)
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(define-type-alias (name v ...) t)]]{
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The first form defines @scheme[name] as type, with the same meaning as
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@scheme[t]. The second form is equivalent to
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@scheme[(define-type-alias name (All (v ...) t))]. Type aliases may
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refer to other type aliases or types defined in the same module, but
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cycles among type aliases are prohibited.}
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@subsection{Type Annotation and Instantiation}
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@defform[(: v t)]{This declares that @scheme[v] has type @scheme[t].
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The definition of @scheme[v] must appear after this declaration. This
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can be used anywhere a definition form may be used.}
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@defform[(provide: [v t] ...)]{This declares that the @scheme[v]s have
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the types @scheme[t], and also provides all of the @scheme[v]s.}
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@litchar{#{v : t}} This declares that the variable @scheme[v] has type
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@scheme[t]. This is legal only for binding occurences of @scheme[_v].
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@defform[(ann e t)]{Ensure that @scheme[e] has type @scheme[t], or
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some subtype. The entire expression has type @scheme[t].
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This is legal only in expression contexts.}
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@litchar{#{e :: t}} This is identical to @scheme[(ann e t)].
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@defform[(inst e t ...)]{Instantiate the type of @scheme[e] with types
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@scheme[t ...]. @scheme[e] must have a polymorphic type with the
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appropriate number of type variables. This is legal only in expression
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contexts.}
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@schemevarfont|{#{e @ t ...}}| This is identical to @scheme[(inst e t ...)].
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@subsection{Require}
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Here, @scheme[_m] is a module spec, @scheme[_pred] is an identifier
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naming a predicate, and @scheme[_r] is an optionally-renamed identifier.
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@defform*[[
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(require/typed r t m)
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(require/typed m [r t] ...)
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]]{The first form requires @scheme[r] from module @scheme[m], giving
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it type @scheme[t]. The second form generalizes this to multiple
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identifiers.
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In both cases, the identifiers are protected with @rtech{contracts} which
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enforce the type @scheme[t]. If this contract fails, the module
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@scheme[m] is blamed.
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Some types, notably polymorphic types constructed with @scheme[All],
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cannot be converted to contracts and raise a static error when used in
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a @scheme[require/typed] form.}
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@defform[(require/opaque-type t pred m)]{
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This defines a new type @scheme[t]. @scheme[pred], imported from
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module @scheme[m], is a predicate for this type. The type is defined
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as precisely those values to which @scheme[pred] produces
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@scheme[#t]. @scheme[pred] must have type @scheme[(Any -> Boolean)].}
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@defform*[[(require-typed-struct name ([f : t] ...) m)
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(require-typed-struct (name parent) ([f : t] ...) m)]]{
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Requires all the functions associated with the structure @scheme[name] from the module @scheme[m],
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with the appropriate types. The structure predicate has the
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appropriate Typed Scheme filter type so that it may be used as a
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predicate in @scheme[if] expressions in Typed Scheme.
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In the second form, @scheme[parent] must already be a structure type
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known to Typed Scheme, either via @scheme[define-struct:] or
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@scheme[require-typed-struct].
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}
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@defform/subs[(do: : u ([id : t init-expr step-expr-maybe] ...)
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(stop?-expr finish-expr ...)
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expr ...+)
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([step-expr-maybe code:blank
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step-expr])]{
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Like @scheme[do], but each @scheme[id] having the associated type @scheme[t], and
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the final body @scheme[expr] having the type @scheme[u].
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}
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