Evaluation of APL direct functions -

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here snippet testing recently. takes 2 diameters (⍺,⍵) , computes circumference of circle:

10{(○1×⍺){⍺ ⍵}○1×⍵}10 ⍝ note brackets around ⍺   31.4159 31.4159 10{○1×⍺{⍺ ⍵}○1×⍵}10   31.4159 98.696

i understand how evaluation of expression works - why first 1 evaluating correctly , second 1 isn't?

i using dyalog apl.

you have nested functions. in both cases, inner function returns right , left argument. in first case, left argument inner function expression (○ 1×⍺), in second case left argument inner function ⍺, or unaltered left argument of outer function -- entire result of inner function multiplied ○ , 1.

note argument circle function right 1 x totally redundant.

in apl, expressions evaluated right left. can function applies right unless modified parens. therefore in first expression ○ takes 1 multiplied right ⍺ due parentheses. in second expression ○ takes 1 multiplied right result of inner function.

furthermore, note due scalar extension, can compute 2 numbers no braces @ all:

      ○10 10 31.415926535898 31.415926535898

more interesting different diameters:

     ○10 15 20 31.415926535898 47.123889803847 62.831853071796

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