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| The ω refers to the argument of the function, a list (or 1-dimensional array) of numbers. The ρ denotes the shape function, which returns here the length of (number of elements in) the argument ω. The divide symbol ÷ has its usual meaning. | The {{{ω}}} refers to the argument of the function, a list (or 1-dimensional array) of numbers. The {{{ρ}}} denotes the shape function, which returns here the length of (number of elements in) the argument {{{ω}}}. The divide symbol {{{÷}}} has its usual meaning. |
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| The parenthesised +/ω denotes the sum of all the elements of ω. The / operator combines with the + function: the / fixes the + function between each element of ω, so that | The parenthesised {{{+/ω}}} denotes the sum of all the elements of {{{ω}}}. The {{{/}}} operator combines with the {{{+}}} function: the {{{/}}} fixes the {{{+}}} function between each element of {{{ω}}}, so that {{{ |
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Operators like / can be used to derive new functions not only from primitive functions like +, but also from defined functions. For example |
}}} Operators like {{{/}}} can be used to derive new functions not only from primitive functions like {{{+}}}, but also from defined functions. For example {{{ |
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So back to our mean example. (+/ω) gives the sum of the list, which is then divided by ρω, the number of its elements. |
}}} So back to our mean example. {{{(+/ω)}}} gives the sum of the list, which is then divided by {{{ρω}}}, the number of its elements. {{{ |
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| The same program in J | == The same program in J == |
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>> [:DiscoveringApl/AplAndTypography: APL & Typography] |
Discovering APL
Some APL Examples
Here is an APL program to calculate the average (arithmetic mean) of a list of numbers. It is written in D, the ‘direct’ form of Dyalog APL.
{(+/ω)÷ρω}
It is unnamed: the enclosing braces mark it as a function definition. It can be assigned a name for use later, or used anonymously in a more complex expression.
The ω refers to the argument of the function, a list (or 1-dimensional array) of numbers. The ρ denotes the shape function, which returns here the length of (number of elements in) the argument ω. The divide symbol ÷ has its usual meaning.
The parenthesised +/ω denotes the sum of all the elements of ω. The / operator combines with the + function: the / fixes the + function between each element of ω, so that
+/ 1 2 3 4 5 6 21
is the same as
1+2+3+4+5+6 21
Operators like / can be used to derive new functions not only from primitive functions like +, but also from defined functions. For example
{α,', ',ω}/will transform a list of strings representing words into a comma-separated list:
{α,', ',ω}/'cow' 'sheep' 'cat' 'dog'
cow, sheep, cat, dogSo back to our mean example. (+/ω) gives the sum of the list, which is then divided by ρω, the number of its elements.
{(+/ω)÷ρω} 3 4.5 7 21
8.875
The same program in J
In J’s tacit definition no braces are needed to mark the definition of a function: primitive functions just combine in a way that enables us to omit any reference to the function arguments — hence tacit.
Here is the same calculation written in J:
- (+/%#) 3 4.5 7 21
8.875
In J’s terminology, functions are called verbs and operators adverbs. So: the verb # gives the length of the argument. Division is marked by % instead of ÷. The sum verb is again marked by +/: the verb + is modified by the adverb /.
The adverb \ can be used to modify the +/%# verb to produce a moving average.
- 2 (+/%#)\ 3 4.5 7 21
3.75 5.75 14
or, more verbosely
- ave =: +/%# ave 3 4.5 7 21
8.875
- mave =: ave\ 2 mave 3 4.5 7 21
3.75 5.75 14
The J Wiki contains a selection of essays in which you can see similarly succinct solutions to a range of problems.
>> [:DiscoveringApl/AplAndTypography: APL & Typography]