Difference between revisions of "Compose"

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(New page: In the following descriptions, <apll><i>f</i></apll> and <apll><i>g</i></apll> represent functions and <apll><i>a</i></apll> and <apll><i>b</i></apll> represent variables. * The form <apl...)
 
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:Monadic:  <apll>Z←<i>f</i>∘<i>g</i>R</apll> is identical to <apll>Z←<i>f</i><i>g</i>R</apll>.
 
:Monadic:  <apll>Z←<i>f</i>∘<i>g</i>R</apll> is identical to <apll>Z←<i>f</i><i>g</i>R</apll>.
 
:
 
:
:Dyadic:  <apll>Z←L<i>f</i>∘<i>g</i>R</apll> is identical to <apll>Z←(<i>g</i>L)<i>f</i><i>g</i>R</apll>.
+
:Dyadic:  <apll>Z←L<i>f</i>∘<i>g</i>R</apll> is identical to <apll>Z←L<i>f</i><i>g</i>R</apll>.
  
 
* The form <apll><i>f</i>∘b</apll> may be used monadically only.
 
* The form <apll><i>f</i>∘b</apll> may be used monadically only.

Revision as of 17:30, 15 December 2008

In the following descriptions, f and g represent functions and a and b represent variables.

  • The form fg may be used both monadically and dyadically.
Monadic: Z←fgR is identical to Z←fgR.
Dyadic: Z←LfgR is identical to Z←LfgR.
  • The form f∘b may be used monadically only.
Monadic: Z←(fb) R is identical to Z←R f b.
Note that parentheses are required around the function to avoid interpreting b R as a strand.
  • The form ag may be used monadically only.
Monadic: Z←agR is identical to Z←a g R.
  • The derived function from the form ab always signals a SYNTAX ERROR.