User-Defined Functions/Operators/Hyperators - Revision history

WikiSysop at 19:34, 3 April 2019

2019-04-03T19:34:56Z

WikiSysop at 14:31, 19 March 2019

2019-03-19T14:31:01Z

← Older revision		Revision as of 10:31, 19 March 2019
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	<li><p>'''User-defined Functions, Operators, and Hyperators'''</p>		<li><p>'''User-defined Functions, Operators, and Hyperators'''</p>
	<ul>		<ul>
	<li><p>Within a user-defined function/operator/hyperator header, the '''left''' and '''right''' arguments may consist of one or more names each separated by one or more blanks and enclosed in parentheses. In this context, the caller of the function/operator must pass a scalar (which is extended to each name) or anappropriate length vector argument. Upon invocation of the function/operator/hyperator, these values are assigned one item per name.</p>		<li><p>Within a user-defined function/operator/hyperator header, the '''left''' and '''right''' arguments may consist of one or more names each separated by one or more blanks and enclosed in parentheses. In this context, the caller of the function/operator/hyperator must pass a scalar (which is extended to each name) or anappropriate length vector argument. Upon invocation of the function/operator/hyperator, these values are assigned one item per name.</p>

	<p>For example, a function whose header looks like</p>		<p>For example, a function whose header looks like</p>
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	<li><p>A user-defined function/operator/hyperator may define a '''separate entry point''' for when it is called on a prototype — use the line label <apll>⎕PRO:</apll>. For example, the monadic function <apll>FOO</apll> when used in <apll>FOO¨R</apll> where <apll>R</apll> is an empty array is entered at the line labeled <apll>⎕PRO:</apll>. If there is no such line with that label, a <apll>DOMAIN ERROR</apll> is signaled.</p></li>		<li><p>A user-defined function/operator/hyperator may define a '''separate entry point''' for when it is called on a prototype — use the line label <apll>⎕PRO:</apll>. For example, the monadic function <apll>FOO</apll> when used in <apll>FOO¨R</apll> where <apll>R</apll> is an empty array is entered at the line labeled <apll>⎕PRO:</apll>. If there is no such line with that label, a <apll>DOMAIN ERROR</apll> is signaled.</p></li>

	<li><p>The local names to a user-defined function/operator appear in the header to the right of the syntax part as above. The first local name is separated from the start of the header by a single semicolon; the second and subsequent local names are separated from each other by either a single semicolon or one or more blanks depending upon your own preference. For example</p>		<li><p>The local names to a user-defined function/operator/hyperator appear in the header to the right of the syntax part as above. The first local name is separated from the start of the header by a single semicolon; the second and subsequent local names are separated from each other by either a single semicolon or one or more blanks depending upon your own preference. For example</p>

	<apll>∇ Z←FOO R;g1 g2 g3 g4;h1 h2 h3</apll></li>		<apll>∇ Z←FOO R;g1 g2 g3 g4;h1 h2 h3</apll></li>

WikiSysop: WikiSysop moved page User-Defined Functions/Operators to User-Defined Functions/Operators/Hyperators

2019-03-10T00:43:02Z

WikiSysop moved page User-Defined Functions/Operators to User-Defined Functions/Operators/Hyperators

← Older revision	Revision as of 20:43, 9 March 2019
(No difference)

WikiSysop at 03:08, 7 March 2019

2019-03-07T03:08:52Z

Show changes

WikiSysop at 16:44, 28 April 2018

2018-04-28T16:44:02Z

← Older revision		Revision as of 12:44, 28 April 2018
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	<li><p>Within a recursive user-defined function, a del symbol (<apll>∇</apll>) refers to the user-defined function without having to name it. For example,</p>		<li><p>Within a recursive user-defined function, a del symbol (<apll>∇</apll>) refers to the user-defined function without having to name it. For example,</p>
	<apll>~~    ~~∇ Z←fibonacci R~~<br />~~		<apll><pre>
	[1]~~   ~~:if R≤1 ⋄ Z←1 ⋄ →0 ⋄ :end~~<br />~~		∇ Z←fibonacci R
	[2]~~   ~~Z←(∇R-1) + ∇R-2~~<br />~~		[1] :if R≤1 ⋄ Z←1 ⋄ →0 ⋄ :end
	~~    ~~∇<br /></apll>		[2] Z←(∇R-1) + ∇R-2
			∇
			</pre></apll>
	</li>		</li>

