On this page:
2.1 Binding Forms
let
letrec
let*
let-values
letrec-values
let*-values
let/  cc
let/  ec
2.2 Anonymous Functions
lambda
λ
case-lambda
2.3 Loops
for
for/  list
for/  hash
for/  hasheq
for/  hasheqv
for/  hashalw
for/  vector
for/  or
for/  sum
for/  product
for/  last
for/  set
for*/  list
for*/  hash
for*/  hasheq
for*/  hasheqv
for*/  hashalw
for*/  vector
for*/  or
for*/  sum
for*/  product
for*/  last
for*/  set
for/  and
for/  first
for*/  and
for*/  first
for/  lists
for/  fold
for/  foldr
for*
for*/  lists
for*/  fold
for*/  foldr
do
2.4 Definitions
define
2.5 Structure Definitions
struct
define-struct
2.6 Names for Types
define-type
2.7 Generating Predicates Automatically
make-predicate
define-predicate
2.8 Type Annotation and Instantiation
:
provide:
ann
cast
inst
row-inst
2.9 Require
require/  typed
require/  typed/  provide
2.10 Other Forms
with-handlers
with-handlers*
default-continuation-prompt-tag
#%module-begin
#%top-interaction
2.11 Special Structure Type Properties
prop:  procedure
8.9.0.5

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 var are names, type is a type. e is an expression and body is a block.

syntax

(let maybe-tvars (binding ...) maybe-ret . body)

(let loop maybe-ret (binding ...) . body)
 
binding = [var e]
  | [var : type e]
     
maybe-tvars = 
  | #:forall (tvar ...)
  | #:∀ (tvar ...)
     
maybe-ret = 
  | : type0
Local bindings, like let, each with associated types.

In the first form, maybe-ret can only appear with maybe-tvars, so if you only want to specify the return type, you should set maybe-tvars to #:forall ().

Examples:
> (let ([x : Zero 0]) x)

- : Integer [more precisely: Zero]

0

> (let #:forall () ([x : Zero 0]) : Natural x)

- : Integer [more precisely: Zero]

0

> (let ([x : Zero 0]) : Natural x)

eval:4:0: :: bad syntax

  in: :

If polymorphic type variables are provided, they are bound in the type expressions for variable bindings.

Example:
> (let #:forall (A) ([x : A 0]) x)

- : Integer [more precisely: Zero]

0

In the second form, type0 is the type of the result of loop (and thus the result of the entire expression as well as the final expression in body). Type annotations are optional.

Examples:
> (: filter-even (-> (Listof Natural) (Listof Natural) (Listof Natural)))
> (define (filter-even lst accum)
    (if (null? lst)
        accum
        (let ([first : Natural (car lst)]
              [rest  : (Listof Natural) (cdr lst)])
          (if (even? first)
              (filter-even rest (cons first accum))
              (filter-even rest accum)))))
> (filter-even (list 1 2 3 4 5 6) null)

- : (Listof Nonnegative-Integer)

'(6 4 2)

Examples:
> (: filter-even-loop (-> (Listof Natural) (Listof Natural)))
> (define (filter-even-loop lst)
    (let loop : (Listof Natural)
         ([accum : (Listof Natural) null]
          [lst   : (Listof Natural) lst])
      (cond
        [(null? lst)       accum]
        [(even? (car lst)) (loop (cons (car lst) accum) (cdr lst))]
        [else              (loop accum (cdr lst))])))
> (filter-even-loop (list 1 2 3 4))

- : (Listof Nonnegative-Integer)

'(4 2)

syntax

(letrec (binding ...) . body)

syntax

(let* (binding ...) . body)

syntax

(let-values ([(var+type ...) e] ...) . body)

syntax

(letrec-values ([(var+type ...) e] ...) . body)

syntax

(let*-values ([(var+type ...) e] ...) . body)

Type-annotated versions of letrec, let*, let-values, letrec-values, and let*-values. As with let, type annotations are optional.

syntax

(let/cc v : t . body)

syntax

(let/ec v : t . body)

Type-annotated versions of let/cc and let/ec. As with let, the type annotation is optional.

