Trains - Revision history

Sudleyplace at 19:32, 15 April 2018

2018-04-15T19:32:30Z

← Older revision		Revision as of 15:32, 15 April 2018
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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>L</apll> and <apll>R</apll> are arbitrary arrays, <apll>f</apll>, <apll>g</apll>, <apll>h</apll>, etc, are arbitrary functions of any type: primitive, user-defined, system, and/or derived.</td>		<td><apll>L</apll> and <apll>R</apll> are arbitrary arrays, <apll>f</apll>, <apll>g</apll>, <apll>h</apll>, etc, are arbitrary functions of any type: primitive, user-defined, system, anonymous, and/or derived.</td>
	</tr>		</tr>
	</table>		</table>
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	<p>For example,</p>		<p>For example,</p>

	<apll>~~      ~~(,⍎)'2+3'</apll><br />		<apll> (,⍎)'2+3'</apll><br />
	<apll>←→~~    ~~'2+3',⍎'2+3'</apll><br />		<apll>←→ '2+3',⍎'2+3'</apll><br />
	<apll>←→~~    ~~'2+3',5</apll><br />		<apll>←→ '2+3',5</apll><br />
	<apll>2+3 5</apll><br />		<apll>2+3 5</apll><br />

	<apll>~~      ~~avg{is}(+⌿ ÷ ≢)</apll> defines a function that computes the average of a numeric vector.<br />		<apll> avg{is}(+⌿ ÷ ≢)</apll> defines a function that computes the average of a numeric vector.<br />
	<apll>~~      ~~avg 1 2 3 4</apll><br />		<apll> avg 1 2 3 4</apll><br />
	<apll>←→~~    ~~(+⌿ ÷ ≢) 1 2 3 4</apll><br />		<apll>←→ (+⌿ ÷ ≢) 1 2 3 4</apll><br />
	<apll>←→~~    ~~(+⌿1 2 3 4) ÷ ≢1 2 3 4</apll><br />		<apll>←→ (+⌿1 2 3 4) ÷ ≢1 2 3 4</apll><br />
	<apll>←→~~    ~~10 ÷ 4</apll><br />		<apll>←→ 10 ÷ 4</apll><br />
	<apll>2.5</apll>		<apll>2.5</apll>

	<p>Longer Trains are defined as follows:</p>		<p>Longer Trains are defined as follows:</p>

	<apll>~~  ~~(e f g h) ←→ ~~  ~~(e (f g h))</apll><br />		<apll> (e f g h) ←→ (e (f g h))</apll><br />
	<apll>(d e f g h) ←→ (d e (f g h))</apll><br />		<apll>(d e f g h) ←→ (d e (f g h))</apll><br />

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	{\|border="0"		{\|border="0"
	\|Even length: \|\| <apll>(a b c ...) ←→ (a (b ~~ ~~c ...))</apll>		\|Even length: \|\| <apll>(a b c ...) ←→ (a (b c ...))</apll>
	\|-		\|-
	\|Odd length: \|\| <apll>(a b c ...) ←→ (a ~~ ~~b (c ...))</apll>		\|Odd length: \|\| <apll>(a b c ...) ←→ (a b (c ...))</apll>
	\|}		\|}

WikiSysop at 13:42, 25 May 2013

2013-05-25T13:42:00Z

← Older revision		Revision as of 09:42, 25 May 2013
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	<apll>2+3 5</apll><br />		<apll>2+3 5</apll><br />

	<apll>      avg{is}(+/ ÷ >)</apll> defines a function that computes the average of a numeric vector.<br />		<apll>      avg{is}(+⌿ ÷ ≢)</apll> defines a function that computes the average of a numeric vector.<br />
	<apll>      avg 1 2 3 4</apll><br />		<apll>      avg 1 2 3 4</apll><br />
	<apll>←→    (+/ ÷ >) 1 2 3 4</apll><br />		<apll>←→    (+⌿ ÷ ≢) 1 2 3 4</apll><br />
	<apll>←→    (+/1 2 3 4) ÷ >1 2 3 4</apll><br />		<apll>←→    (+⌿1 2 3 4) ÷ ≢1 2 3 4</apll><br />
	<apll>←→    10 ÷ 4</apll><br />		<apll>←→    10 ÷ 4</apll><br />
	<apll>2.5</apll>		<apll>2.5</apll>

WikiSysop at 21:59, 29 August 2010

2010-08-29T21:59:46Z

← Older revision		Revision as of 17:59, 29 August 2010
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	<apll>2+3 5</apll><br />		<apll>2+3 5</apll><br />