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	<li>A jot (<apll>∘</apll>) may be used as an operand to a user-defined operator in which case the corresponding name in the header is undefined, that is <apll>⎕NC</apll> returns <apll>0</apll>. For example,		<li>A jot (<apll>∘</apll>) may be used as an operand to a user-defined operator in which case the corresponding name in the header is undefined, that is <apll>⎕NC</apll> returns <apll>0</apll>. For example,

	<p><~~apll~~>~~    ~~∇ (Z1 Z2)←(LO DydOp RO) R~~<br />~~		<apll><pre>
	[1]~~   ~~:select ⍬⍴⎕NC 'LO'~~<br />~~		∇ (Z1 Z2)←(LO DydOp RO) R
	[2]~~   ~~:case 0 ⋄ Z1←'LO is undefined'~~<br />~~		[1] :select ⍬⍴⎕NC 'LO'
	[3]~~   ~~:case 2 ⋄ Z1←'LO is a variable'~~<br />~~		[2] :case 0 ⋄ Z1←'LO is undefined'
	[4]~~   ~~:case 3 ⋄ Z1←'LO is a function'~~<br />~~		[3] :case 2 ⋄ Z1←'LO is a variable'
	[5]~~   ~~:end~~<br />~~		[4] :case 3 ⋄ Z1←'LO is a function'
	[6]~~<br />~~		[5] :end
	[7]~~   ~~:select ⍬⍴⎕NC 'RO'~~<br />~~		[6]
	[8]~~   ~~:case 0 ⋄ Z2←'RO is undefined'~~<br />~~		[7] :select ⍬⍴⎕NC 'RO'
	[9]~~   ~~:case 2 ⋄ Z2←'RO is a variable'~~<br />~~		[8] :case 0 ⋄ Z2←'RO is undefined'
	[10]~~  ~~:case 3 ⋄ Z2←'RO is a function'~~<br />~~		[9] :case 2 ⋄ Z2←'RO is a variable'
	[11]~~  ~~:end~~<br />~~		[10] :case 3 ⋄ Z2←'RO is a function'
	~~    ~~∇~~<br />~~		[11] :end
	~~<br />~~		∇
	~~      ~~∘DydOp⍴ 12~~<br />~~
	LO is undefined  RO is a function~~<br />~~		∘DydOp⍴ 12
	~~      ~~⍴DydOp∘ 12~~<br />~~		LO is undefined  RO is a function
	LO is a function  RO is undefined~~<br />~~		⍴DydOp∘ 12
	~~      ~~∘DydOp∘ 12~~<br />~~		LO is a function  RO is undefined
	LO is undefined  RO is undefined<br />		∘DydOp∘ 12
	</apll~~></p~~>		LO is undefined  RO is undefined
			</pre></apll>
	</li>		</li>
	</ul>		</ul>
	</li>		</li>
	</ul>		</ul>

WikiSysop at 04:26, 5 June 2015

2015-06-05T04:26:55Z

← Older revision		Revision as of 00:26, 5 June 2015
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	</li>		</li>

	<li><p>Within a recursive user-defined operator, a del symbol (<apll>∇</apll>) refers to the derived function of the user-defined operator with the current operands bound to the operator name. For example, with a monadic operator whose header looks like</p>		<li><p>Within a recursive user-defined operator, a del symbol (<apll>∇</apll>) refers to the derived function of the user-defined operator with the current operands bound to the operator name without having to name it. For example, with a monadic operator whose header looks like</p>

	<apll>∇ Z←(LO mop) R</apll>		<apll>∇ Z←(LO mop) R</apll>
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	<p>a del in the body of the operator is a shorthand for <apll>(LO dop RO)</apll>.</p></li>		<p>a del in the body of the operator is a shorthand for <apll>(LO dop RO)</apll>.</p></li>

	<li><p>Within a recursive user-defined operator, two del symbols (<apll>∇∇</apll>) refer to the operator ~~itself~~ with no bound operands.</p></li>		<li><p>Within a recursive user-defined operator, two del symbols (<apll>∇∇</apll>) refer to the operator name with no bound operands. For example, in the monadic operator case above in the body of the operator, <apll>∇∇</apll> refers to <apll>mop</apll>, and in the dyadic operator case above, <apll>∇∇</apll> refers to <apll>dop</apll>, and in both cases without having to know the actual name.</p></li>
	</ul>		</ul>
	</li>		</li>