2.2 Anonymous Functions

syntax

(lambda maybe-tvars formals maybe-ret . body)

 
formals = (formal ...)
  | (formal ... . rst)
     
formal = var
  | [var default-expr]
  | [var : type]
  | [var : type default-expr]
  | keyword var
  | keyword [var : type]
  | keyword [var : type default-expr]
     
rst = var
  | [var : type *]
  | [var : type ooo bound]
     
maybe-tvars = 
  | #:forall (tvar ...)
  | #:∀ (tvar ...)
  | #:forall (tvar ... ooo)
  | #:∀ (tvar ... ooo)
     
maybe-ret = 
  | : type
Constructs an anonymous function like the lambda form from racket/base, but allows type annotations on the formal arguments. If a type annotation is left out, the formal will have the type Any.

Examples:
> (lambda ([x : String]) (string-append x "bar"))

- : (-> String String)

#<procedure>

> (lambda (x [y : Integer]) (add1 y))

- : (-> Any Integer Integer)

#<procedure>

> (lambda (x) x)

- : (-> Any Any)

#<procedure>

Type annotations may also be specified for keyword and optional arguments:

Examples:
> (lambda ([x : String "foo"]) (string-append x "bar"))

- : (->* () (String) (String : (Top | Bot)))

#<procedure:eval:15:0>

> (lambda (#:x [x : String]) (string-append x "bar"))

- : (-> #:x String String)

#<procedure:eval:16:0>

> (lambda (x #:y [y : Integer 0]) (add1 y))

- : (-> Any [#:y Integer] Integer)

#<procedure:eval:17:0>

> (lambda ([x 'default]) x)

- : (->* () (Any) Any)

#<procedure:eval:18:0>

The lambda expression may also specify polymorphic type variables that are bound for the type expressions in the formals.

Examples:
> (lambda #:forall (A) ([x : A]) x)

- : (All (A) (-> A A))

#<procedure>

> (lambda #:∀ (A) ([x : A]) x)

- : (All (A) (-> A A))

#<procedure>

In addition, a type may optionally be specified for the rest argument with either a uniform type or using a polymorphic type. In the former case, the rest argument is given the type (Listof type) where type is the provided type annotation.

Examples:
> (lambda (x . rst) rst)

- : (-> Any Any * (Listof Any))

#<procedure>

> (lambda (x    rst : Integer *)  rst)

- : (-> Any Integer * (Listof Integer))

#<procedure>

> (lambda #:forall (A ...) (x    rst : A ... A)  rst)

- : (All (A ...) (-> Any A ... A (List A ... A)))

#<procedure>

syntax

(λ maybe-tvars formals maybe-ret . body)

An alias for the same form using lambda.

syntax

(case-lambda maybe-tvars [formals body] ...)

A function of multiple arities. The formals are identical to those accepted by the lambda form except that keyword and optional arguments are not allowed.

Polymorphic type variables, if provided, are bound in the type expressions in the formals.

Note that each formals must have a different arity.

Example:
> (define add-map
    (case-lambda
     [([lst : (Listof Integer)])
      (map add1 lst)]
     [([lst1 : (Listof Integer)]
       [lst2 : (Listof Integer)])
      (map + lst1 lst2)]))

To see how to declare a type for add-map, see the case-> type constructor.

2.3 Loops

syntax

(for void-ann-maybe (for-clause ...) void-ann-maybe expr ...+)

 
void-ann-maybe = 
  | : Void
     
type-ann-maybe = 
  | : u
     
for-clause = [id : t seq-expr]
  | [(binding ...) seq-expr]
  | [id seq-expr]
  | #:when guard
     
binding = id
  | [id : t]
Like for from racket/base, but each id has the associated type t. The latter ann-maybe will be used first, and then the previous one. Since the return type is always Void, annotating the return type of a for form is optional. Type annotations in clauses are optional for all for variants.

