Hyperators - Revision history

WikiSysop: /* Syntax Glitch */

2024-02-12T22:12:47Z

Syntax Glitch

← Older revision		Revision as of 18:12, 12 February 2024
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	* <apll>dhdo</apll> Dyadic Hyperand Dyadic Operand ...		* <apll>dhdo</apll> Dyadic Hyperand Dyadic Operand ...

	==~~Syntax Glitch~~==		==Examples==

	~~For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle the case of a Hyperator with two Hyperands and two Operands and where the '''right hyperand''' is~~ a '''function ~~or operator~~''' ~~and the '''right operand''' is a '''function'''. For example~~, ~~if <apll>dhdo</apll> is an example of this kind of Hyperator~~:		The Power Operator can be used to apply a '''function''' iteratively to an argument, such as:

	<apll><pre>		<apll><pre>
	+~~-dhdo×÷ 23~~		+\⍣3 ⍳4
	~~SYNTAX ERROR~~		1 5 15 35
	+~~-dhdo×÷ 23~~		+\+\+\⍳4
	∧		1 5 15 35
	</pre></apll>		</pre></apll>

	~~To get this case~~ to ~~parse correctly~~, ~~use parentheses as in~~		Applying an '''operator''' iteratively to an argument, is a task for Hyperators:

	<apll><pre>		<apll><pre>
	(~~+-dhdo×÷~~) 23		PowEach←{⍺←⊢ ⋄ ⍎'⍺ ⍺⍺ ',(∊⍵⍵⍵⍴⊂'⍺⍺⍺ '),'⍵'} ⍝ It takes a Hyperator to iterate an operator (⍺⍺⍺)

			,¨PowEach 3 4 ⍝ ←→ ,¨¨¨4 Here the hyperand (⍺⍺⍺←¨) is iterated and then
			⍝ the operand (⍺⍺←,) is bound to the iterated hyperand
			┌───────┐
			│┌─────┐│
			││┌───┐││
			│││┌1┐│││
			││││4││││
			│││└~┘2││
			││└∊──┘3│
			│└∊────┘4
			└∊──────┘
			,¨⍣3 4 ⍝ ←→ ,¨,¨,¨4 Here the function (,¨) is iterated
			┌────┐
			│┌1─┐│
			││ 4││
			│└~─┘2
			└∊───┘
	</pre></apll>		</pre></apll>

	~~All other cases of this kind of Hyperator are parsed correctly without needing to resort to extra parentheses.~~

	==References==		==References==

WikiSysop at 20:48, 21 July 2019

2019-07-21T20:48:36Z

← Older revision		Revision as of 16:48, 21 July 2019
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	This yields several interesting cases:		This yields several interesting cases:

	* A dyadic operator written as <~~aplcl~~>… dop 1 2 3 4</~~aplcl~~> is interpreted as having a right '''operand''' ('''short''' right scope) of <~~aplcl~~>1</~~aplcl~~> and a right '''argument''' of <~~aplcl~~>2 3 4</~~aplcl~~>.		* A dyadic operator written as <apll>… dop 1 2 3 4</apll> is interpreted as having a right '''operand''' ('''short''' right scope) of <apll>1</apll> and a right '''argument''' of <apll>2 3 4</apll>.
	* A hyperator written as either <~~aplcl~~>1 2 3 4 mhmo</~~aplcl~~> or <~~aplcl~~>1 2 3 4 mhdo …</~~aplcl~~> is interpreted as having a left '''hyperand''' ('''short''' left scope) of <~~aplcl~~>4</~~aplcl~~> and a left '''operand''' ('''long''' left scope) of <~~aplcl~~>1 2 3</~~aplcl~~>.		* A hyperator written as either <apll>1 2 3 4 mhmo</apll> or <apll>1 2 3 4 mhdo …</apll> is interpreted as having a left '''hyperand''' ('''short''' left scope) of <apll>4</apll> and a left '''operand''' ('''long''' left scope) of <apll>1 2 3</apll>.
	* A dyadic hyperator written as <~~aplcl~~>… dhmo 1 2 3 4</~~aplcl~~> is interpreted as having a right '''hyperand''' ('''short''' right scope) of <~~aplcl~~>1</~~aplcl~~> and a right '''argument''' of <~~aplcl~~>2 3 4</~~aplcl~~>.		* A dyadic hyperator written as <apll>… dhmo 1 2 3 4</apll> is interpreted as having a right '''hyperand''' ('''short''' right scope) of <apll>1</apll> and a right '''argument''' of <apll>2 3 4</apll>.
	* A dyadic hyperator written as <~~aplcl~~>… dhdo 1 2 3 4</~~aplcl~~> is interpreted as having a right '''hyperand''' ('''short''' right scope) of <~~aplcl~~>1</~~aplcl~~>, a right '''operand''' ('''short''' right scope) of <~~aplcl~~>2</~~aplcl~~>, and a right '''argument''' of <~~aplcl~~>3 4</~~aplcl~~>.		* A dyadic hyperator written as <apll>… dhdo 1 2 3 4</apll> is interpreted as having a right '''hyperand''' ('''short''' right scope) of <apll>1</apll>, a right '''operand''' ('''short''' right scope) of <apll>2</apll>, and a right '''argument''' of <apll>3 4</apll>.

