![]() A formal theory is a formal system which captures the notion of the abstract notion of computable functions. ![]() You may noticed that formal system, theory and model are used to refer to those formalisms, lets say what that means. In other words it states that any compuable function is definable indistinctly in any of those systems. The fact that every attempt to build a system to capture the notion of computation resulted in a theory equivalent to each other is a strong indication that no other "more powerful" system exists, that can not be proved, for that reason is known as the Churrch-Turing thesis. Recursive functions can be expressed in the lambda calculus, and vice versa, also an universal Turing machine can be defined in the lambda calculus and recursive functions and the lambda calculus in the universal Turing machine, the same with the other computation models not described here. Turing a Universal abstract machine, later called Universal Turing Machine, among other formal systems. Kleene developed recursive functions and Alan M. ![]() This calculus was developed by Alonzo Church in the 1930s at the same time which other researchers developed other models of computation which later were proved to be equivalent. a formal system which formalize the abstract notion of computable functions. Lambda Calculus is a theory of computable functions, i.e. ![]()
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