FP (programming language): Difference between revisions

Revision as of 18:22, 14 August 2004

Revision as of 18:32, 14 August 2004

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if '''x'''₁,...,'''x'''_n are '''values''', then the '''sequence''' ⟨'''x'''₁,...,'''x'''_n⟩ is also a '''value'''

These values can be built from any set of atoms: booleans, integers, reals, characters, etc. '''⊥''' is the '''undefined''' value, or '''bottom'''. Sequences are ''bottom-preserving'':

⟨'''x'''₁,...,'''⊥''',...,'''x'''_n⟩ = '''⊥'''

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

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'''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 one such operation is '''constant''', which transforms a value '''x''' into the constant-valued function '''x̄'''. '''⊥'''Functions are [[strict function|strict]]: is the '''undefined''' value, which all functions map into itself, due to their [[strict function|strict]] nature.

and '''x̄f''':'''⊥''' = '''⊥'''

==Functionals==

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'''constant''' '''x̄''' where '''x̄''':'''y''' = '''x'''

and '''x̄''':'''⊥''' = '''⊥'''

'''composition''' '''f'''&#x°'''g''' where '''f'''&#x°'''g''':'''x''' = '''f''':('''g''':'''x''')