## Functional Programming

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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