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{{Built-in|High minus|¯}} or '''Negative''' is the character used in [[numeric literal]]s to indicate that a number is [[negate]]d. [[APL syntax]] dictates that it be distinct from the function [[Negate]] in order to allow all [[number]]s to be expressed as numeric literals. This ability is particularly useful in [[stranding]] or vector notation, since a number obtained from [[function]] application is harder to use in a strand—depending on the type of stranding available, it must either be parenthesized or cannot be stranded at all. It also allows negative numbers to be used as left [[argument]]s to functions, or as [[operand]]s.
{{Built-in|High minus|¯}} or '''Negative''' is the [[glyph]] used in [[numeric literal]]s to indicate that a number is [[negate]]d. [[APL syntax]] dictates that it be distinct from the function [[Negate]] in order to allow all [[number]]s to be expressed as numeric literals. This ability is particularly useful in [[stranding]] or vector notation, since a number obtained from [[function]] application is harder to use in a strand—depending on the type of stranding available, it must either be parenthesized or cannot be stranded at all. It also allows negative numbers to be used as left [[argument]]s to functions, or as [[operand]]s.


A high minus is also used in the TI-Basic programming language to differentiate negation from subtraction.<ref>TI-Basic Developer: [http://tibasicdev.wikidot.com/68k:negative The ‾ Command]</ref>
A high minus is also used in the TI-Basic programming language to differentiate negation from subtraction.<ref>TI-Basic Developer: [http://tibasicdev.wikidot.com/68k:negative The ‾ Command]</ref>


[[J]] uses a "low minus" (an underscore; <source lang=j inline>_</source>) as negative sign, while [[K]] requires at least one space between a dash (<code>-</code>) and a numeric literal to access the subtraction function as opposed to having the dash be interpreted as a negative sign.
[[J]] uses a "low minus" (an underscore; <syntaxhighlight lang=j inline>_</syntaxhighlight>) as negative sign, while [[K]] requires at least one space between a dash (<code>-</code>) and a numeric literal to access the subtraction function as opposed to having the dash be interpreted as a negative sign.


== Examples ==
== Examples ==


Using a high minus in a [[vector]] of [[number]]s allows one number to be negated. With an ordinary minus, the expression is instead parsed as [[subtraction]], where <source lang=apl inline>2 3</source> is subtracted from <source lang=apl inline>1</source>. In both cases, APL expresses negative results using the high minus.
Using a high minus in a [[vector]] of [[number]]s allows one number to be negated. With an ordinary minus, the expression is instead parsed as [[subtraction]], where <syntaxhighlight lang=apl inline>2 3</syntaxhighlight> is subtracted from <syntaxhighlight lang=apl inline>1</syntaxhighlight>. In both cases, APL expresses negative results using the high minus.
<source lang=apl>
<syntaxhighlight lang=apl>
       1 ¯2 3
       1 ¯2 3
1 ¯2 3
1 ¯2 3
       1 -2 3
       1 -2 3
¯1 ¯2
¯1 ¯2
</source>
</syntaxhighlight>
Because the high minus is part of a number and not a separate operation, it can be used as the left argument to a function without parenthesizing it. An ordinary minus will instead apply the function to the positive number and [[Negate]] the final result.
Because the high minus is part of a number and not a separate operation, it can be used as the left argument to a function without parenthesizing it. An ordinary minus will instead apply the function to the positive number and [[Negate]] the final result.
<source lang=apl>
<syntaxhighlight lang=apl>
       ¯2 ↓ 3 4 5
       ¯2 ↓ 3 4 5
3
3
       -2 ↓ 3 4 5
       -2 ↓ 3 4 5
¯5
¯5
</source>
</syntaxhighlight>
In langauges which allow array [[operand]]s, a negative number can be passed directly as an operand without parenthesizing it. Using an ordinary minus in the right operand will cause the minus alone to be used as the operand, while the number is not. In the expression below, it is passed as the left argument of [[Right]] (<source lang=apl inline>⊢</source>), causing it to be discarded.
In languages which allow array [[operand]]s, a negative number can be passed directly as an operand without parenthesizing it. Using an ordinary minus in the right operand will cause the minus alone to be used as the operand, while the number is not. In the expression below, it is passed as the left argument of [[Right]] (<syntaxhighlight lang=apl inline>⊢</syntaxhighlight>), causing it to be discarded.
<source lang=apl>
<syntaxhighlight lang=apl>
       +∘¯1 ⊢3
       +∘¯1 ⊢3
2
2
       +∘-1 ⊢3
       +∘-1 ⊢3
¯3
¯3
</source>
</syntaxhighlight>
== External links ==
== External links ==
=== Lessons ===
=== Lessons ===
Line 33: Line 33:
=== Documentation ===
=== Documentation ===
* [https://help.dyalog.com/latest/index.htm#Language/Introduction/Variables/Numbers.htm Dyalog]
* [https://help.dyalog.com/latest/index.htm#Language/Introduction/Variables/Numbers.htm Dyalog]
* [https://www.jsoftware.com/help/dictionary/d030.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/under J NuVoc] (as <source lang=j inline>_</source>)
* [https://www.jsoftware.com/help/dictionary/d030.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/under J NuVoc] (as <syntaxhighlight lang=j inline>_</syntaxhighlight>)
== References ==
== References ==
<references/>
<references/>
{{APL built-ins}}
{{APL glyphs}}[[Category:APL syntax]][[Category:Glyphs]]

Latest revision as of 22:10, 26 August 2024

¯

High minus (¯) or Negative is the glyph used in numeric literals to indicate that a number is negated. APL syntax dictates that it be distinct from the function Negate in order to allow all numbers to be expressed as numeric literals. This ability is particularly useful in stranding or vector notation, since a number obtained from function application is harder to use in a strand—depending on the type of stranding available, it must either be parenthesized or cannot be stranded at all. It also allows negative numbers to be used as left arguments to functions, or as operands.

A high minus is also used in the TI-Basic programming language to differentiate negation from subtraction.[1]

J uses a "low minus" (an underscore; _) as negative sign, while K requires at least one space between a dash (-) and a numeric literal to access the subtraction function as opposed to having the dash be interpreted as a negative sign.

Examples

Using a high minus in a vector of numbers allows one number to be negated. With an ordinary minus, the expression is instead parsed as subtraction, where 2 3 is subtracted from 1. In both cases, APL expresses negative results using the high minus. 

      1 ¯2 3
1 ¯2 3
      1 -2 3
¯1 ¯2

Because the high minus is part of a number and not a separate operation, it can be used as the left argument to a function without parenthesizing it. An ordinary minus will instead apply the function to the positive number and Negate the final result. 

      ¯2 ↓ 3 4 5
3
      -2 ↓ 3 4 5
¯5

In languages which allow array operands, a negative number can be passed directly as an operand without parenthesizing it. Using an ordinary minus in the right operand will cause the minus alone to be used as the operand, while the number is not. In the expression below, it is passed as the left argument of Right (⊢), causing it to be discarded. 

      +∘¯1 ⊢3
2
      +∘-1 ⊢3
¯3

External links

Lessons

Documentation

References

  1. ↑ TI-Basic Developer: The ‾ Command
APL glyphs [edit]
Information Glyph ∙ Typing glyphs (on Linux) ∙ Unicode ∙ Fonts ∙ Mnemonics ∙ Overstrikes ∙ Migration level
Individual glyphs Jot (∘) ∙ Right Shoe (⊃) ∙ Up Arrow (↑) ∙ Zilde (⍬) ∙ High minus (¯) ∙ Dot (.) ∙ Del (∇)
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