FP (programming language): Difference between revisions

Revision as of 17:40, 14 August 2004

Revision as of 18:22, 14 August 2004

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

==Functionals==

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

These are are the principal functionals of FP:

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

for all values '''y''' (except the '''undefined''' value, '''⊥''', which all functions map into itself, due to their being [[strict function|strict]]). Next there are the remaining principal functionals of FP:

and '''x̄''':'''⊥''' = '''⊥'''

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

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'''insert-right''' /'''f''' where /'''f''':⟨'''x'''⟩ = '''x'''

and /'''f''':⟨'''x'''₁,'''x'''₂,...,'''x'''_n⟩ = '''f''':⟨'''x'''₁,/'''f''':⟨'''x'''₂,...,'''x'''_n⟩⟩

'''insert-left''' \'''f''' where \'''f''':⟨'''x'''⟩ = '''x'''

and \'''f''':⟨'''x'''₁,'''x'''₂,...,'''x'''_n⟩ = '''f''':⟨\'''f''':⟨'''x'''₁,...,'''x'''_n-1⟩,'''x'''_n⟩

[[es:FP (lenguaje de programación)]]