►Math Library
▼6 Arrays
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Array
Settable-Array
Mutable-Array
Indexes
In-Indexes
array?
settable-array?
mutable-array?
array-shape
array-size
array-dims
mutable-array-data
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6.6 Types, Predicates and Accessors

syntax

(Array A)

The parent array type. Its type parameter is the type of the array’s elements.

The polymorphic Array type is covariant, meaning that (Array A) is a subtype of (Array B) if A is a subtype of B:
> (define arr (array #[1 2 3 4 5]))
> arr

- : (Array Positive-Byte)

(array #[1 2 3 4 5])

> (ann arr (Array Real))

- : (Array Real)

(array #[1 2 3 4 5])

> (ann arr (Array Any))

- : (Array Any)

(array #[1 2 3 4 5])

Because subtyping is transitive, the (Array A) in the preceeding subtyping rule can be replaced with any of (Array A)’s subtypes, including descendant types of Array. For example, (Mutable-Array A) is a subtype of (Array B) if A is a subtype of B:
> (define arr (mutable-array #[1 2 3 4 5]))
> arr

- : (Mutable-Array Integer)

(mutable-array #[1 2 3 4 5])

> (ann arr (Array Real))

- : (Array Real)

(mutable-array #[1 2 3 4 5])

> (ann arr (Array Any))

- : (Array Any)

(mutable-array #[1 2 3 4 5])

syntax

(Settable-Array A)

The parent type of arrays whose elements can be mutated. Functions like array-set! and array-slice-set! accept arguments of this type. Examples of subtypes are Mutable-Array, FlArray and FCArray.

This type is invariant, meaning that (Settable-Array A) is not a subtype of (Settable-Array B) if A and B are different types, even if A is a subtype of B:
> (define arr (mutable-array #[1 2 3 4 5]))
> arr

- : (Mutable-Array Integer)

(mutable-array #[1 2 3 4 5])

> (ann arr (Settable-Array Integer))

- : (Settable-Array Integer)

(mutable-array #[1 2 3 4 5])

> (ann arr (Settable-Array Real))

eval:93:0: Type Checker: Expected (Settable-Array Real), but

got (Mutable-Array Integer)

  in: (#%top . arr26)

syntax

(Mutable-Array A)

The type of mutable arrays. Its type parameter is the type of the array’s elements.

Arrays of this type store their elements in a (Vectorof A):
> (define arr (mutable-array #[#[1 2] #[3 4]]))
> (vector-set! (mutable-array-data arr) 0 -10)
> arr

- : (Mutable-Array Integer)

(mutable-array #[#[-10 2] #[3 4]])

Mutable arrays are always strict.

syntax

Indexes

The type of array shapes and array indexes produced by math/array functions. Defined as (Vectorof Index).

Example:

> (array-shape (array #[#[#[0]]]))

- : Indexes

'#(1 1 1)

syntax

In-Indexes

The type of array shapes and array indexes accepted by math/array functions. Defined as (U Indexes (Vectorof Integer)).

Examples:

> (define ds #(3 2))
> ds

- : (Vector Integer Integer)

'#(3 2)

> (make-array ds (void))

- : (Array Void)

(array #[#[#<void> #<void>] #[#<void> #<void>] #[#<void> #<void>]])

This makes indexes-accepting functions easier to use, because it is easier to convince Typed Racket that a vector contains Integer elements than that a vector contains Index elements.

In-Indexes is not defined as (Vectorof Integer) because mutable container types like Vector and Vectorof are invariant. In particular, (Vectorof Index) is not a subtype of (Vectorof Integer):
> (define js ((inst vector Index) 3 4 5))
> js

- : Indexes

'#(3 4 5)

> (ann js (Vectorof Integer))

eval:103:0: Type Checker: Expected (Vectorof Integer), but

got Indexes

  in: (#%top . js29)

> (ann js In-Indexes)

- : In-Indexes

'#(3 4 5)

procedure

(array? v) → Boolean

  v : Any

procedure

(settable-array? v) → Boolean

  v : Any

procedure

(mutable-array? v) → Boolean

  v : Any
Predicates for the types Array, Settable-Array, and Mutable-Array.

Because Settable-Array and its descendants are invariant, settable-array? and its descendants’ predicates are generally not useful in occurrence typing. For example, if we know we have an Array but would like to treat it differently if it happens to be a Mutable-Array, we are basically out of luck:
> (: maybe-array-data (All (A) ((Array A) -> (U #f (Vectorof A)))))
> (define (maybe-array-data arr)
    (cond [(mutable-array? arr)  (mutable-array-data arr)]
          [else  #f]))

Type Checker: Polymorphic function mutable-array-data could

not be applied to arguments:

Argument 1:

  Expected: (Mutable-Array A)

  Given:    (Struct Mutable-Array)

  in: #%top-interaction

In general, predicates with a Struct filter do not give conditional branches access to a struct’s accessors. Because Settable-Array and its descendants are invariant, their predicates have Struct filters:
> array?

- : (Any -> Boolean : (Array Any))

#<procedure:Array?>

> settable-array?

- : (Any -> Boolean : (Struct Settable-Array))

#<procedure:Settable-Array?>

> mutable-array?

- : (Any -> Boolean : (Struct Mutable-Array))

#<procedure:Mutable-Array?>

procedure

(array-shape arr) → Indexes

  arr : (Array A)
Returns arr’s shape, a vector of indexes that contains the lengths of arr’s axes.

Examples:

> (array-shape (array 0))

- : Indexes

'#()

> (array-shape (array #[0 1]))

- : Indexes

'#(2)

> (array-shape (array #[#[0 1]]))

- : Indexes

'#(1 2)

> (array-shape (array #[]))

- : Indexes

'#(0)

procedure

(array-size arr) → Index

  arr : (Array A)
Returns the number of elements in arr, which is the product of its axis lengths.

Examples:

> (array-size (array 0))

- : Integer [generalized from Index]

1

> (array-size (array #[0 1]))

- : Integer [generalized from Index]

2

> (array-size (array #[#[0 1]]))

- : Integer [generalized from Index]

2

> (array-size (array #[]))

- : Integer [generalized from Index]

0

procedure

(array-dims arr) → Index

  arr : (Array A)
Returns the number of arr’s dimensions. Equivalent to (vector-length (array-shape arr)).

procedure

(mutable-array-data arr) → (Vectorof A)

  arr : (Mutable-Array A)
Returns the vector of data that arr contains.

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