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A Programming Language: Difference between revisions
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Ordering is written with theta, not 0
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'''''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 book's title later was used to form the | '''''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 == | ||
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* [[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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* [[Catenate]] uses a circled comma. | * [[Catenate]] uses a circled comma. | ||
* [[Indexing]] is written with a subscript, or <math>\textstyle\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>. | ||