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We introduce a new way of formalizing the intensional identity type based onthe fact that a entity known as computational paths can be interpreted as termsof the identity type. Our approach enjoys the fact that our elimination rule iseasy to understand and use. We make this point clear constructing terms of somerelevant types using our proposed elimination rule. We also show that theidentity type, as defined by our approach, induces a groupoid structure. Thisresult is on par with the fact that the traditional identity type induces agroupoid, as exposed by Hofmann \& Streicher (1994).

On the Identity Type as the Type of Computational Paths