Function Repository Resource:

RandomCombinator

Source Notebook

Generate a pseudorandom combinator

Contributed by: Robert Nachbar

ResourceFunction["RandomCombinator"][k]

gives a pseudorandom combinator with k symbols.

ResourceFunction["RandomCombinator"][k,syms]

uses symbols from the list syms.

ResourceFunction["RandomCombinator"][k,syms,n]

gives a list of n pseudorandom combinators.

ResourceFunction["RandomCombinator"][k,syms,{n₁,n₂,…}]

gives an n₁×n₂×… array of pseudorandom combinators.

Details and Options

ResourceFunction["RandomCombinator"][k,syms] chooses combinators from the set of all possible combinators with k symbols from the list syms with equal probability.

ResourceFunction["RandomCombinator"] gives a different sequence of pseudorandom combinators whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom.

ResourceFunction["RandomCombinator"][n] is equivalent to ResourceFunction["RandomCombinator"][n,{CombinatorS,CombinatorK}].

ResourceFunction["RandomCombinator"] has the following options:

CombinerFunction

Construct

function to use for combining symbols

Examples

Basic Examples (3)

A random combinator with 5 symbols:

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Ten random combinators with 5 symbols:

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A 3×4 array of random combinators with 5 symbols:

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Scope (2)

Generate random combinators with any list of symbols:

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$ResourceFunction[ "RandomCombinator"][5, {\[FormalF], \[FormalG], \[FormalH]}]$

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Generate random combinators of any size:

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Options (1)

CombinerFunction (1)

Use CombinerFunction→Application to combine the symbols:

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Properties and Relations (2)

Use SeedRandom to get repeatable random combinators:

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RandomCombinator generates a uniform distribution. The set of combinators with n symbols from an alphabet of k symbols has cardinality kⁿ×CatalanNumber[n-1]. First compute the cardinality: