2931	 Logic and Programming Languages	 Logic has been long in terested in whether answers to certain questions are computable in principle since the outcome puts bounds on the possibilities of formalization. More recently precise comparisons in the efficiency of decision methods have become available through the developments in complexity theory. These however are applications to logic and a big question is whether methods of logic have significance in the other direction for the more applied parts of computability theory. Programming languages offer an obvious opportunity as their syntactic formalization is well advanced however the semantical theory can hardly be said to be complete. Though we have many examples we have still to give wide-ranging mathematical answers to these queries What is a machine What is a computable process How or how well does a machine simulate a process Programs naturally enter in giving descriptions of processes. The definition of the precise meaning of a program then requires us to explain what are the objects of computation in a way the statics of the problem and how they are to be transformed the dynamics . So far the theories of automata and of nets though most in teresting for dynamics have formalized only a portion of the field and there has been perhaps too much concentration on the finite-state and algebraic aspects. It would seem that the understanding of higher-level program features involves us with infinite objects and forces us to pass through several levels of explanation to go from the conceptual ideas to the final simulation on a real machine. These levels can be made mathematically exact if we can find the right abstractions to represent the necessary structures. The experience of many independent workers with the method of data types as lattices or partial orderings under an information content ordering and with their continuous mappings has demonstrated the flexibility of this approach in providing definitions and proofs which are clean and without undue dependence on implementations. Nevertheless much remains to be done in showing how abstract conceptualizations can or cannot be actualized before we can say we have a unified theory. logic programming languages automata denotational semantics a-calculus models computability partial functions approximation function spaces
