Filter

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

Return the elements of the collection for which the predicate function returns True. Equivalent to [x for x in xs if p(x)].

✓ checked against that system · ! checked, with disagreements (hover a chip)Fungrim entryWolfram LanguageSelect✓↗

Filter(collection<T>, predicate: (T) any -> boolean) -> collection where Tas compute-engine declares it

Filter(predicate)the operator form, $\mathrm{Filter}(p)(xs) = \mathrm{Filter}(xs, p)$.

Typed signatures

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

Domain: Compute engine

Examples

Basic #

Keeps the elements that satisfy the predicate

live ↗

In$\mathrm{Filter}(\bigl\lbrack1, 2, 4, 7, 6, 2\bigr\rbrack, \mathrm{IsEven})$Out$\bigl\lbrack2, 4, 6, 2\bigr\rbrack$

The complementary predicate keeps the rest

live ↗

In$\mathrm{Filter}(\bigl\lbrack1, 2, 4, 7, 6, 2\bigr\rbrack, \mathrm{IsOdd})$Out$\bigl\lbrack1, 7\bigr\rbrack$

live ↗

In$\mathrm{Filter}(\mathrm{IsEven})\lhd\bigl\lbrack1, 2, 4, 7, 6, 2\bigr\rbrack$Out$\bigl\lbrack2, 4, 6, 2\bigr\rbrack$

Scope #

Keeps the pairs that mention x

live ↗

In$\mathrm{Filter}(\bigl\lbrack\bigl\lbrack1, y\bigr\rbrack, \bigl\lbrack2, x\bigr\rbrack, \bigl\lbrack3, x\bigr\rbrack, \bigl\lbrack4, z\bigr\rbrack, \bigl\lbrack5, x\bigr\rbrack, \bigl\lbrack6, y\bigr\rbrack\bigr\rbrack, \operatorname{\_1}↦\mathrm{Contains}(\operatorname{\_1}, x))$Out$\bigl\lbrack\bigl\lbrack2, x\bigr\rbrack, \bigl\lbrack3, x\bigr\rbrack, \bigl\lbrack5, x\bigr\rbrack\bigr\rbrack$

A different test selects a single pair

live ↗

In$\mathrm{Filter}(\bigl\lbrack\bigl\lbrack1, y\bigr\rbrack, \bigl\lbrack2, x\bigr\rbrack, \bigl\lbrack3, x\bigr\rbrack, \bigl\lbrack4, z\bigr\rbrack, \bigl\lbrack5, x\bigr\rbrack, \bigl\lbrack6, y\bigr\rbrack\bigr\rbrack, \operatorname{\_1}↦\mathrm{Contains}(\operatorname{\_1}, z))$Out$\bigl\lbrack\bigl\lbrack4, z\bigr\rbrack\bigr\rbrack$

An anonymous test keeps elements greater than 2; duplicates and order preserved

live ↗

In$\mathrm{Filter}(\bigl\lbrack1, 2, 4, 7, 6, 2\bigr\rbrack, \operatorname{\_1}↦2\lt\operatorname{\_1})$Out$\bigl\lbrack4, 7, 6\bigr\rbrack$

Applications #

Numbers that are 1 mod both 3 and 5 are those 1 mod 15

live ↗

In$\mathrm{Filter}(1..100, \operatorname{\_1}↦\operatorname{\_1}\bmod3=1∧\operatorname{\_1}\bmod5=1)$Out$\bigl\lbrack1, 16, 31, 46, 61, 76, 91\bigr\rbrack$

Properties #

Evens in a range

live ↗

In$\mathrm{Filter}(1..10, \mathrm{IsEven})$Out$\bigl\lbrack2, 4, 6, 8, 10\bigr\rbrack$

About

Examples	8
Checked against	Wolfram Language 8 agree
Crosswalk	Fungrim entry ×13Wolfram Language

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

The elements where the predicate holds; a predicate that is not a Bool or decidable Prop fails to elaborate.