Informal proof of application of the theory of groups to computer programs.
First we take a binary operation we call our computer program. A binary operation in groups can be any abstract thing. This abstract thing is founded upon the idea of In this proof we use the binary operation as the evaluation of a computer program. Closure can be proven in the computer program by the simple fact that anything evaluated by the computer returns a value that is specified inside of the definition language. Here is an excerpt from my paper on the subject.
A informal definition of a Group which is a set of axioms that has closure, associativity , identity and inverse. Closure can be reasoned by given two functions the output is always something that the program could reason as an output which is provided by the language the program is programmed in. Associativity could be reasoned by taking the output of one program and then taking that output and evaluating that output into another function. Inverse can be reasoned with a program that returns the output given the input. Lastly there is a program that returns the identity of the function. This would be quotation of the function and then evaluating the quotation. We use first order logic to confirm these hypothesis's given a computer program and this hypothesis will prove that a set of instructions is a group.