Formalization of the Computational Theory of a Turing Complete Functional Language Model

This work presents a formalization in PVS of the computational theory for a computational model given as a class of partial recursive functions called PVS0. The model is built over basic operators, which, when restricted to constants, successor, projections, greater-than, and bijections from tuples of naturals to naturals, results in a proven (formalized) Turing complete model. Complete formalizations of the Recursion theorem and Rice’s theorem are discussed in detail. Other relevant results, such as the undecidability of the Halting problem and the fixed-point theorem, were also fully formalized.