FP (programming language)

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 x̄. Functions are strict:

'''f''':'''⊥''' = '''⊥'''

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