Anonymous Functions/Operators/Hyperators - Revision history

WikiSysop: /* Axis Operator */

2022-09-10T19:06:53Z

Axis Operator

← Older revision		Revision as of 15:06, 10 September 2022
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	== Axis Operator ==		== Axis Operator ==

	Just as with [[User-Defined Functions/Operators/Hyperators]], Anonymous Functions/Operators/Hyperators can accept an optional Axis Operator via the <apll>χ</apll> symbol. Also, in a manner similar to the optional left argument for Ambivalent AFOHs (see above), a default value for the Axis Operator may be assigned in case the caller doesn't provide one; if the user provides a value for the Axis Operator, the statement which assigns <apll>χ</apll> is ignored.		Just as with [[User-Defined Functions/Operators/Hyperators]], Anonymous Functions/Operators/Hyperators can accept an optional Axis Operator via the <apll>χ</apll> symbol (Alt-Shift-'c' or Ctrl-Shift-'c' depending upon your keyboard layout). Also, in a manner similar to the optional left argument for Ambivalent AFOHs (see above), a default value for the Axis Operator may be assigned in case the caller doesn't provide one; if the user provides a value for the Axis Operator, the statement which assigns <apll>χ</apll> is ignored.
	<apll><pre> avg←{χ←⎕IO ⋄ (+/[χ] ⍵)÷≢⍵}		<apll><pre> avg←{χ←⎕IO ⋄ (+/[χ] ⍵)÷≢⍵}
	avg 1 2 3		avg 1 2 3

WikiSysop at 21:08, 23 April 2022

2022-04-23T21:08:57Z

@@ Line 16: / Line 16: @@
 4 23 14 11 38 443
+       f
-4 23 14 11 39 72
+4 23 14 11 39 72</pre></apll>
 == Operator Operands ==
@@ Line 150: / Line 147: @@
 </pre></apll>
 == Valences ==

WikiSysop: /* Function Arguments */

2022-04-23T19:55:02Z

Function Arguments

← Older revision		Revision as of 15:55, 23 April 2022
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	== Function Arguments ==		== Function Arguments ==

	To define an anonymous '''function''', use <apll>⍺</apll> as the name of the (optional) left argument, <apll>∇</apll> as the name of the (optional) anonymous function (for [[#Recursion\|recursion]] only), ~~and~~ <apll>⍵</apll> as the name of the right argument. For example,		To define an anonymous '''function''', use <apll>⍺</apll> as the name of the (optional) left argument, <apll>∇</apll> as the name of the (optional) anonymous function (for [[#Recursion\|recursion]] only), <apll>⍵</apll> as the name of the (optional) right argument, and <apll>χ</apll> as the name of the (optional) Axis Operator. For example,

	<apll><pre>		<apll><pre>
	3 5{√+/⍺ ⍵*2}4 12 ⍝ Pythagorean theorem		3 5{√+/⍺ ⍵*2}4 12 ⍝ Pythagorean theorem (Dyadic function)
	5 13		5 13
	{s←(+/⍵)÷2 ⋄ √×/s-0,⍵}3 4 5 ⍝ Heron's formula for triangle area		{s←(+/⍵)÷2 ⋄ √×/s-0,⍵}3 4 5 ⍝ Heron's formula for triangle area (Monadic function)
	6</pre></apll>		6
			f←{⎕TS} ⍝ Niladic function
			f
			2022 4 23 14 11 38 443
			f
			2022 4 23 14 11 39 72


			</pre></apll>

	== Operator Operands ==		== Operator Operands ==

WikiSysop: /* Guards */

2019-08-05T22:23:18Z

Guards

@@ Line 210: / Line 210: @@
 Guards appear as a Boolean-valued APL expression (<apll>Cond</apll>) followed by a colon, followed by a single APL statement (<apll>CondStmt</apll>) as in
-<apll>{... ⋄ Cond:CondStmt ⋄ ....}</apll>
+<apll>{... ⋄ Cond:CondStmt ⋄ ...}</apll>
 which executes <apll>CondStmt</apll> and terminates the AFOH if and only if <apll>Cond</apll> evaluates to TRUE (<apll>1</apll>).
@@ Line 216: / Line 216: @@
 For example,
-<apll>{... ⋄ 0∊⍴⍵:'empty right argument' ⋄ ....}</apll>
+<apll>{... ⋄ 0∊⍴⍵:'empty right argument' ⋄ ...}</apll>
 As many guard statements may appear in an AFOH as desired.  They are executed in turn until one of them evaluates to TRUE, at which time the statement following the colon is executed and the function terminates with any result of that conditional statement as the result of the AFOH.
@@ Line 223: / Line 223: @@
 If the rightmost statement is executed and it is a guard statement whose <apll>Cond</apll> evaluates to FALSE (<apll>0</apll>), the AFOH terminates with no value; if the result of that AFOH is assigned, a <apll>VALUE ERROR</apll> is signalled.
 == Shy Results ==