	To reduce confusion, use parentheses such as <~~aplcl~~>(LO (LH dhdo 1) 2) 3</~~aplcl~~>.		To reduce confusion, use parentheses such as <apll>(LO (LH dhdo 1) 2) 3</apll>.

	Abbreviations:		Abbreviations:
	* <~~aplcl~~>dop</~~aplcl~~> Dyadic Operator		* <apll>dop</apll> Dyadic Operator
	* <~~aplcl~~>mhmo</~~aplcl~~> Monadic Hyperand Monadic Operand Hyperator		* <apll>mhmo</apll> Monadic Hyperand Monadic Operand Hyperator
	* <~~aplcl~~>mhdo</~~aplcl~~> Monadic Hyperand Dyadic Operand ...		* <apll>mhdo</apll> Monadic Hyperand Dyadic Operand ...
	* <~~aplcl~~>dhmo</~~aplcl~~> Dyadic Hyperand Monadic Operand ...		* <apll>dhmo</apll> Dyadic Hyperand Monadic Operand ...
	* <~~aplcl~~>dhdo</~~aplcl~~> Dyadic Hyperand Dyadic Operand ...		* <apll>dhdo</apll> Dyadic Hyperand Dyadic Operand ...

	==Syntax Glitch==		==Syntax Glitch==

WikiSysop: /* Syntax Glitch */

2019-07-01T16:15:42Z

Syntax Glitch

← Older revision		Revision as of 12:15, 1 July 2019
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	==Syntax Glitch==		==Syntax Glitch==

	For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle the case of a Hyperator with two Hyperands and two Operands and where the ~~right~~ '''hyperand''' is a function or operator and the ~~right~~ '''operand''' is a function. For example, if <apll>dhdo</apll> is an example of this kind of Hyperator:		For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle the case of a Hyperator with two Hyperands and two Operands and where the '''right hyperand''' is a '''function or operator''' and the '''right operand''' is a '''function'''. For example, if <apll>dhdo</apll> is an example of this kind of Hyperator:

	<apll><pre>		<apll><pre>

WikiSysop: /* Scoping */

2019-03-24T10:15:33Z

Scoping

← Older revision		Revision as of 06:15, 24 March 2019
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	but this violates the APL2 rule on Redundant Parentheses ("Parentheses surrounding a primitive or constructed name, a character string (enclosed in quotation marks), or an already parenthesized expression are always redundant."<ref name="RedundantParens">[https://www.ibm.com/downloads/cas/ZOKMYKOY APL2 Reference Manual, Second Edition, 1994, SH21-1061-01, p. 37]</ref>), so that example is equivalent to the previous one.		but this violates the APL2 rule on Redundant Parentheses ("Parentheses surrounding a primitive or constructed name, a character string (enclosed in quotation marks), or an already parenthesized expression are always redundant."<ref name="RedundantParens">[https://www.ibm.com/downloads/cas/ZOKMYKOY APL2 Reference Manual, Second Edition, 1994, SH21-1061-01, p. 37]</ref>), so that example is equivalent to the previous one.

	Only if Hyperators have '''short left scope''' can we pass function as a left operand and an operator as the left hyperand to a Hyperator as in the example <apll>+/mhmo</apll>.		Only if Hyperators have '''short left scope''' can we pass a function as a left operand and an operator as the left hyperand to a Hyperator as in the example <apll>+/mhmo</apll>.

	FWIW, there is another example with this scoping rule that also illustrates a change in [[Binding Strength]] in NARS2000: '''Vector Notation''' (a.k.a. '''Numeric Strands''').		FWIW, there is another example with this scoping rule that also illustrates a change in [[Binding Strength]] in NARS2000: '''Vector Notation''' (a.k.a. '''Numeric Strands''').