WikiSysop at 04:20, 5 June 2015

2015-06-05T04:20:27Z

← Older revision		Revision as of 00:20, 5 June 2015
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	</li>		</li>

	<li><p>Within a recursive user-defined operator, a del symbol (<apll>∇</apll>) refers to the derived function of the user-defined operator with the ~~existing~~ operands bound to the operator name.</p></li>		<li><p>Within a recursive user-defined operator, a del symbol (<apll>∇</apll>) refers to the derived function of the user-defined operator with the current operands bound to the operator name. For example, with a monadic operator whose header looks like</p>

			<apll>∇ Z←(LO mop) R</apll>

			<p>a del symbol in the body of the operator is a shorthand for <apll>(LO mop)</apll>, and for a dyadic operator whose header looks like</p>

			<apll>∇ Z←(LO dop RO) R</apll>

			<p>a del in the body of the operator is a shorthand for <apll>(LO dop RO)</apll>.</p></li>

	<li><p>Within a recursive user-defined operator, two del symbols (<apll>∇∇</apll>) refer to the operator itself with no bound operands.</p></li>		<li><p>Within a recursive user-defined operator, two del symbols (<apll>∇∇</apll>) refer to the operator itself with no bound operands.</p></li>

WikiSysop at 00:44, 5 June 2015

2015-06-05T00:44:40Z

← Older revision		Revision as of 20:44, 4 June 2015
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	<apll>∇ Z←(LO FOO[X] RO) R</apll> for a dyadic operator.</p></li>		<apll>∇ Z←(LO FOO[X] RO) R</apll> for a dyadic operator.</p></li>

	<li>A user-defined function/operator may define a '''separate entry point''' for when it is called on a prototype — use the line label <apll>⎕PRO:</apll>. For example, the monadic function <apll>FOO</apll> when used in <apll>FOO¨R</apll> where <apll>R</apll> is an empty array is entered at the line labeled <apll>⎕PRO:</apll>. If there is no such line with that label, a <apll>DOMAIN ERROR</apll> is signaled.</li>		<li><p>A user-defined function/operator may define a '''separate entry point''' for when it is called on a prototype — use the line label <apll>⎕PRO:</apll>. For example, the monadic function <apll>FOO</apll> when used in <apll>FOO¨R</apll> where <apll>R</apll> is an empty array is entered at the line labeled <apll>⎕PRO:</apll>. If there is no such line with that label, a <apll>DOMAIN ERROR</apll> is signaled.</p></li>

			<li><p>The local names to a user-defined function/operator appear in the header to the right of the syntax part as above. The first local name is separated from the start of the header by a single semicolon; the second and subsequent local names are separated from each other by either a single semicolon or one or more blanks depending upon your own preference. For example</p>

			<apll>∇ Z←FOO R;g1 g2 g3 g4;h1 h2 h3</apll></li>

			<li><p>Within a recursive user-defined function, a del symbol (<apll>∇</apll>) refers to the user-defined function without having to name it. For example,</p>
			<apll>    ∇ Z←fibonacci R<br />
			[1]   :if R≤1 ⋄ Z←1 ⋄ →0 ⋄ :end<br />
			[2]   Z←(∇R-1) + ∇R-2<br />
			∇<br /></apll>
			</li>

			<li><p>Within a recursive user-defined operator, a del symbol (<apll>∇</apll>) refers to the derived function of the user-defined operator with the existing operands bound to the operator name.</p></li>

			<li><p>Within a recursive user-defined operator, two del symbols (<apll>∇∇</apll>) refer to the operator itself with no bound operands.</p></li>
	</ul>		</ul>
	</li>		</li>

