# Operators

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 | ||||||||||||||

A+S | ⍪ | ≡ | ≢ | ⍒ | ⍋ | ⌽ | ⍉ | ⊖ | ⍟ | ⍱ | ⍲ | ⍠ | ⌹ | |

Alt | ⋄ | ¨ | ¯ | < | ≤ | ∅ | ≥ | > | ≠ | ∨ | ∧ | × | ÷ | |

Sh | ~ | ! | @ | # | $ | % | ^ | & | * | ( | ) | _ | + | |

Key | ` | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | - | = | |

A+S | ⍷ | √ | ⍨ | ⍸ | ⍥ | ⍣ | ⍞ | ⍬ | ⊣ | |||||

Alt | ? | ⍵ | ∊ | ⍴ | § | ↑ | ↓ | ⍳ | ○ | π | ← | → | ⊢ | |

Sh | Q | W | E | R | T | Y | U | I | O | P | { | } | | | |

Key | q | w | e | r | t | y | u | i | o | p | [ | ] | \ | |

A+S | ∫ | ∂ | ⌻ | ⍢ | ⍙ | ⍤ | ⍫ | ⌷ | ||||||

Alt | ⍺ | ⌈ | ⌊ | ∞ | ∇ | ∆ | ∘ | ‼ | ⎕ | ⍎ | ⍕ | |||

Sh | A | S | D | F | G | H | J | K | L | : | " | |||

Key | a | s | d | f | g | h | j | k | l | ; | ' | |||

A+S | ⊆ | ⊇ | ⍡ | ⍭ | ⊙ | |||||||||

Alt | ⊂ | ⊃ | ∩ | ∪ | ⊥ | ⊤ | ⍦ | ⍝ | ⍀ | ⌿ | ||||

Sh | 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 |

*This NARS2000 article is a stub and needs further work.*