The ς-Semantics: A Comprehensive Semantics for Functional Programs

A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameterpassing mechanism. Thus common and distinguishing features of all instances of the ς-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the ς-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixedpoint based) and two operational (reduction based) definitions of the ς-semantics. We present and apply means for very simple proofs of equivalence with the denotational ςsemantics for a large class of reduction-based ς-semantics. Our basis are simple first-order constructor-based functional programs with patterns.