| Expression (mathematics) |
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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 expression may be undefined. Thus an expression represents a Function whose inputs are the values assigned the free variables and whose output is the resulting value of the expression. For example, the expression : evaluated for ''x'' = 10, ''y'' = 5, outputs the number 2; but is undefined for ''y'' = 0. The evaluation of an expression is dependent on the definition of the mathematical operators and on the system of values that is its context. Two expressions are said to be Equivalent if, for each combination of values for the free variables, they have the same output, i.e., they represent the same function. Example: The expression : has free variable ''x'', bound variable ''n'', constants 1, 2, and 3, two occurrences of an implicit multiplication operator, and a summation operator. The expression is equivalent with the simpler expression 12''x''. The value for ''x''=3 is 36.
Expressions and their evaluation were formalised by Alonzo Church and Stephen Kleene in the 1930s in their Lambda Calculus . The lambda calculus has been a major influence in the development of modern mathematics and computer Programming Language s. One of the more interesting results of the lambda calculus is that the equivalence of two expressions in the lambda calculus is in some cases Undecidable . This is also true of any expression in any system that has power equivalent to the lambda calculus. SEE ALSO EXTERNAL LINKS
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