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2. Free variables and bound variables - Wikipedia

   en.wikipedia.org/wiki/Free_variables_and_bound...

   A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer ...

3. Quantifier (logic) - Wikipedia

   en.wikipedia.org/wiki/Quantifier_(logic)

   the occurrence of both x and y in C(y, x) is free, while the occurrence of x and y in B(y, x) is bound (i.e. non-free). Syntax tree of the formula ((,)) (,), illustrating scope and variable capture. Bound and free variable occurrences are colored in red and green, respectively.

4. Lambda calculus definition - Wikipedia

   en.wikipedia.org/wiki/Lambda_calculus_definition

   Substitution, written [:=], is the process of replacing all free occurrences of the variable in the expression with expression . Substitution on terms of the lambda calculus is defined by recursion on the structure of terms, as follows (note: x and y are only variables while M and N are any λ expression).

5. Expression (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Expression_(mathematics)

   For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the value of the expression may be undefined. Thus an expression represents an operation over constants and free variables and whose output is the resulting value of the expression. [22]

6. Lambda calculus - Wikipedia

   en.wikipedia.org/wiki/Lambda_calculus

   Substitution, written M[x := N], is the process of replacing all free occurrences of the variable x in the expression M with expression N. Substitution on terms of the lambda calculus is defined by recursion on the structure of terms, as follows (note: x and y are only variables while M and N are any lambda expression):

7. Equality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Equality_(mathematics)

   In logic, a predicate is a proposition which may have some free variables. Equality is a predicate, which may be true for some values of the variables (if any) and false for other values. More specifically, equality is a binary relation (i.e., a two-argument predicate) which may produce a truth value (true or false) from its arguments.