2470	 Fen-An Axiomatic Basis for Program Semantics	 A formal system is presented which abstracts the notions of data item function and relation. It is argued that the system is more suitable than set theory or its derivatives for the concise and accurate description of program semantics. It is shown how the system can be used to build composite data types out of simper ones with the operations of rowing structuring and uniting. It is also demonstrated that completely new primitive types can be introduced into languages through the mechanism of singleton data types. Both deterministic and nondeterministic functions are shown to be definable in the system. It is described how the local environment can be modeled as a data item and how imperative statements can be considered functions on the environment. The nature of recursive functions is briefly discussed and a technique is presented by which they can be introduced into the system. The technique is contrasted with the use of the paradoxical combinator Y. The questions of local and global environments and of various modes of function calling and parameter passing are touched upon. The theory is applied to the proof of several elementary theorems concerning the semantics of the assignment conditional and iterative statements. An appendix is included which presents in detail the formal system governing webs and fen the abstractions used informally in the body of the paper. semantics formal systems lambda-calculus extensible languages data types modes axioms correctness formal language definition formal description data structures description languages models of computation
