Sort

The elements of the collection in increasing order.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageSort!↗

Sort(collection)the elements in increasing numeric order.

Sort(collection, comparator)sorted by a custom Function comparator, e.g. descending order.

Sort(expr)the operands of any expression, sorted in place — not just a collection's.

Typed signatures

Type	Package	Applies
((T, order: (((character) any -> unknown) | ((character, character) any -> boolean | number))?) -> T where T: string) & ((indexed_collection<T>, order: (((T) any -> unknown) | ((any, any) any -> boolean | number))?) -> list<T> where T: any)	combinatoricsreplaces compute-engine	always
((T, order: (((character) any -> unknown) | ((character, character) any -> boolean | number))?) -> T where T: string) & ((indexed_collection<T>, order: (((T) any -> unknown) | ((any, any) any -> boolean | number))?) -> list<T> where T: any)	compute-engine	always

Domain: Collections

Details

• Idempotent: sorting an already-sorted collection changes nothing.
• $Sort(c) = At(c, Ordering(c))$. See Ordering and At.
• Sort(c, p) puts a before b when p(a, b) holds and p(b, a) does not. Elements p holds both ways (a non-strict p, like <=) keep their input order; elements it holds neither way (a strict p, like <) come out in reverse input order, as Wolfram's does.
• Orders numbers numerically, strings in Wolfram's order (letters compare ignoring case, lowercase before uppercase on a tie, numbers before strings), and symbols alphabetically by name.
• The comparator form Sort(list, p) takes a predicate p reporting whether a pair is already in order.
• Works on the operands of any expression, not just a collection's elements.
• Differs from Wolfram: strings sort by code point, so "B" comes before "a"; Wolfram's canonical order puts a, b, B.

Examples

1 more kept as data, checked against the oracles

Basic #

live ↗

In$\mathrm{Sort}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3\bigr\rbrack$

live ↗

In$\mathrm{Sort}(\bigl\lbrack4, 2, 5, 1, 3\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3, 4, 5\bigr\rbrack$

Symbols sort alphabetically

live ↗

In$\mathrm{Sort}(\bigl\lbrack d, b, c, a\bigr\rbrack)$Out$\bigl\lbrack a, b, c, d\bigr\rbrack$

live ↗

In$\mathrm{Sort}(\bigl\lbrack\text{cat}, \text{fish}, \text{catfish}, \text{Cat}\bigr\rbrack)$Out$\bigl\lbrack\text{cat}, \text{Cat}, \text{catfish}, \text{fish}\bigr\rbrack$

live ↗

In$\mathrm{Sort}(\bigl\lbrack\text{b}, 1, \text{a}, 2\bigr\rbrack)$Out$\bigl\lbrack1, 2, \text{a}, \text{b}\bigr\rbrack$

Scope #

A custom comparator sorts in a different order, here descending

live ↗

In$\mathrm{Sort}(\bigl\lbrack3, 1, 2\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_1}\gt\operatorname{\_2})$Out$\bigl\lbrack3, 2, 1\bigr\rbrack$

A list of strings sorts lexicographically

live ↗

In$\mathrm{Sort}(\bigl\lbrack\mathrm{banana}, \mathrm{apple}, \mathrm{cherry}\bigr\rbrack)$Out$\bigl\lbrack\mathrm{apple}, \mathrm{banana}, \mathrm{cherry}\bigr\rbrack$

Integers, rationals and floats together sort by value

live ↗

In$\mathrm{Sort}(\bigl\lbrack\frac{3}{2}, 1, 0.5, -2\bigr\rbrack)$Out$\bigl\lbrack-2, 0.5, 1, \frac{3}{2}\bigr\rbrack$

Exact numeric constants sort by their value

live ↗

In$\mathrm{Sort}(\bigl\lbrack π, e, 2, 3, 1, \sqrt{2}\bigr\rbrack)$Out$\bigl\lbrack1, \sqrt{2}, 2, e, 3, π\bigr\rbrack$

$Less$ as the ordering function sorts by numeric value

live ↗

In$\mathrm{Sort}(\bigl\lbrack π, e, 2, 3, 1, \sqrt{2}\bigr\rbrack, \mathrm{Less})$Out$\bigl\lbrack1, \sqrt{2}, 2, e, 3, π\bigr\rbrack$

A named ordering function: $Greater$ sorts in descending order

live ↗

In$\mathrm{Sort}(\bigl\lbrack4, 1, 3, 2, 2\bigr\rbrack, \mathrm{Greater})$Out$\bigl\lbrack4, 3, 2, 2, 1\bigr\rbrack$

Sorting pairs by their second element with a custom comparator

live ↗

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

Sorts the arguments of any head, not just a list

live ↗

In$\mathrm{Sort}(f(b, a, c))$Out$f(a, b, c)$

A predicate that holds on a tie, like $\le$, keeps input order

live ↗

In$\mathrm{Sort}(\bigl\lbrack\bigl\lbrack1, \text{z}\bigr\rbrack, \bigl\lbrack2, \text{b}\bigr\rbrack, \bigl\lbrack1, \text{a}\bigr\rbrack, \bigl\lbrack1, "m"\bigr\rbrack\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_1}[1]≤\operatorname{\_2}[1])$Out$\bigl\lbrack\bigl\lbrack1, \text{z}\bigr\rbrack, \bigl\lbrack1, \text{a}\bigr\rbrack, \bigl\lbrack1, "m"\bigr\rbrack, \bigl\lbrack2, \text{b}\bigr\rbrack\bigr\rbrack$

