Function Repository Resource:

CombinatorConvert

Source Notebook

Convert between different combinator formats

Contributed by: Mano Namuduri and Jan Mangaldan

ResourceFunction["CombinatorConvert"][cmb,format]

converts a combinator expression cmb to the specified format.

ResourceFunction["CombinatorConvert"][transform]

interconverts a combinator transformation rule transform between the RuleDelayed and Function formats.

ResourceFunction["CombinatorConvert"][transform,name]

interconverts a combinator transformation rule transform using the symbol name to designate the combinator on the left-hand side when converting to RuleDelayed.

Details

The following settings for format are supported:

"Application"

combinator represented in terms of Application,S

I))

"List"

combinator represented as a list, {{{{S, {K, {S,I}}}, {{S, {K,K}}, I}}, x}, y}

"Nested"

combinator in nested bracket format, S[K[S[I]]][S[K[K]][I]][x][y]

"String"

combinator represented as a left-associative string, "S(K(SI))(S(KK)I)xy"

Accordingly, the argument cmb can be given in any of the above formats.

If transform is given as a RuleDelayed (lhs ⧴ rhs), then ResourceFunction["CombinatorConvert"] will return a pure Function. If transform is given as a Function (arg

body), then ResourceFunction["CombinatorConvert"] will return a RuleDelayed.

The argument name, if specified, should be given as a Symbol (default is λ).

Examples

Basic Examples (5)

Convert a combinator expression in application format to each of the possible formats:

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$ResourceFunction["CombinatorConvert"][ CombinatorS\[Application](CombinatorK\[Application]CombinatorS)\[Application]CombinatorK, "Application"]$

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$ResourceFunction["CombinatorConvert"][ CombinatorS\[Application](CombinatorK\[Application]CombinatorS)\[Application]CombinatorK, "List"]$

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$ResourceFunction["CombinatorConvert"][ CombinatorS\[Application](CombinatorK\[Application]CombinatorS)\[Application]CombinatorK, "Nested"]$

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$ResourceFunction["CombinatorConvert"][ CombinatorS\[Application](CombinatorK\[Application]CombinatorS)\[Application]CombinatorK, "String"]$

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Convert a combinator expression in nested bracket format to each of the possible formats:

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Convert a combinator expression in list format to each of the possible formats:

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Convert a combinator expression in list format to each of the possible formats (note that the conversion from string format only allows single-character symbols, so combinator glyphs would need to be inserted retroactively):

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Convert between the RuleDelayed and Function formats of the CombinatorB transformation:

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When converting from Function to RuleDelayed, a second argument must be supplied for the correct symbol to appear on the left-hand side:

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Possible Issues (3)

Input strings containing any symbol other than letters, digits or parentheses are currently not supported:

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$ResourceFunction["CombinatorConvert"][ "S\[Application](S\[Application]S)\[Application]S\[Application](S\[Application]K)", #] & /@ {"Application", "List", "Nested", "String"}$