Function Programming (FP) is a programming language created by John Backus to support the function-level programming paradigm. This allows eliminating named variables.

Overview

The values that FP programs map into one another comprise a set which is closed under sequence formation:

if \(x_1, \dots, x_n\) are values, then the sequence \(\langle x_1, \dots, x_n \rangle\) is also a value

These values can be built from any set of atoms: booleans, integers, reals, characters, etc.:

boolean \(: \{T, F\}\)

integer \(: \{0, 1, 2, \dots \}\)

character \(: \{'a', 'b', \dots \}\)

symbol \(: \{x, y, \dots \}\)

The notation \(\bot\) is for a undefined value. Sequences are \(\bot\)-preserving: \[\langle x_1, \dots, \bot, \dots, x_n \rangle = \bot\]

Functionals

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Equational functions

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Conclusion

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