We propose a general framework for “non-standard type inference based” static analyses of typed functional programs and study inference systems (with and without conjunction) for strictness, totality, and dead-code analyses. A key feature of our framework is that it provides a foundation of the program analyses which is based directly on the operational semantics of the programming language considered. This results in a rather direct presentation which involves relatively little mathematical overhead. We develop a semantical investigation of the systems and discuss in some detail possible implementations of the presented analyses. In particular we give sound and complete inference algorithms for strictness and dead-code analyses without conjunction.