Examples:
> (for ([i '()]) i)
> (for : Void ([i '()]) i)
> (for ([i '()]) : Void i)
> (for : Void ([i '()]) : Void i)
> (for ([i '()]) : Any i)

eval:29:0: :: bad syntax

  in: :

> (for/or : False ([i '()]) : False #f)

- : False

#f

> (for/or : Boolean ([i '()]) : False #f)

- : Boolean

#f

> (for/or : False ([i '()]) : Boolean #f)

eval:32:0: Type Checker: type mismatch

  expected: False

  given: Boolean

  in: #f

syntax

(for/list type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/hash type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/hasheq type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/hasheqv type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/hashalw type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/vector type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/or type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/sum type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/product type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/last type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/set type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/list type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/hash type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/hasheq type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/hasheqv type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/hashalw type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/vector type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/or type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/sum type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/product type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/last type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/set type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

These behave like their non-annotated counterparts, with the exception that #:when clauses can only appear as the last for-clause. The return value of the entire form must be of type u. For example, a for/list form would be annotated with a Listof type. All annotations are optional.

syntax

(for/and type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for/first type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/and type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

syntax

(for*/first type-ann-maybe (for-clause ...) type-ann-maybe expr ...+)

Like the above, except they are not yet supported by the typechecker.

syntax

(for/lists type-ann-maybe
           ([id : t] ... maybe-result)
           (for-clause ...)
           type-ann-maybe
  expr ...+)

syntax

(for/fold type-ann-maybe
          ([id : t init-expr] ... maybe-result)
          (for-clause ...)
          type-ann-maybe
  expr ...+)

syntax

(for/foldr type-ann-maybe
           ([id : t init-expr] ... maybe-result)
           (for-clause ...)
           type-ann-maybe
  expr ...+)
 
maybe-result = 
  | #:result result-expr
These behave like their non-annotated counterparts. Unlike the above, #:when clauses can be used freely with these.

Changed in version 1.11 of package typed-racket-lib: Added the #:result form.

Changed in version 1.12 of package typed-racket-lib: Added for/foldr.

syntax

(for* void-ann-maybe (for-clause ...) void-ann-maybe expr ...+)

syntax

(for*/lists type-ann-maybe
            ([id : t] ... maybe-result)
            (for-clause ...)
            type-ann-maybe
  expr ...+)

syntax

(for*/fold type-ann-maybe
           ([id : t init-expr] ... maybe-result)
           (for-clause ...)
           type-ann-maybe
  expr ...+)

syntax

(for*/foldr type-ann-maybe
            ([id : t init-expr] ... maybe-result)
            (for-clause ...)
            type-ann-maybe
  expr ...+)
 
maybe-result = 
  | #:result result-expr
These behave like their non-annotated counterparts.

Changed in version 1.11 of package typed-racket-lib: Added the #:result form.

Changed in version 1.12 of package typed-racket-lib: Added for*/foldr.

syntax

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

2.4 Definitions

syntax

(define maybe-tvars v maybe-ann e)

(define maybe-tvars header maybe-ann . body)
 
header = (function-name . formals)
  | (header . formals)
     
formals = (formal ...)
  | (formal ... . rst)
     
formal = var
  | [var default-expr]
  | [var : type]
  | [var : type default-expr]
  | keyword var
  | keyword [var : type]
  | keyword [var : type default-expr]
     
rst = var
  | [var : type *]
  | [var : type ooo bound]
     
maybe-tvars = 
  | #:forall (tvar ...)
  | #:∀ (tvar ...)
  | #:forall (tvar ... ooo)
  | #:∀ (tvar ... ooo)
     
maybe-ann = 
  | : type
Like define from racket/base, but allows optional type annotations for the variables.

The first form defines a variable v to the result of evaluating the expression e. The variable may have an optional type annotation.

Examples:
> (define foo "foo")
> (define bar : Integer 10)

If polymorphic type variables are provided, then they are bound for use in the type annotation.

Example:
> (define #:forall (A) mt-seq : (Sequenceof A) empty-sequence)

The second form allows the definition of functions with optional type annotations on any variables. If a return type annotation is provided, it is used to check the result of the function.

Like lambda, optional and keyword arguments are supported.