	<li><p>'''User-defined Operators'''</p>		<li><p>'''User-defined Operators'''</p>
	<ul>		<ul>
	<li><p>A user-defined <font color=purple><strong>operator</strong></font> is distinguished from a user-defined <u>function</u> by its <font color=purple><strong>header</strong></font>, such that in the place where the function <font color=purple><strong>name</strong></font> normally appears, it contains a left operand name, an operator name, and an optional right operand name (for dyadic operators only), all enclosed in <font color=purple><strong>a single set of parentheses</strong></font>. For example, the operator part of the header for a monadic operator looks like <font color=purple><strong><apll>(LO MonOp)</apll></strong></font>, and a dyadic operator looks like <font color=purple><strong><apll>(LO DydOp RO)</apll></strong></font> where <apll>LO</apll> and <apll>RO</apll> are the left and right operands (~~functions~~).</p>		<li><p>A user-defined <font color=purple><strong>operator</strong></font> is distinguished from a user-defined <u>function</u> by its <font color=purple><strong>header</strong></font>, such that in the place where the function <font color=purple><strong>name</strong></font> normally appears, it contains a left operand name, an operator name, and an optional right operand name (for dyadic operators only), all enclosed in <font color=purple><strong>a single set of parentheses</strong></font>. For example, the operator part of the header for a monadic operator looks like <font color=purple><strong><apll>(LO MonOp)</apll></strong></font>, and a dyadic operator looks like <font color=purple><strong><apll>(LO DydOp RO)</apll></strong></font> where <apll>LO</apll> and <apll>RO</apll> are the left and right operands (a function, variable, or jot).</p>
	<font color=purple><strong>		<font color=purple><strong>
	<p>Both types of user-defined operators may be called monadically or dyadically, as in</p>		<p>Both types of user-defined operators may be called monadically or dyadically, as in</p>

Robert Wallick: added context to operators

2015-02-14T00:40:16Z

added context to operators

← Older revision		Revision as of 20:40, 13 February 2015
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	</table>		</table>
	</strong></font>		</strong></font>
			<p>Operators exist to modify behaviors of functions as well as operate on data. An operator may be applied to a function to derive a ''different'' function or ''modify'' data(/\+-×÷). An attribute of operators are their precedence '''over''' functions; operators are executed '''before''' functions. One indication an Operator should be used instead of a function is - when a function always includes parentheses during its call. Proper structuring of commonly used operators prevents, for instance, multiple layers of parentheses, thus clarifying code, speeding execution and increasing parallelization. Operator usage situations: Statisticians - regression operators (power, multiple, growth, natural, cubic, cylical, etc.); Astronomers - integration and differentiation operators; Engineers - curve fitting, approximating, equation root derivations.
			</p>
	<p>Just like user-defined functions, user-defined operators may have multiple names in the result, left, and right arguments (but not the left and/or right operands), an optional left argument, an axis operator, and a non-displayable result.</p>		<p>Just like user-defined functions, user-defined operators may have multiple names in the result, left, and right arguments (but not the left and/or right operands), an optional left argument, an axis operator, and a non-displayable result.</p>

Robert Wallick: wording, fmt'ing

2015-02-13T23:47:45Z

wording, fmt'ing

← Older revision		Revision as of 19:47, 13 February 2015
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	<li><p>'''User-defined Operators'''</p>		<li><p>'''User-defined Operators'''</p>
	<ul>		<ul>
	<li><p>A user-defined operator is distinguished from a user-defined function by its header, such that in the place where the function name normally appears, it contains a left operand name, an operator name, and an optional right operand name (for dyadic operators only), all enclosed in a single set of parentheses. For example, the operator part of the header for a monadic operator looks like <apll>(LO MonOp)</apll>, and a dyadic operator looks like <apll>(LO DydOp RO)</apll> where <apll>LO</apll> and <apll>RO</apll> are the left and right operands (functions).</p>		<li><p>A user-defined <font color=purple><strong>operator</strong></font> is distinguished from a user-defined <u>function</u> by its <font color=purple><strong>header</strong></font>, such that in the place where the function <font color=purple><strong>name</strong></font> normally appears, it contains a left operand name, an operator name, and an optional right operand name (for dyadic operators only), all enclosed in <font color=purple><strong>a single set of parentheses</strong></font>. For example, the operator part of the header for a monadic operator looks like <font color=purple><strong><apll>(LO MonOp)</apll></strong></font>, and a dyadic operator looks like <font color=purple><strong><apll>(LO DydOp RO)</apll></strong></font> where <apll>LO</apll> and <apll>RO</apll> are the left and right operands (functions).</p>
			<font color=purple><strong>
	<p>Both types of user-defined operators may be called monadically or dyadically, as in</p>		<p>Both types of user-defined operators may be called monadically or dyadically, as in</p>

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	</tr>		</tr>
	</table>		</table>
			</strong></font>
	<p>Just like user-defined functions, user-defined operators may have multiple names in the result, left, and right arguments (but not the left and/or right operands), an optional left argument, an axis operator, and a non-displayable result.</p>		<p>Just like user-defined functions, user-defined operators may have multiple names in the result, left, and right arguments (but not the left and/or right operands), an optional left argument, an axis operator, and a non-displayable result.</p>