WikiSysop at 20:37, 21 July 2019

2019-07-21T20:37:27Z

← Older revision		Revision as of 16:37, 21 July 2019
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	== Operator Operands ==		== Operator Operands ==

	To define an anonymous '''operator''', use the above special names along with <apll>⍺⍺</apll> as the name of the left operand, <apll>∇∇</apll> as the name of the (optional) operator (for [[#Recursion\|recursion]]), and <apll>⍵⍵</apll> as the name of the (optional) right operand. If neither <apll>⍺⍺</apll> nor <apll>⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function, not an operator. For example,		To define an anonymous '''operator''', use the above special names along with <apll>⍺⍺</apll> as the name of the left operand, <apll>∇∇</apll> as the name of the (optional) operator (for [[#Recursion\|recursion]] only), and <apll>⍵⍵</apll> as the name of the (optional) right operand. If neither <apll>⍺⍺</apll> nor <apll>⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function, not an operator. For example,

	<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">		<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">
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	== Hyperator Hyperands ==		== Hyperator Hyperands ==

	To define an anonymous '''hyperator''', use the above special names along with <apll>⍺⍺⍺</apll> as the name of the left hyperand, <apll>∇∇∇</apll> as the name of the (optional) hyperator (for [[#Recursion\|recursion]]), and <apll>⍵⍵⍵</apll> as the name of the (optional) right hyperand. If neither <apll>⍺⍺⍺</apll> nor <apll>⍵⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function or operator, not a hyperator. For example,		To define an anonymous '''hyperator''', use the above special names along with <apll>⍺⍺⍺</apll> as the name of the left hyperand, <apll>∇∇∇</apll> as the name of the (optional) hyperator (for [[#Recursion\|recursion]] only), and <apll>⍵⍵⍵</apll> as the name of the (optional) right hyperand. If neither <apll>⍺⍺⍺</apll> nor <apll>⍵⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function or operator, not a hyperator. For example,

	<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">		<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">

WikiSysop: /* Function Arguments */

2019-07-21T20:36:24Z

Function Arguments

← Older revision		Revision as of 16:36, 21 July 2019
Line 5:		Line 5:
	== Function Arguments ==		== Function Arguments ==

	To define an anonymous '''function''', use <apll>⍺</apll> as the (optional) left argument, <apll>∇</apll> as the name of the anonymous function (for [[#Recursion\|recursion]]), and <apll>⍵</apll> as the name of the right argument. For example,		To define an anonymous '''function''', use <apll>⍺</apll> as the name of the (optional) left argument, <apll>∇</apll> as the name of the (optional) anonymous function (for [[#Recursion\|recursion]] only), and <apll>⍵</apll> as the name of the right argument. For example,

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

WikiSysop at 20:34, 21 July 2019

2019-07-21T20:34:03Z

← Older revision		Revision as of 16:34, 21 July 2019
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	== Operator Operands ==		== Operator Operands ==

	To define an anonymous '''operator''', use the above special names along with <apll>⍺⍺</apll> as the name of the left operand, <apll>∇∇</apll> as the name of the operator (for [[#Recursion\|recursion]]), and <apll>⍵⍵</apll> as the name of the (optional) right operand. If neither <apll>⍺⍺</apll> nor <apll>⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function, not an operator. For example,		To define an anonymous '''operator''', use the above special names along with <apll>⍺⍺</apll> as the name of the left operand, <apll>∇∇</apll> as the name of the (optional) operator (for [[#Recursion\|recursion]]), and <apll>⍵⍵</apll> as the name of the (optional) right operand. If neither <apll>⍺⍺</apll> nor <apll>⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function, not an operator. For example,

	<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">		<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">
Line 64:		Line 64:
	== Hyperator Hyperands ==		== Hyperator Hyperands ==

	To define an anonymous '''hyperator''', use the above special names along with <apll>⍺⍺⍺</apll> as the name of the left hyperand, <apll>∇∇∇</apll> as the name of the hyperator (for [[#Recursion\|recursion]]), and <apll>⍵⍵⍵</apll> as the name of the (optional) right hyperand. If neither <apll>⍺⍺⍺</apll> nor <apll>⍵⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function or operator, not a hyperator. For example,		To define an anonymous '''hyperator''', use the above special names along with <apll>⍺⍺⍺</apll> as the name of the left hyperand, <apll>∇∇∇</apll> as the name of the (optional) hyperator (for [[#Recursion\|recursion]]), and <apll>⍵⍵⍵</apll> as the name of the (optional) right hyperand. If neither <apll>⍺⍺⍺</apll> nor <apll>⍵⍵⍵</apll> appears as a token between the braces and outside of character constants, then the object is a function or operator, not a hyperator. For example,

	<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">		<table cellpadding="0" cellspacing="0" style="border-collapse: separate; border-spacing: 5em 0px;">

