All

Whether every element of a collection satisfies a predicate.

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

All(xs, predicate)$True$ if $predicate$ holds for every element of $xs$, else $False$.

All(xs, predicate, level)the elements at exactly level tested instead of the top-level ones.

Typed signatures

Type	Package	Applies
(collection<T>, predicate: ((T) any -> boolean)?) -> boolean where T	combinatoricsreplaces compute-engine	always
(collection<T>, predicate: ((T) any -> boolean)?) -> boolean where T	compute-engine	always

Domain: Collections

Examples

Basic #

live ↗

In$\mathrm{All}(\bigl\lbrack2, 4, 6\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\bmod2=0)$Out$\mathrm{True}$

live ↗

In$\mathrm{All}(\bigl\lbrack2, 4, 5\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\bmod2=0)$Out$\mathrm{False}$

A named predicate

live ↗

In$\mathrm{All}(\bigl\lbrack2, 3, 5, 7\bigr\rbrack, \mathrm{IsPrime})$Out$\mathrm{True}$

live ↗

In$\mathrm{All}(\bigl\lbrack1, 2, 3\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\gt0)$Out$\mathrm{True}$

One odd element makes the test false

live ↗

In$\mathrm{All}(\bigl\lbrack2, 3, 4, 6, 8\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{False}$

True when every element passes

live ↗

In$\mathrm{All}(\bigl\lbrack2, 4, 6, 8\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{True}$

The element 15 already fails, so symbols don't matter

live ↗

In$\mathrm{All}(\bigl\lbrack2, 6, x, 4, y, 15\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\lt10)$Out$\mathrm{False}$

Unresolved $x<10$ is not provably true, so the test is false

live ↗

In$\mathrm{All}(\bigl\lbrack2, 6, x, 4, y\bigr\rbrack, \operatorname{\_1}↦\mathrm{IsTrue}(\operatorname{\_1}\lt10))$Out$\mathrm{False}$

Scope #

One definite failure decides the answer, even beside a symbolic element

live ↗

In$\mathrm{All}(\bigl\lbrack1, x\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{False}$

Without a predicate, tests the elements themselves

live ↗

In$\mathrm{All}(\bigl\lbrack\mathrm{True}, \mathrm{True}\bigr\rbrack)$Out$\mathrm{True}$

A level argument tests the elements at depth 2 of a nested list

live ↗

In$\mathrm{All}(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\gt0, 2)$Out$\mathrm{True}$

An undecided predicate gives the conjunction of its values, as Wolfram's AllTrue does

live ↗

In$\mathrm{All}(\bigl\lbrack a, b\bigr\rbrack, f)$Out$f(a)∧f(b)$

One False settles it, whatever else is undecided

live ↗

In$\mathrm{All}(\bigl\lbrack a, 3\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{False}$

Properties #

Vacuously true on an empty list

live ↗

In$\mathrm{All}(\bigl\lbrack\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{True}$

About

Examples	14
Checked against	Wolfram Language 13 agree1 differ
Crosswalk	FungrimWolfram Language

See also: Any, NoneTrue