Anonymous Functions/Operators/Hyperators - Revision history

WikiSysop: /* Scoping */

2026-08-24T15:55:29Z

Scoping

← Older revision		Revision as of 11:55, 24 August 2026
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	When calls to user-defined functions are nested, a reference to a name by an inner function is resolved by looking up the chain of nested functions for the nearest level at which that name is localized. Looked at from a different perspective, when a name is localized to a function, its scope consists of all functions called by that function. This is called '''dynamic scoping'''.		When calls to user-defined functions are nested, a reference to a name by an inner function is resolved by looking up the chain of nested functions for the nearest level at which that name is localized. Looked at from a different perspective, when a name is localized to a function, its scope consists of all functions called by that function. This is called '''dynamic scoping'''.

	~~AFOHs~~ use a different mechanism where names referenced by an AFOH are resolved by the context in which the AFOH is defined, not where it is used. This is called '''lexical scoping''' or '''static scoping'''.		Anonymous Functions Operators Hyperators (AFOH) use a different mechanism where names referenced by an AFOH are resolved by the context in which the AFOH is defined, not where it is used. This is called '''lexical scoping''' or '''static scoping'''.

	In other words, to paraphrase [http://en.wikipedia.org/wiki/Scope_%28computer_science%29#Lexical_scoping_and_dynamic_scoping Wikipedia], "This means that if function <apll>f</apll> invokes function <apll>g</apll> that is defined outside the context of <apll>f</apll>, then under lexical scoping, function <apll>g</apll> does not have access to <apll>f</apll>'s local variables (since the definition of <apll>g</apll> is not inside the definition of <apll>f</apll>), while under dynamic scoping, function <apll>g</apll> does have access to <apll>f</apll>'s local variables (since the invocation of <apll>g</apll> is inside the invocation of <apll>f</apll>)".		In other words, to paraphrase [http://en.wikipedia.org/wiki/Scope_%28computer_science%29#Lexical_scoping_and_dynamic_scoping Wikipedia], "This means that if function <apll>f</apll> invokes function <apll>g</apll> that is defined outside the context of <apll>f</apll>, then under lexical scoping, function <apll>g</apll> does not have access to <apll>f</apll>'s local variables (since the definition of <apll>g</apll> is not inside the definition of <apll>f</apll>), while under dynamic scoping, function <apll>g</apll> does have access to <apll>f</apll>'s local variables (since the invocation of <apll>g</apll> is inside the invocation of <apll>f</apll>)".

			In terms of the implementation, each function has a Symbol Table (ST) along with a link to the next higher order ST. Name lookups follow this sequence, first the local ST, and if not found, look up the chain until the name is found or VALUE ERROR. If a name is localized to a function, it appears in the local ST. When an AFOH is defined, its ST is consulted first before any other

	For example,		For example,

	<apll><pre>		<apll><pre>
	∇ ~~foo~~;f g a		∇ fn1;f g a
	[1] a←'static'		[1] a←'static'
	[2] ~~←⎕fx~~ 'f R;a' 'a←"dynamic"' 'g R'		[2] ←⎕FX 'f R;a' 'a←"dynamic"' 'g R'
	[3] ~~←⎕fx~~ 'g R' '"scope ←→ ",a'		[3] ←⎕FX 'g R' '"scope ←→ ",a'
	[4] f 'a'		[4] f 'a'
	∇		∇

	~~foo~~		fn1
	scope ←→ dynamic		scope ←→ dynamic
	{a←'static' ⋄ f←{a←'dynamic' ⋄ g ⍵} ⋄ g←{'scope ←→ ',a ~~⋄ ⍵~~} ⋄ f ~~'a'~~}		fn2←{a←'static' ⋄ f←{a←'dynamic' ⋄ g} ⋄ g←{'scope ←→ ',a} ⋄ f}
			fn2
	scope ←→ static		scope ←→ static
			<_com>⍝ In <red>fn2</red>, <red>g</red>'s ST is linked to <red>fn2</red>'s ST, so regardless of where <i>g</i></_com>
			<_com>⍝ is called, <i>a</i> is found in <i>fn2</i>'s ST</_com>

			∇ fn3
	∇ ~~fop~~		[1] x←'root'
	[1] x←'root'		[2] ←⎕FX 'Z←get_x' 'Z←x' <_com>⍝ <i>get_x</i>'s ST is linked to <i>fn3</i>'s ST</_com>
	[2] ←⎕FX 'Z←get_x' 'Z←x'		[3] ←⎕FX 'Z←(fn op)' 'Z←fn' <_com>⍝ <i>op</i> is linked to <i>fn3</i>'s ST</_com>
	[3] ←⎕FX 'Z←(fn op)' 'Z←fn'		[4] f←{x get_x} <_com>⍝ <i>x</i> is global to <i>f</i>, so <i>fn3</i>'s ST applies</_com>
	[4] f←{x get_x}		[5] {x←'test' ⋄ ⎕←f ⋄ f op} <_com>⍝ Although <i>x</i> is local to this anonymous function,</_com>
	[5] {x←'test' ⋄ ⎕←f ⋄ f op}		<_com>⍝ the other references to <i>x</i> refer to <i>fn3</i>'s ST</_com>
	∇		∇

	~~fop~~		fn3
	root root		root root
	root root		root root

WikiSysop: /* Scoping */

2026-08-06T01:04:53Z

Scoping

@@ Line 351: / Line 351: @@
        {a←'static' ⋄ f←{a←'dynamic' ⋄ g ⍵} ⋄ g←{'scope ←→ ',a ⋄ ⍵} ⋄ f 'a'}
 scope ←→ static
 </pre></apll>
 == Recursion ==

WikiSysop: /* Multi-Line AFOHs */

2026-07-12T22:36:48Z

Multi-Line AFOHs

← Older revision		Revision as of 18:36, 12 July 2026
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	== Multi-Line AFOHs ==		== Multi-Line AFOHs ==

	An AFOH may be defined on multiple lines (just like User-Defined Functions/Operators/Hyperators) by first naming it (e.g. <apll>h←{s←(+/⍵)÷2 ⋄ √×/s-0,⍵}</apll>), and then editing it in the usual ~~way~~ (e.g., <apll>∇h</apll>). For more details, see [[Function_Editing\|Function Editing]].		An AFOH may be defined on multiple lines (just like User-Defined Functions/Operators/Hyperators) by first naming it (e.g. <apll>h←{s←(+/⍵)÷2 ⋄ √×/s-0,⍵}</apll> or just use <apll>h←{}</apll> to initialize the name), and then editing it in the usual ways (e.g., <apll>∇h</apll> or <apll>)EDIT h</apll>). For more details, see [[Function_Editing\|Function Editing]].

	== Guards ==		== Guards ==

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;">