Editing FP (programming language) (section)

==Functionals==

In contrast to primitive functions, functionals operate on other functions.  For example, some functions have a ''unit'' value, such as 0 for ''addition'' and 1 for ''multiplication''. The functional '''unit''' produces such a '''value''' when applied to a '''function f''' that has one:
 '''unit +'''   =  0
 '''unit ×'''   =  1
 '''unit foo''' =  ⊥

These are the core functionals of FP:

 '''composition'''  '''f'''∘'''g'''        where    '''f'''∘'''g''':'''x''' = '''f''':('''g''':'''x''')

 '''construction''' ['''f'''<sub>1</sub>,...,'''f'''<sub>n</sub>] where   ['''f'''<sub>1</sub>,...,'''f'''<sub>n</sub>]:'''x''' =  〈'''f'''<sub>1</sub>:'''x''',...,'''f'''<sub>n</sub>:'''x'''〉

 '''condition''' ('''h''' ⇒ '''f''';'''g''')    where   ('''h''' ⇒ '''f''';'''g'''):'''x'''   =  '''f''':'''x'''   if   '''h''':'''x'''  =  '''T'''
                                              =  '''g''':'''x'''   if   '''h''':'''x'''  =  '''F'''
                                              =  '''⊥'''    otherwise

 '''apply-to-all'''  ''α'''''f'''       where   ''α'''''f''':〈'''x'''<sub>1</sub>,...,'''x'''<sub>n</sub>〉  = 〈'''f''':'''x'''<sub>1</sub>,...,'''f''':'''x'''<sub>n</sub>〉

 '''insert-right'''  /'''f'''       where   /'''f''':〈'''x'''〉             =  '''x'''
                        and     /'''f''':〈'''x'''<sub>1</sub>,'''x'''<sub>2</sub>,...,'''x'''<sub>n</sub>〉  =  '''f''':〈'''x'''<sub>1</sub>,/'''f''':〈'''x'''<sub>2</sub>,...,'''x'''<sub>n</sub>〉〉
                        and     /'''f''':〈 〉             =  '''unit f'''

 '''insert-left'''  \'''f'''       where   \'''f''':〈'''x'''〉             =  '''x'''
                       and     \'''f''':〈'''x'''<sub>1</sub>,'''x'''<sub>2</sub>,...,'''x'''<sub>n</sub>〉  =  '''f''':〈\'''f''':〈'''x'''<sub>1</sub>,...,'''x'''<sub>n-1</sub>〉,'''x'''<sub>n</sub>〉
                       and     \'''f''':〈 〉             =  '''unit f'''