Examples:
> (define (add [first : Integer]
               [second  : Integer]) : Integer
    (+ first second))
> (define #:forall (A)
          (poly-app [func : (A A -> A)]
                    [first : A]
                    [second  : A]) : A
    (func first second))

The function definition form also allows curried function arguments with corresponding type annotations.

Examples:
> (define ((addx [x : Number]) [y : Number]) (+ x y))
> (define add2 (addx 2))
> (add2 5)

- : Number

7

Note that unlike define from racket/base, define does not bind functions with keyword arguments to static information about those functions.

2.5 Structure Definitions

syntax

(struct maybe-type-vars name-spec ([f : t] ...) options ...)

 
maybe-type-vars = 
  | (v ...)
     
name-spec = name-id
  | name-id parent
     
options = #:transparent
  | #:mutable
  | #:prefab
  | #:constructor-name constructor-id
  | #:extra-constructor-name constructor-id
  | #:property property-id property-expr
  | #:type-name type-id
Defines a structure with the name name-id, where the fields f have types t, similar to the behavior of struct from racket/base.

Examples:
> (struct camelia-sinensis ([age : Integer]))
> (struct camelia-sinensis-assamica camelia-sinensis ())

If type-id is not specified, name-id will be used for the name of the type associated with instances of the declared structure. Otherwise, type-id will be used for the type name, and using name-id in this case will cause a type error.

Examples:
> (struct apple () #:type-name BigApple)
> (ann (apple) BigApple)

- : BigApple

#<apple>

> (ann (apple) apple)

eval:45:0: Type Checker: parse error in type;

 type name `apple' is unbound

  in: apple

type-id can be also used as an alias to name-id, i.e. it will be a transformer binding that encapsulates the same structure information as name-id does.

Examples:
> (struct avocado ([amount : Integer]) #:type-name Avocado)
> (struct hass-avocado Avocado ())
> (struct-copy Avocado (avocado 0) [amount 42])

- : Avocado

#<avocado>

When parent is present, the structure is a substructure of parent.

When maybe-type-vars is present, the structure is polymorphic in the type variables v. If parent is also a polymorphic struct, then there must be at least as many type variables as in the parent type, and the parent type is instantiated with a prefix of the type variables matching the amount it needs.

Examples:
> (struct (X Y) 2-tuple ([first : X] [second : Y]))
> (struct (X Y Z) 3-tuple 2-tuple ([third :  Z]))

Options provided have the same meaning as for the struct form from racket/base (with the exception of #:type-name, as described above).

A prefab structure type declaration will bind the given name-id or type-id to a Prefab type. Unlike the struct form from racket/base, a non-prefab structure type cannot extend a prefab structure type.

Examples:
> (struct a-prefab ([x : String]) #:prefab)
> (:type a-prefab)

(Prefab a-prefab String)

> (struct not-allowed a-prefab ())

eval:53:0: Type Checker: Error in macro expansion -- parent

type not a valid structure name: a-prefab

  in: ()

Changed in version 1.4 of package typed-racket-lib: Added the #:type-name option.

syntax

(define-struct maybe-type-vars name-spec ([f : t] ...) options ...)

 
maybe-type-vars = 
  | (v ...)
     
name-spec = name-id
  | (name-id parent)
     
options = #:transparent
  | #:mutable
  | #:type-name type-id
Legacy version of struct, corresponding to define-struct from racket/base.

Changed in version 1.4 of package typed-racket-lib: Added the #:type-name option.

2.6 Names for Types

syntax

(define-type name t maybe-omit-def)

(define-type (name v ...) t maybe-omit-def)
 
maybe-omit-def = #:omit-define-syntaxes
  | 
The first form defines name as type, with the same meaning as t. The second form defines name to be a type constructor, whose parameters are v ... and body is t. If no parameters are declared, the defined type constructor is equivalent to (define-type name t maybe-omit-def). Type names may refer to other types defined in the same or enclosing scopes.

Examples:
> (define-type IntStr (U Integer String))
> (define-type (ListofPairs A) (Listof (Pair A A)))

If #:omit-define-syntaxes is specified, no definition of name is created. In this case, some other definition of name is necessary.

