FP (Programming Language)

Programming Language
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# FP (programming language)

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Description:
FP (short for Function Programming) 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'''<sub>1</sub>,...,'''x'''<sub>n</sub> are '''values''', then the '''sequence''' 〈'''x'''<sub>1</sub>,...,'''x'''<sub>n</sub>〉 is also a '''value'''
```

These values can be built from any set of atoms: booleans, integers, reals, characters, etc.:
```'''boolean'''   :
'''integer'''   :
'''character''' :
'''symbol'''    :
```

is the undefined value, or bottom. Sequences are bottom-preserving:

```〈'''x'''<sub>1</sub>,...,'''⊥''',...,'''x'''<sub>n</sub>〉  =  '''⊥'''
```

FP programs are functions f that each map a single value x into another:

```'''f''':'''x''' represents the '''value''' that results from applying the '''function''' '''f'''
to the '''value''' '''x'''
```

Functions are either primitive (i.e., provided with the FP environment) or are built from the primitives by program-forming operations (also called functionals).

An example of primitive function is constant, which transforms a value x into the constant-valued function . Functions are strict:
```'''f''':'''⊥''' = '''⊥'''
```

Another example of a primitive function is the selector function family, denoted by 1,2,.........

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