If I am not wrong, FP-people say that absence of side effects simplify proofs of correctness (wrt specifications), not that proofs of programs with side effects are impossible.
For a comparison of 4 methods of proving programs with side effects ( Floyd–Hoare logic, E. W. Dijkstra's Discipline of Programming, Cliff B. Jones' Vienna Development Method (VDM) and E. C. R. Hehner's Practical Theory of Programming) see:
E.C.R.Hehner, What's wrong with formal programming methods? (PDF), Conference on Computing and Information, Ottawa, 1991 May (keynote address, invited); chapter in Advances in Computing and Information, Lecture Notes in Computer Science v.497, Springer, Berlin, 1991, p.2-23
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