A Programming Language: Difference between revisions

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''A Programming Language'' features precursors of many APL [[primitive functions]]. These include:

* The [[shape]] vector is not used, but dimension functions are present: <math>ν</math> gives the length of a vector, and <math>ν</math> and <math>μ</math> give the row length and column length of a matrix.

* The [[shape]] vector is not used, but dimension functions are present: <math>\nu</math> gives the length of a vector, and <math>\nu</math> and <math>\mu</math> give the row length and column length of a matrix.

* [[Comparison functions]] are defined using the symbols <math><</math>, <math>></math>, and <math>=</math> and the rules that a vertical bar negates a relation and that an underline combines it with <math>=</math> (relations are combined by or-ing them together).

* The arithmetic [[scalar functions]] [[Sum]] (<math>+</math>), [[Difference]] (<math>-</math>), [[Product]] (<math>×</math>), and [[Quotient]] (<math>÷</math>) are defined as in mathematics.

* The arithmetic [[scalar functions]] [[Sum]] (<math>+</math>), [[Difference]] (<math>-</math>), [[Product]] (<math>\times</math>), and [[Quotient]] (<math>\div</math>) are defined as in mathematics.

* The logical functions [[And]] (<math>∧</math>) and [[Or]] (<math>∨</math>) also match mathematical usage. [[Logical negation]] is denoted with an overbar.

* The logical functions [[And]] (<math>\wedge</math>) and [[Or]] (<math>\vee</math>) also match mathematical usage. [[Logical negation]] is denoted with an overbar.

* The functions [[Absolute Value]], [[Ceiling]], and [[Floor]] use paired symbols (<math>|a|</math>, <math>~~⌈a⌉~~</math>, and <math>~~⌊a⌋~~</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]].

* [[Iota]] is called "Interval" and uses the letter <math>\iota</math> with an optional [[index origin]] subscript.

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* [[Membership]] is <math>\epsilon</math> as in APL.

* [[Reduction]] (<math>/</math>, or <math>//</math> instead of <source lang=apl inline>⌿</source>) starts from the left rather than the right. For reductions of [[empty]] arrays, the [[identity element]] is returned.

* [[Rotate]] is written with arrows: <math>↑</math> for left rotation and <math>↓</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.

* [[Transpose]] is written with a tilde (<math>\tilde{}</math>) above a matrix, e.g. <math>\tilde M</math>.

* [[Compress|Compression]] and [[Expand|Expansion]] use <math>/</math> and <math>\backslash</math> as in APL.

* [[Catenate]] uses a circled comma.

* [[Indexing]] is written with a subscript, or <math>~~∫_j~~</math> to allow [[index origin]] specification.

* [[Indexing]] is written with a subscript, or <math>\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>0_j/x</math>

* [[Base]] (<math>⊥</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>∩</math> and <math>∪</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\,^+~~_×v~~</math>, and the [[Outer Product]] by using <math>∘</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.

@@ Line 11: / Line 11: @@
 ''A Programming Language'' features precursors of many APL [[primitive functions]]. These include:
-* The [[shape]] vector is not used, but dimension functions are present: <math>ν</math> gives the length of a vector, and <math>ν</math> and <math>μ</math> give the row length and column length of a matrix.
+* The [[shape]] vector is not used, but dimension functions are present: <math>\nu</math> gives the length of a vector, and <math>\nu</math> and <math>\mu</math> give the row length and column length of a matrix.
 * [[Comparison functions]] are defined using the symbols <math><</math>, <math>></math>, and <math>=</math> and the rules that a vertical bar negates a relation and that an underline combines it with <math>=</math> (relations are combined by or-ing them together).
-* The arithmetic [[scalar functions]] [[Sum]] (<math>+</math>), [[Difference]] (<math>-</math>), [[Product]] (<math>×</math>), and [[Quotient]] (<math>÷</math>) are defined as in mathematics.
+* The arithmetic [[scalar functions]] [[Sum]] (<math>+</math>), [[Difference]] (<math>-</math>), [[Product]] (<math>\times</math>), and [[Quotient]] (<math>\div</math>) are defined as in mathematics.
-* The logical functions [[And]] (<math>∧</math>) and [[Or]] (<math>∨</math>) also match mathematical usage. [[Logical negation]] is denoted with an overbar.
+* The logical functions [[And]] (<math>\wedge</math>) and [[Or]] (<math>\vee</math>) also match mathematical usage. [[Logical negation]] is denoted with an overbar.
-* The functions [[Absolute Value]], [[Ceiling]], and [[Floor]] use paired symbols (<math>|a|</math>, <math>⌈a⌉</math>, and <math>⌊a⌋</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]].
 * [[Iota]] is called "Interval" and uses the letter <math>\iota</math> with an optional [[index origin]] subscript.
@@ Line 21: / Line 21: @@
 * [[Membership]] is <math>\epsilon</math> as in APL.
 * [[Reduction]] (<math>/</math>, or <math>//</math> instead of <source lang=apl inline>⌿</source>) starts from the left rather than the right. For reductions of [[empty]] arrays, the [[identity element]] is returned.
-* [[Rotate]] is written with arrows: <math>↑</math> for left rotation and <math>↓</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.
 * [[Transpose]] is written with a tilde (<math>\tilde{}</math>) above a matrix, e.g. <math>\tilde M</math>.
 * [[Compress|Compression]] and [[Expand|Expansion]] use <math>/</math> and <math>\backslash</math> as in APL.
 * [[Catenate]] uses a circled comma.
-* [[Indexing]] is written with a subscript, or <math>∫_j</math> to allow [[index origin]] specification.
+* [[Indexing]] is written with a subscript, or <math>\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>0_j/x</math>
-* [[Base]] (<math>⊥</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>∩</math> and <math>∪</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\,^+_×v</math>, and the [[Outer Product]] by using <math>∘</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}}

A Programming Language: Difference between revisions

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