	In the same example as above with a ~~monadic operand monadic hyperand~~ hyperator, how can we pass (say) a <apll>12</apll> as a left '''operand''' and a <apll>34</apll> as a left '''hyperand'''? This can be accomplished with		In the same example as above with a Monadic Hyperand Monadic Operand hyperator, how can we pass (say) a <apll>12</apll> as a left '''operand''' and a <apll>34</apll> as a left '''hyperand'''? This can be accomplished with

	<apll> 12 34 mhmo</apll>		<apll> 12 34 mhmo</apll>

	because the rules for Binding Strength used by NARS2000 dictate that Vector Notation has a lower Binding Strength than both a right operand to its operator and either hyperand to its hyperator. In these three ~~case~~, the scope is '''short''' which is interpreted by NARS2000 as extracting the number nearest to the operator/hyperator from the numeric strand and using it for the operand/hyperand.		because the rules for Binding Strength used by NARS2000 dictate that Vector Notation has a lower Binding Strength than both a right operand to its operator and either hyperand to its hyperator. In these three cases, the scope is '''short''' which is interpreted by NARS2000 as extracting the number nearest to the operator/hyperator from the numeric strand and using it for the operand/hyperand.

	This yields several interesting cases:		This yields several interesting cases:

	* A dyadic operator written as <~~apll~~>… dop 1 2 3</~~apll~~> is interpreted as having a right operand ('''short''' right scope) of <~~apll~~>1</~~apll~~> and a right argument of <~~apll~~>2 3</~~apll~~>.		* A dyadic operator written as <aplcl>… dop 1 2 3 4</aplcl> is interpreted as having a right '''operand''' ('''short''' right scope) of <aplcl>1</aplcl> and a right '''argument''' of <aplcl>2 3 4</aplcl>.
	* A hyperator written as <~~apll~~>1 2 3 mhmo</~~apll~~> is interpreted as having a left hyperand ('''short''' left scope) of <~~apll~~>3</~~apll~~> and a left operand ('''long''' left scope) of <~~apll~~>1 2</~~apll~~>.		* A hyperator written as either <aplcl>1 2 3 4 mhmo</aplcl> or <aplcl>1 2 3 4 mhdo …</aplcl> is interpreted as having a left '''hyperand''' ('''short''' left scope) of <aplcl>4</aplcl> and a left '''operand''' ('''long''' left scope) of <aplcl>1 2 3</aplcl>.
	* A dyadic hyperator written as <~~apll~~>… dhmo 1 2 3</~~apll~~> is interpreted as having a right hyperand ('''short''' right scope) of <~~apll~~>1</~~apll~~> and a right argument of <~~apll~~>2 3</~~apll~~>.		* A dyadic hyperator written as <aplcl>… dhmo 1 2 3 4</aplcl> is interpreted as having a right '''hyperand''' ('''short''' right scope) of <aplcl>1</aplcl> and a right '''argument''' of <aplcl>2 3 4</aplcl>.
	* A dyadic hyperator written as <~~apll~~>… dhdo 1 2 3</~~apll~~> is interpreted as having a right hyperand ('''short''' right scope) of <~~apll~~>1</~~apll~~>, a right operand ('''short''' right scope) of <~~apll~~>2</~~apll~~>, and a right argument of <~~apll~~>3</~~apll~~>.		* A dyadic hyperator written as <aplcl>… dhdo 1 2 3 4</aplcl> is interpreted as having a right '''hyperand''' ('''short''' right scope) of <aplcl>1</aplcl>, a right '''operand''' ('''short''' right scope) of <aplcl>2</aplcl>, and a right '''argument''' of <aplcl>3 4</aplcl>.

	To reduce confusion, use parentheses such as <~~apll~~>(LO (LH dhdo 1) 2) 3</~~apll~~>.		To reduce confusion, use parentheses such as <aplcl>(LO (LH dhdo 1) 2) 3</aplcl>.

			Abbreviations:
			* <aplcl>dop</aplcl> Dyadic Operator
			* <aplcl>mhmo</aplcl> Monadic Hyperand Monadic Operand Hyperator
			* <aplcl>mhdo</aplcl> Monadic Hyperand Dyadic Operand ...
			* <aplcl>dhmo</aplcl> Dyadic Hyperand Monadic Operand ...
			* <aplcl>dhdo</aplcl> Dyadic Hyperand Dyadic Operand ...

