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'''''A Programming Language''''' is a book published in 1962 by [[Kenneth E. Iverson]] | '''''A Programming Language''''' is the title of a book and a paper, both published in 1962 by [[Kenneth E. Iverson]]. It describes one iteration of [[Iverson notation|his notation]]. The initials of the book's title later was used to form [[the name APL]]. At the time of writing Iverson notation was used for mathematics and description of IBM's hardware, and its purely human purposes are reflected in the loose conventions (relative to APL) and two-dimensional structure of the notation presented in ''A Programming Language''. | ||
== Notation == | == Notation == | ||
''A Programming Language'' does not feature a full multidimensional [[array model]]. Rather, operations are defined on [[scalar]]s, [[vector]]s, and [[Matrix|matrices]] | ''A Programming Language'' does not feature a full multidimensional [[array model]]. Rather, operations are defined on [[scalar]]s, [[vector]]s, and [[Matrix|matrices]] while higher-[[rank]] arrays are not discussed. Nonetheless, it features many of the array conveniences that became characteristics of APL: | ||
* [[Scalar functions]] are present with the name "basic operations". | * [[Scalar functions]] are present with the name "basic operations". | ||
* While [[scalar extension]] is not defined in general, a scalar can be multiplied by an array as a "scalar multiple". | * While [[scalar extension]] is not defined in general, a scalar can be multiplied by an array as a "scalar multiple". | ||
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* The functions [[Absolute Value]], [[Ceiling]], and [[Floor]] use paired symbols (<math>|a|</math>, <math>\lceil a\rceil</math>, and <math>\lfloor a\rfloor</math>). The paired symbols for ceiling and floor were adopted by mathematicians (absolute value was already in use), but APL implementations dropped the closing symbol for consistency with monadic function syntax. | * The functions [[Absolute Value]], [[Ceiling]], and [[Floor]] use paired symbols (<math>|a|</math>, <math>\lceil a\rceil</math>, and <math>\lfloor a\rfloor</math>). The paired symbols for ceiling and floor were adopted by mathematicians (absolute value was already in use), but APL implementations dropped the closing symbol for consistency with monadic function syntax. | ||
* [[Residue]] uses <math>|</math> as in APL, but allows a subscript to indicate the smallest value allowed—mirroring [[index origin]]. | * [[Residue]] uses <math>|</math> as in APL, but allows a subscript to indicate the smallest value allowed—mirroring [[index origin]]. | ||
* [[ | * [[Interval]] (renamed "Index Generator" in [[APL\360]]) uses the letter <math>\iota</math> with an optional [[index origin]] subscript. | ||
* [[Index-Of]] is also written with <math>\iota</math> and an [[index origin]] subscript. It is defined on vector left arguments and vector or scalar right arguments. | * [[Index-Of]] is also written with <math>\iota</math> and an [[index origin]] subscript. It is defined on vector left arguments and vector or scalar right arguments. | ||
* [[Membership]] is <math>\epsilon</math> as in APL. | * [[Membership]] is <math>\epsilon</math> as in APL. | ||
* [[Reduction]] (<math>/</math>, or <math>//</math> instead of < | * [[Reduction]] (<math>/</math>, or <math>/\!/</math> instead of <syntaxhighlight lang=apl inline>⌿</syntaxhighlight>) starts from the left rather than the right. For reductions of [[empty]] arrays, the [[identity element]] is returned. | ||
* [[Rotate]] is written with arrows: <math>\uparrow</math> for left rotation and <math>\downarrow</math> for right rotation. | * [[Rotate]] is written with arrows: <math>\uparrow</math> for left rotation and <math>\downarrow</math> for right rotation. | ||
* [[Reverse]] is written with an arrow in some direction above the argument. | * [[Reverse]] is written with an arrow in some direction above the argument. | ||
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* [[Compress|Compression]] and [[Expand|Expansion]] use <math>/</math> and <math>\backslash</math> as in APL. | * [[Compress|Compression]] and [[Expand|Expansion]] use <math>/</math> and <math>\backslash</math> as in APL. | ||
* [[Catenate]] uses a circled comma. | * [[Catenate]] uses a circled comma. | ||
* [[Indexing]] is written with a subscript, or <math>\int_j</math> to allow [[index origin]] specification. | * [[Indexing]] is written with a subscript, or <math>\textstyle\int_j</math> to allow [[index origin]] specification. | ||
* [[Grade]] is called "ordering", and the Grade of <math>x</math> with [[index origin]] <math>j</math> is written <math> | * [[Grade]] is called "ordering", and the Grade of <math>x</math> with [[index origin]] <math>j</math> is written <math>\theta_j/x</math> | ||
* [[Base]] (<math>\bot</math>) on vectors works like in APL. On matrices, rows are paired up, or columns with a doubled base symbol. | * [[Base]] (<math>\bot</math>) on vectors works like in APL. On matrices, rows are paired up, or columns with a doubled base symbol. | ||
* The [[Intersection]] and [[Union]] are written with <math>\cap</math> and <math>\cup</math>, and the [[Set Difference]] with <math>\Delta</math>. | * The [[Intersection]] and [[Union]] are written with <math>\cap</math> and <math>\cup</math>, and the [[Set Difference]] with <math>\Delta</math>. | ||
* The [[Inner Product]] is written by placing one scalar function above another, e.g. <math>u\,^+_\times{}v</math>, and the [[Outer Product]] by using <math>\circ</math> in place of the top function with two vector arguments. | * The [[Inner Product]] is written by placing one scalar function above another, e.g. <math>u\,^+_\times{}v</math>, and the [[Outer Product]] by using <math>\circ</math> in place of the top function with two vector arguments | ||
{{APL dialects}} | == External links == | ||
* [https://www.jsoftware.com/papers/AFIPS196205.htm Digitised version of the paper] | |||
* [https://www.jsoftware.com/papers/APL.htm Partially digitised version of the book] | |||
* [http://www.softwarepreservation.org/projects/apl/Books/APROGRAMMING%20LANGUAGE Scan of the full book] | |||
{{APL dialects}}[[Category:Iverson notation]][[Category:Publications]] | |||