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Variable-binding operators are logical operators that occur in almost every formal language. A binding operator Q takes two arguments: a variable v and an expression P, and when applied to its arguments produces a new expression Q(v, P). The meaning of binding operators is supplied by the semantics of the language and does not concern us here.
The binding of operators in C and C++ is specified by a factored language grammar, rather than a precedence table. This creates some subtle conflicts. For example, in C, the syntax for a conditional expression is:
In Germany, the convention is simply taught as Punktrechnung vor Strichrechnung, "dot operations before line operations" referring to the graphical shapes of the taught operator signs U+00B7 · MIDDLE DOT (multiplication), U+2236 ∶ RATIO (division), and U+002B + PLUS SIGN (addition), U+2212 − MINUS SIGN (subtraction).
Logical operators over bit vectors (corresponding to finite Boolean algebras) are bitwise operations. But not every usage of a logical connective in computer programming has a Boolean semantic. For example, lazy evaluation is sometimes implemented for P ∧ Q and P ∨ Q , so these connectives are not commutative if either or both of the ...
There are three ways of eliminating quantified variables from first-order logic that do not involve replacing quantifiers with other variable binding term operators: Cylindric algebra, by Alfred Tarski and colleagues; Polyadic algebra, by Paul Halmos; Predicate functor logic, mainly due to Willard Quine.
The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
If the operator ~ has left associativity, this expression would be interpreted as (a ~ b) ~ c. If the operator has right associativity, the expression would be interpreted as a ~ (b ~ c). If the operator is non-associative, the expression might be a syntax error, or it might have some special meaning. Some mathematical operators have inherent ...