	==Syntax Glitch==		==Syntax Glitch==

WikiSysop: /* Syntax Glitch */

2019-03-24T09:58:05Z

Syntax Glitch

← Older revision		Revision as of 05:58, 24 March 2019
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	==Syntax Glitch==		==Syntax Glitch==

	For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle the case of a Hyperator with ~~a Dyadic Hyperand~~ and ~~Dyadic Operand~~ and where the right '''hyperand''' is a function or operator and the right '''operand''' is a function. For example, if <apll>dhdo</apll> is an example of this kind of Hyperator:		For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle the case of a Hyperator with two Hyperands and two Operands and where the right '''hyperand''' is a function or operator and the right '''operand''' is a function. For example, if <apll>dhdo</apll> is an example of this kind of Hyperator:

	<apll><pre>		<apll><pre>

WikiSysop: /* Object Orders */

2019-03-24T09:54:59Z

Object Orders

← Older revision		Revision as of 05:54, 24 March 2019
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	==Object Orders==		==Object Orders==

	The sequence of objects: Arrays, Functions, and Operators appear in ascending order with the property that each later object consumes one or two of the earlier objects and produces an object in the sequence one order less. For example, a Function takes ~~Arrays~~ and produces an Array; an Operator takes ~~Arrays~~ and/or ~~Functions~~ and produces a (derived) Function.		The sequence of objects: Arrays, Functions, and Operators appear in ascending order with the property that each later object consumes one or two of the earlier objects and produces an object in the sequence one order less. For example, a Function takes Array(s) and produces an Array; an Operator takes Array(s) and/or Function(s) and produces a (derived) Function.

	Hyperators extend this sequence by one. That is, in the object hierarchy:		Hyperators extend this sequence by one:

			* a '''Hyperator''' has one or two '''Hyperands''' (any of Arrays, Functions, and/or Operators) and yields ...
			* an '''Operator''' which has one or two '''Operands''' (any of Arrays and/or Functions) and yields ...
			* a '''Function''' which has zero, one, or two '''Arguments''' (Arrays) and yields...
			* an '''Array'''.

			That is, in the object hierarchy:

	{\| border="1" cellpadding="5" cellspacing="0"		{\| border="1" cellpadding="5" cellspacing="0"
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	\|align="center" valign="top"\|Function		\|align="center" valign="top"\|Function
	\|align="center" valign="top"\|0, 1, 2<br/>Arguments		\|align="center" valign="top"\|0, 1, 2<br/>Arguments
	\|valign="top"\|<apll>∇Z← f0<br/>∇Z← f1 R<br/>∇Z←L f2 R</apll>		\|valign="top"\|<apll>∇Z← fn0<br/>∇Z← fn1 R<br/>∇Z←L fn2 R</apll>
	\|-		\|-
	\|align="center" valign="top"\|2		\|align="center" valign="top"\|2

WikiSysop: /* Syntax Glitch */

2019-03-21T21:09:25Z

Syntax Glitch

← Older revision		Revision as of 17:09, 21 March 2019
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	</pre></apll>		</pre></apll>

	All other cases of this kind of Hyperator are parsed correctly.		All other cases of this kind of Hyperator are parsed correctly without needing to resort to extra parentheses.

	==References==		==References==

WikiSysop: /* Syntax Glitch */

2019-03-21T21:08:33Z

Syntax Glitch

← Older revision		Revision as of 17:08, 21 March 2019
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	==Syntax Glitch==		==Syntax Glitch==

	For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle ~~certain cases~~ of a Hyperator with a Dyadic Hyperand and Dyadic Operand where the right '''hyperand''' is a function or operator and the right '''operand''' is a function. For example, if <apll>dhdo</apll> is an example of this kind of Hyperator:		For technical reasons I'm still working on, the Syntax Analyzer does not correctly handle the case of a Hyperator with a Dyadic Hyperand and Dyadic Operand and where the right '''hyperand''' is a function or operator and the right '''operand''' is a function. For example, if <apll>dhdo</apll> is an example of this kind of Hyperator:

	<apll><pre>		<apll><pre>

WikiSysop: /* Scoping */

2019-03-21T21:06:14Z

Scoping

← Older revision		Revision as of 17:06, 21 March 2019
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	* A dyadic hyperator written as <apll>… dhdo 1 2 3</apll> is interpreted as having a right hyperand ('''short''' right scope) of <apll>1</apll>, a right operand ('''short''' right scope) of <apll>2</apll>, and a right argument of <apll>3</apll>.		* A dyadic hyperator written as <apll>… dhdo 1 2 3</apll> is interpreted as having a right hyperand ('''short''' right scope) of <apll>1</apll>, a right operand ('''short''' right scope) of <apll>2</apll>, and a right argument of <apll>3</apll>.