If the body of the type definition refers to itself, then the type definition is recursive. Recursion may also occur mutually, if a type refers to a chain of other types that eventually refers back to itself.

Examples:
> (define-type BT (U Number (Pair BT BT)))
> (let ()
    (define-type (Even A) (U Null (Pairof A (Odd A))))
    (define-type (Odd A) (Pairof A (Even A)))
    (: even-lst (Even Integer))
    (define even-lst '(1 2))
    even-lst)

- : (Even Integer)

'(1 2)

However, the recursive reference is only allowed when it is passed to a productive type constructor:

Examples:
> (define-type Foo Foo)

eval:58:0: Type Checker: Error in macro expansion -- parse

error in type;

 not in a productive position

  variable: Foo

  in: Foo

> (define-type Bar (U Bar False))

eval:59:0: Type Checker: Error in macro expansion -- parse

error in type;

 not in a productive position

  variable: Bar

  in: False

> (define-type Bar (U (Listof Bar) False))

2.7 Generating Predicates Automatically

syntax

(make-predicate t)

Evaluates to a predicate for the type t, with the type (Any -> Boolean : t). t may not contain function types, or types that may refer to mutable data such as (Vectorof Integer).

syntax

(define-predicate name t)

Equivalent to (define name (make-predicate t)).

2.8 Type Annotation and Instantiation

syntax

(: v t)

(: 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.

Examples:
> (: var1 Integer)
> (: var2 String)

The second form allows type annotations to elide one level of parentheses for function types.

Examples:
> (: var3 : -> Integer)
> (: var4 : String -> Integer)

syntax

(provide: [v t] ...)

This declares that the vs have the types t, and also provides all of the vs.

syntax

#{v : t}

This declares that the variable v has type t. This is legal only for binding occurrences of v.

If a dispatch macro on #\{ already exists in the current readtable, this syntax will be disabled.

syntax

(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.

syntax

#{e :: t}

A reader abbreviation for (ann e t).

If a dispatch macro on #\{ already exists in the current readtable, this syntax will be disabled.

syntax

(cast e t)

The entire expression has the type t, while e may have any type. The value of the entire expression is the value returned by e, protected by a contract ensuring that it has type t. This is legal only in expression contexts.

Examples:
> (cast 3 Integer)

- : Integer

3

> (cast 3 String)

broke its own contract

  promised: string?

  produced: 3

  in: string?

  contract from: cast

  blaming: cast

   (assuming the contract is correct)

  at: eval:66:0

> (cast (lambda ([x : Any]) x) (String -> String))

- : (-> String String)

#<procedure:val>

> ((cast (lambda ([x : Any]) x) (String -> String)) "hello")

- : String

"hello"

The value is actually protected with two contracts. The second contract checks the new type, but the first contract is put there to enforce the old type, to protect higher-order uses of the value.

Examples:
> ((cast (lambda ([s : String]) s) (Any -> Any)) "hello")

- : Any

"hello"

> ((cast (lambda ([s : String]) s) (Any -> Any)) 5)

contract violation

  expected: string?

  given: 5

  in: the 1st argument of

      (-> string? any)

  contract from: typed-world

  blaming: cast

   (assuming the contract is correct)

  at: eval:70:0

cast will wrap the value e in a contract which will affect the runtime performance of reading and updating the value. This is needed when e is a complex data type, such as a hash table. However, when the type of the value can be checked using a simple predicate, consider using assert instead.

syntax

(inst e t ...)

(inst e t ... t ooo bound)
Instantiate the type of e with types t ... or with the poly-dotted types t ... t ooo bound. e must have a polymorphic type that can be applied to the supplied number of type variables. For non-poly-dotted functions, however, fewer arguments can be provided and the omitted types default to Any. inst is legal only in expression contexts.