A predicate that fails both ways on a tie, like $<$, puts ties in reverse input order

live ↗

In$\mathrm{Sort}(\bigl\lbrack\bigl\lbrack1, \text{z}\bigr\rbrack, \bigl\lbrack2, \text{b}\bigr\rbrack, \bigl\lbrack1, \text{a}\bigr\rbrack, \bigl\lbrack1, "m"\bigr\rbrack\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_1}[1]\lt\operatorname{\_2}[1])$Out$\bigl\lbrack\bigl\lbrack1, "m"\bigr\rbrack, \bigl\lbrack1, \text{a}\bigr\rbrack, \bigl\lbrack1, \text{z}\bigr\rbrack, \bigl\lbrack2, \text{b}\bigr\rbrack\bigr\rbrack$

Applications #

Numbers sort by value, not magnitude

live ↗

In$\mathrm{Sort}(\bigl\lbrack-11, 10, 2, 1, -4\bigr\rbrack)$Out$\bigl\lbrack-11, -4, 1, 2, 10\bigr\rbrack$

Mixes exact logs and roots in true numeric order, e.g. $\ln 2 < 1 < \ln 3$

live ↗

In$\mathrm{Sort}(\mathrm{Join}(\ln(1..10), \sqrt{1..10}), \mathrm{Less})$Out$\bigl\lbrack0, \ln(2), 1, \ln(3), 2\ln(2), \sqrt{2}, \ln(5), \sqrt{3}, \ln(6), \ln(7), 2, 3\ln(2), 2\ln(3), \sqrt{5}, \ln(10), \sqrt{6}, \sqrt{7}, 2\sqrt{2}, 3, \sqrt{10}\bigr\rbrack$

Strings sort alphabetically, so a shorter prefix comes first

live ↗

In$\mathrm{Sort}(\bigl\lbrack\text{aa}, \text{abb}, \text{ba}, \text{b}, \text{aaa}\bigr\rbrack)$Out$\bigl\lbrack\text{aa}, \text{aaa}, \text{abb}, \text{b}, \text{ba}\bigr\rbrack$

A custom order compares absolute values

live ↗

In$\mathrm{Sort}(\bigl\lbrack-11, 10, 2, 1, -4\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\vert\operatorname{\_1}\vert\lt\vert\operatorname{\_2}\vert)$Out$\bigl\lbrack1, 2, -4, 10, -11\bigr\rbrack$

live ↗

In$\mathrm{Sort}(\mathrm{Join}(\ln(1..10), \sqrt{1..10}))$Out$\bigl\lbrack0, \ln(2), 1, \ln(3), 2\ln(2), \sqrt{2}, \ln(5), \sqrt{3}, \ln(6), \ln(7), 2, 3\ln(2), 2\ln(3), \sqrt{5}, \ln(10), \sqrt{6}, \sqrt{7}, 2\sqrt{2}, 3, \sqrt{10}\bigr\rbrack$

Equal sort keys now follow Wolfram's tie order (our own convention changing, not a known value).

live ↗

In$\mathrm{Sort}(\bigl\lbrack\text{aa}, \text{abb}, \text{ba}, \text{b}, \text{aaa}\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\mathrm{StringLength}(\operatorname{\_1})\lt\mathrm{StringLength}(\operatorname{\_2}))$Out$\bigl\lbrack\text{b}, \text{ba}, \text{aa}, \text{aaa}, \text{abb}\bigr\rbrack$

Equal sort keys now follow Wolfram's tie order (our own convention changing, not a known value).

live ↗

In$\mathrm{Sort}(\bigl\lbrack i, 1+i, 1-i, 2+3i\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\Re(\operatorname{\_1})\lt\Re(\operatorname{\_2}))$Out$\bigl\lbrack i, 1-i, 1+i, 2+3i\bigr\rbrack$

Properties #

$Sort$ is idempotent: sorting an already-sorted collection changes nothing

live ↗

In$\mathrm{Sort}(\mathrm{Sort}(\bigl\lbrack3, 1, 2\bigr\rbrack))=\mathrm{Sort}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$\mathrm{True}$

$Sort(c) = At(c, Ordering(c))$. See Ordering and At

live ↗

In$\mathrm{Sort}(\bigl\lbrack3, 1, 2\bigr\rbrack)=\bigl\lbrack3, 1, 2\bigr\rbrack[\mathrm{Ordering}(\bigl\lbrack3, 1, 2\bigr\rbrack)]$Out$\mathrm{True}$

The result doesn't depend on the input order

live ↗

In$\mathrm{Sort}(\mathrm{Reverse}(\bigl\lbrack3, 1, 2\bigr\rbrack))=\mathrm{Sort}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$\mathrm{True}$

live ↗

In$\mathrm{Sort}(\mathrm{list})$Out$\mathrm{Sort}(\mathrm{list})$

Possible issues #

The empty list sorts to itself

live ↗

In$\mathrm{Sort}(\bigl\lbrack\bigr\rbrack)$Out$\bigl\lbrack\bigr\rbrack$

live ↗

In$\mathrm{Sort}(\bigl\lbrack∞, \sqrt{2}, 1, 2, -∞, \frac{\sqrt{2}}{2}\bigr\rbrack)$Out$\bigl\lbrack-∞, \frac{\sqrt{2}}{2}, 1, \sqrt{2}, 2, ∞\bigr\rbrack$

About

Examples	29
Checked against	Wolfram Language 26 agree3 differmathlib4 6 agree3 error
Crosswalk	Wolfram Language

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

A stable sort of exact rationals, increasing. Strings, symbols and nested lists fail to elaborate, since ours orders them by Wolfram's canonical order. A comparator is unbound.

See also: Ordering