Function

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

A function literal

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Function(expression, (function | symbol)*) -> functionas compute-engine declares it

Typed signatures

Type	Package	Applies
`(expression, (function \| symbol)*) -> function`	`compute-engine`	always

Domain: Compute engine

Examples

Basic #

(u↦u+3)(x)

Out

x+3

(\operatorname{\_1}↦\operatorname{\_1}+3)(x)

Out

x+3

((u, v)↦v^4+u^2)(x, y)

Out

y^4+x^2

((\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_2}^4+\operatorname{\_1}^2)(x, y)

Out

y^4+x^2

Scope #

Tabulates $n^2+1$ using a pure function

\mathrm{Array}(\operatorname{\_1}↦\operatorname{\_1}^2+1, 10)

Out

\bigl\lbrack2, 5, 10, 17, 26, 37, 50, 65, 82, 101\bigr\rbrack

A two-argument function orders pairs by second component

\mathrm{Sort}(\bigl\lbrack\bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack c, 1\bigr\rbrack, \bigl\lbrack d, 3\bigr\rbrack\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_1}[2]\lt\operatorname{\_2}[2])

Out

\bigl\lbrack\bigl\lbrack c, 1\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack d, 3\bigr\rbrack\bigr\rbrack

(x↦x^2)^{\prime}

Out

x↦2x

Properties #

A function with no slots ignores its argument

\mathrm{Map}(()↦17, \bigl\lbrack1, 2, 3\bigr\rbrack)

Out

\bigl\lbrack17, 17, 17\bigr\rbrack

Tabulates the first ten squares

\mathrm{Array}(\operatorname{\_1}↦\operatorname{\_1}^2, 10)

Out

\bigl\lbrack1, 4, 9, 16, 25, 36, 49, 64, 81, 100\bigr\rbrack

\mathrm{ReplaceAll}(\operatorname{\_1}↦p+\operatorname{\_1}, \mathrm{Rule}(p, q))

Out

\operatorname{\_1}↦\operatorname{\_1}+q

(x↦y↦x^{y})(x)\lhd y

Out

x^{y}

(y↦x↦y^{x})(x)\lhd y

Out

x^{y}

(x↦x↦x^{x})(x)\lhd y

Out

y^{y}

(x↦y↦x^{y})(a)\lhd b

Out

a^{b}

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