Examples:
> (foldl (inst cons Integer Integer) null (list 1 2 3 4))

- : (Listof Integer)

'(4 3 2 1)

> (: my-cons (All (A B) (-> A B (Pairof A B))))
> (define my-cons cons)
> (: foldl-list : (All (α) (Listof α) -> (Listof α)))
> (define (foldl-list lst)
    (foldl (inst my-cons α (Listof α)) null lst))
> (foldl-list (list "1" "2" "3" "4"))

- : (Listof String)

'("4" "3" "2" "1")

> (: foldr-list : (All (α) (Listof α) -> Any))
> (define (foldr-list lst)
    (foldr (inst my-cons α) null lst))
> (foldr-list (list "1" "2" "3" "4"))

- : Any

'("1" "2" "3" "4")

> (: my-values : (All (A B ...) (A B ... -> (values A B ... B))))
> (define (my-values arg . args)
    (apply (inst values A B ... B) arg args))

syntax

(row-inst e row)

Instantiate the row-polymorphic type of e with row. This is legal only in expression contexts.

Examples:
> (: id (All (r #:row)
          (-> (Class #:row-var r) (Class #:row-var r))))
> (define (id cls) cls)
> ((row-inst id (Row (field [x Integer])))
   (class object% (super-new) (field [x : Integer 0])))

- : (Class (field (x Integer)))

#<class:eval:84:0>

syntax

#{e @ t ...}

A reader abbreviation for (inst e t ...).

syntax

#{e @ t ... t ooo bound}

A reader abbreviation for (inst e t ... t ooo bound).

2.9 Require

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

syntax

(require/typed m rt-clause ...)

 
rt-clause = [maybe-renamed t]
  | 
[#:struct maybe-tvars name-id ([f : t] ...)
     struct-option ...]
  | 
[#:struct maybe-tvars (name-id parent) ([f : t] ...)
     struct-option ...]
  | [#:opaque t pred]
  | [#:signature name ([id : t] ...)]
     
maybe-renamed = id
  | (orig-id new-id)
     
maybe-tvars = 
  | (type-variable ...)
     
struct-option = #:constructor-name constructor-id
  | #:extra-constructor-name constructor-id
  | #:type-name type-id
This form requires identifiers from the module m, giving them the specified types.

The first case requires maybe-renamed, giving it type t.

The second and third cases require the struct with name name-id and creates a new type with the name type-id, or name-id if no type-id is provided, with fields f ..., where each field has type t. The third case 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.

Examples:
> (module UNTYPED racket/base
    (define n 100)
  
    (struct IntTree
      (elem left right))
  
    (provide n (struct-out IntTree)))
> (module TYPED typed/racket
    (require/typed 'UNTYPED
                   [n Natural]
                   [#:struct IntTree
                     ([elem  : Integer]
                      [left  : IntTree]
                      [right : IntTree])]))

The fourth case defines a new opaque type t using the function pred as a predicate. (Module m must provide pred and pred must have type (Any -> Boolean).) The type t is defined as precisely those values that pred returns #t for. Opaque types must be required lexically before they are used.

Examples:
> (require/typed racket/base
                 [#:opaque Evt evt?]
                 [alarm-evt (Real -> Evt)]
                 [sync (Evt -> Any)])
> evt?

- : (-> Any Boolean : Evt)

#<procedure:evt?>

> (sync (alarm-evt (+ 100 (current-inexact-milliseconds))))

- : Any

#<alarm-evt>

The #:signature keyword registers the required signature in the signature environment. For more information on the use of signatures in Typed Racket see the documentation for typed/racket/unit.

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 the types of predicates such as number?, cannot be converted to contracts and raise a static error when used in a require/typed form. Here is an example of using case-> in require/typed.

(require/typed racket/base
               [file-or-directory-modify-seconds
                (case->
                  [String -> Exact-Nonnegative-Integer]
                  [String (Option Exact-Nonnegative-Integer)
                          ->
                          (U Exact-Nonnegative-Integer Void)]
                  [String (Option Exact-Nonnegative-Integer) (-> Any)
                          ->
                          Any])])

file-or-directory-modify-seconds has some arguments which are optional, so we need to use case->.

Changed in version 1.4 of package typed-racket-lib: Added the #:type-name option.
Changed in version 1.6: Added syntax for struct type variables, only works in unsafe requires.
Changed in version 1.12: Added default type Any for omitted inst args.

syntax

(require/typed/provide m rt-clause ...)

