Definition

1. Noun:
   • An operation with exactly one operand: In logic, mathematics, and computer science, a "monadic operation" is a function or operation that takes a single input (operand) to produce an output. It is also commonly called a unary operation.

Usage Examples

• Noun:
  • Negation is a classic example of a monadic operation in logic.
  • In programming, the increment operator (++) is a monadic operation.
  • The mathematical operation of finding the absolute value is a monadic operation.

Advanced Usage

• Formal Logic: In formal systems, a monadic operation can be a logical connective like negation (¬), which transforms a single proposition.
  • The truth value of a proposition is reversed by the monadic operation of negation.
• Functional Programming: The concept is fundamental, where functions of one argument are central.
  • In this functional language, map is a higher-order function that often applies a monadic operation to each element of a list.

Variants and Related Words

• Unary operation: A direct synonym for monadic operation.
  • The unary minus, as in -5, is a unary operation.
• Monadic (adj): Pertaining to or being a monad or a single unit.
  • The function has a monadic type, meaning it expects one argument.
• Dyadic operation/Binary operation: An operation with exactly two operands, often contrasted with a monadic operation.
  • Addition is a dyadic operation, while absolute value is monadic.

Synonyms

• Unary operation: Operation on a single operand.
• Singulary operation: A less common synonym for a one-place operation.

Related Phrases

• Monadic function: A function that performs a monadic operation; a function of one argument.
  • This library provides several useful monadic functions for data transformation.
• Monadic predicate: In logic, a predicate that takes a single argument.
  • "Is prime" is a monadic predicate applied to numbers.

Related Concepts

• Operand: The object or quantity on which an operation is performed.
  • In the expression -x, x is the operand for the monadic operation of negation.
• Arity: The number of operands an operation takes. A monadic operation has an arity of one.
  • The arity of the logical NOT operator is one, making it monadic.

Noun

1. an operation with exactly one operand