β-reduction

β-reduction is a process used in mathematical logic and computer science to simplify expressions in lambda calculus. It involves applying a function to an argument by replacing the function's placeholder (called a variable) with the actual value or expression provided. Think of it like plugging a specific input into a formula; after substitution, the expression becomes more concrete and often easier to evaluate. This process helps in streamlining complex expressions into simpler forms, making them easier to analyze or compute. Essentially, β-reduction is the formal mechanism for executing functions by substitution.