NoneTrue

Whether no element of a collection satisfies a predicate.

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

NoneTrue(xs, predicate)$True$ if $predicate$ holds for no element of $xs$, else $False$.

Typed signatures

Type	Package	Applies
(indexed_collection<T>, (T) any -> boolean) -> boolean where T	combinatorics	always

Domain: Collections

Details

• The negation of Any: $NoneTrue(xs, p) = Not(Any(xs, p))$.

Examples

Basic #

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack1, 3, 5\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{True}$

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack1, 2, 3\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{False}$

False because some elements are even

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{False}$

True when no element passes the test

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack1, 3, 5, 7, 9\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{True}$

Symbolic entries leave the test undecided, while $8<10$ already settles it

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack12, 16, x, 8, 14, y\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\lt10)$Out$\mathrm{False}$

Wrapping with IsTrue makes undecided tests count as not true

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack12, 16, x, 14, y\bigr\rbrack, \operatorname{\_1}↦\mathrm{IsTrue}(\operatorname{\_1}\lt10))$Out$\mathrm{True}$

Scope #

Vacuously true on an empty list

live ↗

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

An undecided predicate gives the Nor of its values, as Wolfram does

live ↗

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

One True settles it, whatever else is undecided

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack a, 4\bigr\rbrack, \mathrm{IsEven})$Out$\mathrm{False}$

Properties #

The negation of Any

live ↗

In$\mathrm{NoneTrue}(\bigl\lbrack4, 6, 9\bigr\rbrack, \mathrm{IsPrime})=¬\mathrm{Any}(\bigl\lbrack4, 6, 9\bigr\rbrack, \mathrm{IsPrime})$Out$\mathrm{True}$

About

Examples	10
Checked against	Wolfram Language 10 agree
Crosswalk	Wolfram Language

See also: All, Any