	~~If there is any~~ confusion, use parentheses such as <apll>(LO (LH dhdo 1) 2) 3</apll>.		To reduce confusion, use parentheses such as <apll>(LO (LH dhdo 1) 2) 3</apll>.

	==Syntax Glitch==		==Syntax Glitch==

WikiSysop: /* Scoping */

2019-03-21T20:55:26Z

Scoping

← Older revision		Revision as of 16:55, 21 March 2019
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	Only if Hyperators have '''short left scope''' can we pass function as a left operand and an operator as the left hyperand to a Hyperator as in the example <apll>+/mhmo</apll>.		Only if Hyperators have '''short left scope''' can we pass function as a left operand and an operator as the left hyperand to a Hyperator as in the example <apll>+/mhmo</apll>.

	FWIW, there is another example with this scoping rule that also illustrates a change in Binding Strength in NARS2000: '''Vector Notation''' (a.k.a. '''Numeric Strands''').		FWIW, there is another example with this scoping rule that also illustrates a change in [[Binding Strength]] in NARS2000: '''Vector Notation''' (a.k.a. '''Numeric Strands''').

	In the same example as above with a monadic operand monadic hyperand hyperator, how can we pass (say) a <apll>12</apll> as a left '''operand''' and a <apll>34</apll> as a left '''hyperand'''? This can be accomplished with		In the same example as above with a monadic operand monadic hyperand hyperator, how can we pass (say) a <apll>12</apll> as a left '''operand''' and a <apll>34</apll> as a left '''hyperand'''? This can be accomplished with
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	<apll> 12 34 mhmo</apll>		<apll> 12 34 mhmo</apll>

	because the rules for [[Binding Strength]] used by NARS2000 dictate that Vector Notation has a lower Binding Strength than both a right operand to its operator and either hyperand to its hyperator. In these three case, the scope is '''short''' which is interpreted by NARS2000 as extracting the number nearest to the operator/hyperator from the numeric strand and using it for the operand/hyperand.		because the rules for Binding Strength used by NARS2000 dictate that Vector Notation has a lower Binding Strength than both a right operand to its operator and either hyperand to its hyperator. In these three case, the scope is '''short''' which is interpreted by NARS2000 as extracting the number nearest to the operator/hyperator from the numeric strand and using it for the operand/hyperand.

	This yields several interesting cases:		This yields several interesting cases:

	* A dyadic operator written as <apll>… dop 1 2 3</apll> is interpreted as having a right operand ('''short''' right scope) of <apll>1</apll> and a right argument of <apll>2 3</apll>.		* A dyadic operator written as <apll>… dop 1 2 3</apll> is interpreted as having a right operand ('''short''' right scope) of <apll>1</apll> and a right argument of <apll>2 3</apll>.
	* A hyperator written as <apll>1 2 3 mhmo</apll> is interpreted as having a left ~~operand~~ ('''~~long~~''' left scope) of <apll>~~1 2~~</apll> and a left ~~hyperand~~ ('''~~short~~''' left scope) of <apll>3</apll>.		* A hyperator written as <apll>1 2 3 mhmo</apll> is interpreted as having a left hyperand ('''short''' left scope) of <apll>3</apll> and a left operand ('''long''' left scope) of <apll>1 2</apll>.
	* A dyadic hyperator written as <apll>… dhmo 1 2 3</apll> is interpreted as having a right hyperand ('''short''' right scope) of <apll>1</apll> and a right argument of <apll>2 3</apll>.		* A dyadic hyperator written as <apll>… dhmo 1 2 3</apll> is interpreted as having a right hyperand ('''short''' right scope) of <apll>1</apll> and a right argument of <apll>2 3</apll>.
	* A dyadic hyperator written as <apll>… dhdo 1 2 3</apll> is interpreted as having a right hyperand ('''short''' right scope) of <apll>1</apll>, a right operand ('''short''' right scope) of <apll>2</apll>, and a right argument of <apll>3</apll>.		* A dyadic hyperator written as <apll>… dhdo 1 2 3</apll> is interpreted as having a right hyperand ('''short''' right scope) of <apll>1</apll>, a right operand ('''short''' right scope) of <apll>2</apll>, and a right argument of <apll>3</apll>.