	<apll>      avg{is}(+/ ÷ ⍴)</apll> defines a function that computes the average of a numeric vector.<br />		<apll>      avg{is}(+/ ÷ >)</apll> defines a function that computes the average of a numeric vector.<br />
	<apll>      avg 1 2 3 4</apll><br />		<apll>      avg 1 2 3 4</apll><br />
	<apll>←→    (+/ ÷ ⍴) 1 2 3 4</apll><br />		<apll>←→    (+/ ÷ >) 1 2 3 4</apll><br />
	<apll>←→    (+/1 2 3 4) ÷ ⍴1 2 3 4</apll><br />		<apll>←→    (+/1 2 3 4) ÷ >1 2 3 4</apll><br />
	<apll>←→    10 ÷ ,4</apll><br />		<apll>←→    10 ÷ 4</apll><br />
	<apll>2.5</apll>		<apll>2.5</apll>

WikiSysop at 23:17, 10 March 2010

2010-03-10T23:17:30Z

← Older revision		Revision as of 19:17, 10 March 2010
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	<td></td>		<td></td>
	<td></td>		<td></td>
	<td>is called a '''Monadic Hook''' — <apll>Z ≡ R g h R</apll></td>		<td>is called a '''Monadic Hook''' — <apll>Z ≡ R f g R</apll></td>
	</tr>		</tr>
	<tr>		<tr>
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	<td></td>		<td></td>
	<td></td>		<td></td>
	<td>is called a '''Dyadic Hook''' — <apll>Z ≡ L g h R</apll></td>		<td>is called a '''Dyadic Hook''' — <apll>Z ≡ L f g R</apll></td>
	</tr>		</tr>
	<tr>		<tr>

WikiSysop at 00:08, 8 March 2009

2009-03-08T00:08:34Z

← Older revision		Revision as of 20:08, 7 March 2009
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	<table border="0" cellpadding="5" cellspacing="0" summary="">		<table border="0" cellpadding="5" cellspacing="0" summary="">
	<tr>		<tr>
	<td><apll>Z←(f g) R</apll></td>		<td><apll>Z←  (f g) R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>Z←(f g h) R</apll></td>		<td><apll>Z←  (f g h) R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>Z←(f g h ...) R</apll><br /><apll>Z←L (f g h ...) R</apll></td>		<td><apll>Z←  (f g h ...) R</apll><br /><apll>Z←L (f g h ...) R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	</table>		</table>
	<br />		<br />
	<p>This clever idea from the designers of J is called [http://www.jsoftware.com/help/dictionary/dictf.htm Trains] where a parenthesized sequence of functions (which normally would signal a SYNTAX ERROR) can be interpreted as per the above descriptions. Note that the spacing between functions is for visual purposes only — it has no effect on the interpretation.</p>		<p>This clever idea from the designers of J is called [http://www.jsoftware.com/help/dictionary/dictf.htm Trains] where a parenthesized sequence of functions (which normally would signal a SYNTAX ERROR) can be interpreted as per the above descriptions. Very nicely, they fit into and extend the spectrum of function definition syntax from user-defined to dynamic to trains to operator expressions. They are another and very interesting form of functional programming.</p>

			<p>Note that the spacing between functions is for visual purposes only — it has no effect on the interpretation.</p>

	<p>For example,</p>		<p>For example,</p>
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	<p>Longer Trains are defined as follows:</p>		<p>Longer Trains are defined as follows:</p>

	<apll>(e f g h) ←→ (e (f g h))</apll><br />		<apll>  (e f g h) ←→   (e (f g h))</apll><br />
	<apll>(d e f g h) ←→ (d e (f g h))</apll><br />		<apll>(d e f g h) ←→ (d e (f g h))</apll><br />

	and in general		and in general

	Even length: <apll>(a b c ...) ←→ (a (b c ...))</apll>~~<br />~~		{\|border="0"
	Odd length: <apll>(a b c ...) ←→ (a b (c ...))</apll>~~<br />~~		\|Even length: \|\| <apll>(a b c ...) ←→ (a (b  c ...))</apll>
			\|-
			\|Odd length: \|\| <apll>(a b c ...) ←→ (a  b (c ...))</apll>
			\|}

	<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>		<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>

	<p>There is also a series of [[Train_Tables\|tables]] of common function expressions and their corresponding Train.</p>		<p>There is also a series of [[Train_Tables\|tables]] of common function expressions and their corresponding Train.</p>