Similar to require/typed, but also provides the imported identifiers. Uses outside of a module top-level raise an error.

Examples:
> (module evts typed/racket
    (require/typed/provide racket/base
                           [#:opaque Evt evt?]
                           [alarm-evt (Real -> Evt)]
                           [sync (Evt -> Any)]))
> (require 'evts)
> (sync (alarm-evt (+ 100 (current-inexact-milliseconds))))

- : Any

#<alarm-evt>

2.10 Other Forms

Identical to with-handlers from racket/base but provides additional annotations to assist the typechecker.

Identical to with-handlers* from racket/base but provides additional annotations to assist the typechecker.

Added in version 1.12 of package typed-racket-lib.

Identical to default-continuation-prompt-tag, but additionally protects the resulting prompt tag with a contract that wraps higher-order values, such as functions, that are communicated with that prompt tag. If the wrapped value is used in untyped code, a contract error will be raised.

Examples:
> (module typed typed/racket
    (provide do-abort)
    (: do-abort (-> Void))
    (define (do-abort)
      (abort-current-continuation
       ; typed, and thus contracted, prompt tag
       (default-continuation-prompt-tag)
       (λ: ([x : Integer]) (+ 1 x)))))
> (module untyped racket
    (require 'typed)
    (call-with-continuation-prompt
      (λ () (do-abort))
      (default-continuation-prompt-tag)
      ; the function cannot be passed an argument
      (λ (f) (f 3))))
> (require 'untyped)

default-continuation-prompt-tag: broke its own contract

  Attempted to use a higher-order value passed as `Any` in

untyped code: #<procedure>

  in: the range of

      (-> (prompt-tag/c Any #:call/cc Any))

  contract from: untyped

  blaming: untyped

   (assuming the contract is correct)

syntax

(#%module-begin form ...)

Legal only in a module begin context. The #%module-begin form of typed/racket checks all the forms in the module, using the Typed Racket type checking rules. All provide forms are rewritten to insert contracts where appropriate. Otherwise, the #%module-begin form of typed/racket behaves like #%module-begin from racket.

syntax

(#%top-interaction . form)

Performs type checking of forms entered at the read-eval-print loop. The #%top-interaction form also prints the type of form after type checking.

2.11 Special Structure Type Properties

Unlike many other structure type properties, prop:procedure does not have predefined types for its property values. When a structure is assocatied with prop:procedure, its constructors’ return type is an intersection type of the structure type and a function type specified by the property value.

Examples:
> (struct animal ([a : Number] [b : (-> Number Number)])
    #:property prop:procedure
    (struct-field-index b))
> (animal 2 add1)

- : (∩ (-> Number Number) animal)

#<procedure:add1>

> (struct plant ([a : Number])
    #:property prop:procedure
    (lambda ([me : plant] [a1 : String]) : Number
      (+ (plant-a me) (string-length a1))))
> (plant 31)

- : (∩ (-> String Number) plant)

#<procedure:plant>

In other words, a variable that refers to a function is not allowed

Unlike in Racket, only one of the following types of expressions are allowed in Typed Racket: a nonnegative literal, (struct-index-field field-name), or a lambda expression. Note that in the last case, if the type annotation on the codomain is not supplied, the type checker will use Any as the return type.

Similar to other structure type properties, when a structure’s base structure specifies a value for prop:procedure, the structure inherits that value if it does not specify its own.

Examples:
> (struct cat animal ([c : Number]))
> (cat 2 add1 42)

- : (∩ (-> Number Number) cat)

#<procedure:add1>

> (struct a-cat cat ())
> (a-cat 2 add1 42)

- : (∩ (-> Number Number) a-cat)

#<procedure:add1>

Function types for procedural structures do not enforce subtyping relations. A substructure can specify a different field index or a procedure that has a arity and/or types different from its base structures for prop:procedure.

Examples:
> (struct b-cat cat ([d : (-> Number String)])
     #:property prop:procedure (struct-field-index d))
> (b-cat 2 add1 42 number->string)

- : (∩ (-> Number String) b-cat)

#<procedure:number->string>