WikiSysop at 20:29, 21 July 2019

2019-07-21T20:29:30Z

← Older revision		Revision as of 16:29, 21 July 2019
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	<tr>		<tr>
	<td colspan="7">		<td colspan="7">
	<apll>f←{∘.⍺⍺⍨⍳⍵}</apll>		<apll>opr←{∘.⍺⍺⍨⍳⍵}</apll>
	</td>		</td>
	</tr>		</tr>
Line 27:		Line 27:
	<tr>		<tr>
	<td>		<td>
	<apll> =f 4		<apll> =opr 4
	1 0 0 0		1 0 0 0
	0 1 0 0		0 1 0 0
Line 35:		Line 35:

	<td>		<td>
	<apll> ⌈f 4		<apll> ⌈opr 4
	1 2 3 4		1 2 3 4
	2 2 3 4		2 2 3 4
Line 43:		Line 43:

	<td>		<td>
	<apll> *f 4		<apll> *opr 4
	1 1 1 1		1 1 1 1
	2 4 8 16		2 4 8 16
Line 51:		Line 51:

	<td>		<td>
	<apll> ≤f 4		<apll> ≤opr 4
	1 1 1 1		1 1 1 1
	0 1 1 1		0 1 1 1
Line 59:		Line 59:
	</tr>		</tr>
	</table>		</table>

			In the above examples, the functions <apll> = ⌈ * ≤ </apll> are the Left Operands to the Operator <apll>opr</apll>.

	== Hyperator Hyperands ==		== Hyperator Hyperands ==
Line 68:		Line 70:
	<tr>		<tr>
	<td colspan="7">		<td colspan="7">
	<apll>f←{⍺⍺ ⍺⍺⍺⍨⍳⍵}</apll>		<apll>hyp←{⍺⍺ ⍺⍺⍺⍨⍳⍵}</apll>
	</td>		</td>
	</tr>		</tr>
Line 74:		Line 76:
	<tr>		<tr>
	<td>		<td>
	<apll> =∘.f 4		<apll> =∘.hyp 4
	1 0 0 0		1 0 0 0
	0 1 0 0		0 1 0 0
Line 82:		Line 84:

	<td>		<td>
	<apll> ⌈∘.f 4		<apll> ⌈∘.hyp 4
	1 2 3 4		1 2 3 4
	2 2 3 4		2 2 3 4
Line 90:		Line 92:

	<td>		<td>
	<apll> *∘.f 4		<apll> *∘.hyp 4
	1 1 1 1		1 1 1 1
	2 4 8 16		2 4 8 16
Line 98:		Line 100:

	<td>		<td>
	<apll> ≤∘.f 4		<apll> ≤∘.hyp 4
	1 1 1 1		1 1 1 1
	0 1 1 1		0 1 1 1
Line 106:		Line 108:
	</tr>		</tr>
	</table>		</table>

			In the above examples, the Monadic Operator <apll>∘.</apll> is the Left Hyperand and the functions <apll> = ⌈ * ≤ </apll> are the Left Operands to the Hyperator <apll>hyp</apll>.

	== Ambivalent AFOHs ==		== Ambivalent AFOHs ==

WikiSysop: /* Hyperator Hyperands */

2019-07-21T20:10:01Z

Hyperator Hyperands

← Older revision		Revision as of 16:10, 21 July 2019
Line 74:		Line 74:
	<tr>		<tr>
	<td>		<td>
	<apll> =f 4		<apll> =∘.f 4
	1 0 0 0		1 0 0 0
	0 1 0 0		0 1 0 0
Line 82:		Line 82:

	<td>		<td>
	<apll> ⌈f 4		<apll> ⌈∘.f 4
	1 2 3 4		1 2 3 4
	2 2 3 4		2 2 3 4
Line 90:		Line 90:

	<td>		<td>
	<apll> *f 4		<apll> *∘.f 4
	1 1 1 1		1 1 1 1
	2 4 8 16		2 4 8 16
Line 98:		Line 98:

	<td>		<td>
	<apll> ≤f 4		<apll> ≤∘.f 4
	1 1 1 1		1 1 1 1
	0 1 1 1		0 1 1 1

WikiSysop: /* Recursion */

2019-04-07T21:09:17Z

Recursion

← Older revision		Revision as of 17:09, 7 April 2019
Line 394:		Line 394:
	Computing <apll>*/5⍴2<_x/></apll> takes but a fraction of a second and returns a number with 19,729 digits!		Computing <apll>*/5⍴2<_x/></apll> takes but a fraction of a second and returns a number with 19,729 digits!

	'''N.B.:''' All of the <apll>∇</apll>, <apll>∇∇</apll>, and <apll>∇∇∇</apll> names may be used in user-defined functions/operators/hyperators, where they have the same meaning as they do in AFOHs.		'''N.B.:''' All of the <apll>∇</apll>, <apll>∇∇</apll>, and <apll>∇∇∇</apll> names may be used in user-defined recursive functions/operators/hyperators, where they have the same meaning as they do in AFOHs.

	== Termination ==		== Termination ==