WikiSysop at 22:22, 4 March 2009

2009-03-04T22:22:28Z

← Older revision		Revision as of 18:22, 4 March 2009
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	<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>		<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>

	<p>There is also a [[~~TrainList~~\|~~list~~]] of common function expressions and their corresponding Train.</p>		<p>There is also a series of [[Train_Tables\|tables]] of common function expressions and their corresponding Train.</p>

WikiSysop at 19:44, 4 March 2009

2009-03-04T19:44:40Z

← Older revision		Revision as of 15:44, 4 March 2009
Line 68:		Line 68:

	<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>		<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>

			<p>There is also a [[TrainList\|list]] of common function expressions and their corresponding Train.</p>

WikiSysop at 02:38, 18 February 2009

2009-02-18T02:38:14Z

← Older revision		Revision as of 22:38, 17 February 2009
Line 37:		Line 37:
	</tr>		</tr>
	<tr>		<tr>
	<td><apll>L</apll> and <apll>R</apll> are arbitrary arrays. </td>		<td><apll>L</apll> and <apll>R</apll> are arbitrary arrays, <apll>f</apll>, <apll>g</apll>, <apll>h</apll>, etc, are arbitrary functions of any type: primitive, user-defined, system, and/or derived.</td>
	</tr>		</tr>
	</table>		</table>

WikiSysop: New page:

Z←(f g) ...
2009-02-18T02:32:38Z

New page: <table border="1" cellpadding="5" cellspacing="0" rules="none" summary=""> <tr> <td> <table border="0" cellpadding="5" cellspacing="0" summary=""> <tr> <td><apll>Z←(f g) ...

New page
<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
<tr>
<td>
<table border="0" cellpadding="5" cellspacing="0" summary="">
<tr>
<td><apll>Z←(f g) R</apll></td>
<td></td>
<td></td>
<td>is called a '''Monadic Hook''' — <apll>Z ≡ R g h R</apll></td>
</tr>
<tr>
<td><apll>Z←L (f g) R</apll></td>
<td></td>
<td></td>
<td>is called a '''Dyadic Hook''' — <apll>Z ≡ L g h R</apll></td>
</tr>
<tr>
<td><apll>Z←(f g h) R</apll></td>
<td></td>
<td></td>
<td>is called a '''Monadic Fork''' — <apll>Z ≡ (f R) g h R</apll></td>
</tr>
<tr>
<td><apll>Z←L (f g h) R</apll></td>
<td></td>
<td></td>
<td>is called a '''Dyadic Fork''' — <apll>Z ≡ (L f R) g L h R</apll></td>
</tr>
<tr>
<td><apll>Z←(f g h ...) R</apll><br /><apll>Z←L (f g h ...) R</apll></td>
<td></td>
<td></td>
<td>is also defined for longer Trains</td>
</tr>
</table>
</td>
</tr>
<tr>
<td><apll>L</apll> and <apll>R</apll> are arbitrary arrays. </td>
</tr>
</table>
<br />
<p>This clever idea from the designers of J is called [http://www.jsoftware.com/help/dictionary/dictf.htm Trains] where a parenthesized sequence of functions (which normally would signal a SYNTAX ERROR) can be interpreted as per the above descriptions. Note that the spacing between functions is for visual purposes only — it has no effect on the interpretation.</p>

<p>For example,</p>

<apll>      (,⍎)'2+3'</apll><br />
<apll>←→    '2+3',⍎'2+3'</apll><br />
<apll>←→    '2+3',5</apll><br />
<apll>2+3 5</apll><br />

<apll>      avg{is}(+/ ÷ ⍴)</apll> defines a function that computes the average of a numeric vector.<br />
<apll>      avg 1 2 3 4</apll><br />
<apll>←→    (+/ ÷ ⍴) 1 2 3 4</apll><br />
<apll>←→    (+/1 2 3 4) ÷ ⍴1 2 3 4</apll><br />
<apll>←→    10 ÷ ,4</apll><br />
<apll>2.5</apll>

<p>Longer Trains are defined as follows:</p>

<apll>(e f g h) ←→ (e (f g h))</apll><br />
<apll>(d e f g h) ←→ (d e (f g h))</apll><br />

and in general

Even length: <apll>(a b c ...) ←→ (a (b c ...))</apll><br />
Odd length: <apll>(a b c ...) ←→ (a b (c ...))</apll><br />

<p>For more applications of this concept, see the [http://www.jsoftware.com/help/learning/09.htm discussion] in the '''Learning J''' manual.</p>