Function composition: Difference between revisions
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=== Summary of rules === | === Summary of rules === | ||
The above compositions can be summarised as follows: | The above compositions can be summarised as follows, including their [[wikipedia:combinatory logic|combinatory logic]] equivalents: | ||
<syntaxhighlight lang=apl inline> (f⍛g ) ⍵</syntaxhighlight> | {| class=wikitable | ||
<syntaxhighlight lang=apl inline>⍺ (f⍛g ) ⍵</syntaxhighlight> | ! Tacit form !! Explicit form !! Function Abstraction !! Symbol !! Bird Name | ||
<syntaxhighlight lang=apl inline> ( g∘h) ⍵</syntaxhighlight> | |- | ||
<syntaxhighlight lang=apl inline>⍺ ( g∘h) ⍵</syntaxhighlight> | | <syntaxhighlight lang=apl inline> (f⍛g ) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline>( f ⍵) g ⍵ </syntaxhighlight> || λabc.a(bc)c || style="text-align:center" | Σ || Violet Starling | ||
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<syntaxhighlight lang=apl inline> ( g⍤h) ⍵</syntaxhighlight> | | <syntaxhighlight lang=apl inline>⍺ (f⍛g ) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline>( f ⍺) g ⍵ </syntaxhighlight> || λabcd.a(bc)d || style="text-align:center" | Δ || Zebra Dove | ||
<syntaxhighlight lang=apl inline>⍺ ( g⍤h) ⍵</syntaxhighlight> | |- | ||
<syntaxhighlight lang=apl inline> ( g⍥h) ⍵</syntaxhighlight> | | <syntaxhighlight lang=apl inline> ( g∘h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> g ( h ⍵)</syntaxhighlight> || λabc.a(bc) || style="text-align:center" | B || Bluebird | ||
<syntaxhighlight lang=apl inline>⍺ ( g⍥h) ⍵</syntaxhighlight> | |- | ||
| <syntaxhighlight lang=apl inline>⍺ ( g∘h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> ⍺ g ( h ⍵)</syntaxhighlight> || λabcd.ab(cd) || style="text-align:center" | D ||| Dove | |||
<syntaxhighlight lang=apl inline> ( g h) ⍵</syntaxhighlight> | |- | ||
<syntaxhighlight lang=apl inline>⍺ ( g h) ⍵</syntaxhighlight> | | | ||
<syntaxhighlight lang=apl inline> (f g h) ⍵</syntaxhighlight> | |- | ||
<syntaxhighlight lang=apl inline>⍺ (f g h) ⍵</syntaxhighlight> | | <syntaxhighlight lang=apl inline> ( g⍤h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> g ( h ⍵)</syntaxhighlight> || λabc.a(bc) || style="text-align:center" | B || Bluebird | ||
|- | |||
<syntaxhighlight lang=apl inline> (A∘g ) ⍵</syntaxhighlight> | | <syntaxhighlight lang=apl inline>⍺ ( g⍤h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> g (⍺ h ⍵)</syntaxhighlight> || λabcd.a(bcd) || style="text-align:center" | B<sub>1</sub> || Blackbird | ||
<syntaxhighlight lang=apl inline> ( g∘A) ⍵</syntaxhighlight> | |- | ||
<syntaxhighlight lang=apl inline> (A g h) ⍵</syntaxhighlight> | | <syntaxhighlight lang=apl inline> ( g⍥h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> g ( h ⍵)</syntaxhighlight> || λabc.a(bc) || style="text-align:center" | B || Bluebird | ||
<syntaxhighlight lang=apl inline>⍺ (A g h) ⍵</syntaxhighlight> | |- | ||
| <syntaxhighlight lang=apl inline>⍺ ( g⍥h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline>( h ⍺) g ( h ⍵)</syntaxhighlight> || λabcd.a(bc)(bd) || style="text-align:center" | Ψ || | |||
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| <syntaxhighlight lang=apl inline> ( g h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> g ( h ⍵)</syntaxhighlight> || λabc.a(bc) || style="text-align:center" | B || Bluebird | |||
|- | |||
| <syntaxhighlight lang=apl inline>⍺ ( g h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> g (⍺ h ⍵)</syntaxhighlight> || λabcd.a(bcd) || style="text-align:center" | B<sub>1</sub> || Blackbird | |||
|- | |||
| <syntaxhighlight lang=apl inline> (f g h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline>( f ⍵) g ( h ⍵)</syntaxhighlight> || λabcd.a(bd)(cd) || style="text-align:center" | Φ || Phoenix | |||
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| <syntaxhighlight lang=apl inline>⍺ (f g h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline>(⍺ f ⍵) g (⍺ h ⍵)</syntaxhighlight> || λabcde.a(bde)(cde) || style="text-align:center" | Φ<sub>1</sub> || Pheasant | |||
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|- | |||
| <syntaxhighlight lang=apl inline> (A∘g ) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> A g ⍵ </syntaxhighlight> || || || | |||
|- | |||
| <syntaxhighlight lang=apl inline> ( g∘A) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> ⍵ g A </syntaxhighlight> || || || | |||
|- | |||
| <syntaxhighlight lang=apl inline> (A g h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> A g ( h ⍵)</syntaxhighlight> || || || | |||
|- | |||
| <syntaxhighlight lang=apl inline>⍺ (A g h) ⍵</syntaxhighlight> || <syntaxhighlight lang=apl inline> A g (⍺ h ⍵)</syntaxhighlight> || || || | |||
|} | |||
== Additional compositions == | == Additional compositions == |