Operators: Difference between revisions

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In NARS2000, operators are symbols used to perform an action based on the arguments to the left, the right, or the left and right of the operator. Operators can be niladic, monadic, dyadic or a combination of these.
Operators are symbols used to perform an action based on the operands (functions, variables, or jots) to its left (monadic operator) or left and right (dyadic operator), along with the zero, one, or two arguments to the derived function from the operator. That is, the derived function may be niladic (no arguments), monadic (right argument only), or dyadic (left and right arguments).  For example, <apll>⍨</apll> is a monadic operator (a single operand on its left, e.g. <apll>f⍨</apll>), and the derived function from this operator is ambivalent (that is, may be called with a right argument only as in <apll>f⍨ R</apll> or both left and right arguments, as in <apll>L f⍨ R</apll>).




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The list of monadic operators is as follows:
 
{| border="1" cellpadding="5" cellspacing="0"
|-
| <apll>/</apll> || [[Reduction]] || <apll>f/ R</apll> || <apll>L f/ R</apll>
|-
| <apll>\</apll> || [[Scan]] || <apll>f\ R</apll> || <apll>L f\ R</apll>
|-
| <apll>¨</apll> || [[Each]] || <apll>f¨ R</apll> || <apll>L f¨ R</apll>
|-
| <apll>⍨</apll> || [[Commute-Duplicate|Duplicate/Commute]] || <apll>f⍨ R</apll> || <apll>L f⍨ R</apll>
|-
| <apll>⍦</apll> || [[Multisets]] || <apll>f⍦ R</apll> || <apll>L f⍦ R</apll>
|-
| <apll>‼</apll> || [[Combinatorial]] || <apll>v‼ R</apll> ||
|-
| <apll>⊙</apll> || [[Null]] || <apll>f⊙ R</apll> || <apll>L f⊙ R</apll>
|-
| <apll>∫</apll> || [[Integral]] || <apll>f∫ R</apll> || <apll>L f∫ R</apll>
|-
| <apll>∂</apll> || [[Derivative]] || <apll>f∂ R</apll> || <apll>L f∂ R</apll>
|}
 
 
The list of dyadic operators is as follows:
 
{| border="1" cellpadding="5" cellspacing="0"
|-
| <apll>⍤</apll> || [[Rank]] || <apll>f⍤w R</apll> || <apll>L f⍤w R</apll>
|-
| <apll>⍡</apll> || [[Convolution]] || || <apll>L f⍡g R</apll>
|-
| <apll>⍥</apll> || [[Composition]] || || <apll>L f⍥g R</apll>
|-
| <apll>.</apll> || [[Determinant_Operator|Determinant<br />Inner Product<br />Outer product]] || <apll>f.g R</apll><br /><br /><br /> || <br /><apll>L f.g R</apll><br /><apll>L ∘.g R</apll>
|-
| <apll>∘</apll> || [[Compose]] || <apll>f∘g R</apll><br /><apll>f∘w R</apll><br /><apll>v∘g R</apll> || <apll>L f∘g R</apll>
|-
| <apll>⍠</apll> || [[Variant]] || <apll>f⍠w R</apll> || <apll>L f⍠w R</apll>
|}
 
Where <apll>f</apll> and <apll>g</apll> represent functions and <apll>v</apll> and <apll>w</apll> represent variables.
 
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[[Category:Definitions]]
[[Category:Examples]][[Category:Definitions]]

Latest revision as of 15:50, 4 January 2020

Operators are symbols used to perform an action based on the operands (functions, variables, or jots) to its left (monadic operator) or left and right (dyadic operator), along with the zero, one, or two arguments to the derived function from the operator. That is, the derived function may be niladic (no arguments), monadic (right argument only), or dyadic (left and right arguments). For example, ⍨ is a monadic operator (a single operand on its left, e.g. f⍨), and the derived function from this operator is ambivalent (that is, may be called with a right argument only as in f⍨ R or both left and right arguments, as in L f⍨ R).


The list of monadic operators is as follows:

/ Reduction f/ R L f/ R
\ Scan f\ R L f\ R
¨ Each f¨ R L f¨ R
⍨ Duplicate/Commute f⍨ R L f⍨ R
⍦ Multisets f⍦ R L f⍦ R
‼ Combinatorial v‼ R
⊙ Null f⊙ R L f⊙ R
∫ Integral f∫ R L f∫ R
∂ Derivative f∂ R L f∂ R


The list of dyadic operators is as follows:

⍤ Rank f⍤w R L f⍤w R
⍡ Convolution L f⍡g R
⍥ Composition L f⍥g R
. Determinant
Inner Product
Outer product		 f.g R
L f.g R
L ∘.g R
∘ Compose f∘g R
f∘w R
v∘g R		 L f∘g R
⍠ Variant f⍠w R L f⍠w R

Where f and g represent functions and v and w represent variables.


See Also
System Commands System Variables and Functions Operators


Keyboard
Alt+Shift ⍪ ≡ ≢ ⍒ ⍋ ⌽ ⍉ ⊖ ⍟ ⍱ ⍲ ⍠ ⌹
Alt ⋄ ¨ ¯ < ≤ ∅ ≥ > ≠ ∨ ∧ × ÷
Shift ~ ! @ # $ % ^ & * ( ) _ +
Key ` 1 2 3 4 5 6 7 8 9 0 - =
Alt+Shift ⍷ √ ⍨ ⍸ ⍥ ⍣ ⍞ ⍬ ⊣
Alt ? ⍵ ∊ ⍴ § ↑ ↓ ⍳ ○ π ← → ⊢
Shift Q W E R T Y U I O P { } |
Key q w e r t y u i o p [ ] \
Alt+Shift ∫ ∂ ⌻ ⍢ ⍙ ⍤ ⍫ ⌷
Alt ⍺ ⌈ ⌊ ∞ ∇ ∆ ∘ ‼ ⎕ ⍎ ⍕
Shift A S D F G H J K L : "
Key a s d f g h j k l ; '
Alt+Shift ⊆ ⊇ χ ⍡ ⍭ ⊙
Alt ⊂ ⊃ ∩ ∪ ⊥ ⊤ ⍦ ⍝ ⍀ ⌿
Shift Z X C V B N M < > ?
Key z x c v b n m , . /
NARS 2000 Lang
Tool
Bar 		← → + - × ÷ * ⍟ ⌹ ○ ! ? √ | ⌈ ⌊ ⊥ ⊤ ⊣ ⊢
≡ ≢ < ≤ = ≥ > ≠ ∨ ∧ ⍱ ⍲ ↑ ↓ ⊂ ⊃ ⌷ ⍋ ⍒
⍳ ∊ ⍸ ⍷ ∪ ∩ ⊆ ⊇ ~ § π .. , ⍪ ⍴ ⌽ ⊖ ⍉
/ \ ⌿ ⍀ ⊙ ¨ ⍨ ⍤ ⍣ ⍡ ⍥ ⍦ . ∘ ⍠ ‼ ⌻ ∂ ∫ ⍞ ⎕ ⍎ ⍕
⋄ ⍝ ∇ ∆ ⍙ _ ⍺ ⍵ ¯ ⍬ ∞ ∅
Second Row i j k i j k l g p r v x




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