Proof-Theoretic Methods for Analysis of Functional Programs
We investigate how, in a natural deduction setting, we can specify concisely a wide variety of tasks that manipulate programs as data objects. This study will provide us with a better understanding of various kinds of manipulations of programs and also an operational understanding of numerous features and properties of a rich functional programming language. We present a technique, inspired by structural operational semantics and natural semantics, for specifying properties of, or operations on, programs. Specifications of this sort are presented as sets of inference rules and are encoded as clauses in a higher-order, intuitionistic meta-logic. Program properties are then proved by constructing proofs in this meta-logic. We argue the following points regarding these specifications and their proofs: (i) the specifications are clear and concise and they provide intuitive descriptions of the properties being described; (ii) a wide variety of program analysis tools can be specified in a single unified framework, and thus we can investigate and understand the relationship between various tools; (iii) proof theory provides a well-established and formal setting in which to examine meta-theoretic properties of these specifications; and (iv) the meta-logic we use can be implemented naturally in an extended logic programming language and thus we can produce experimental implementations of the specifications. We expect that our efforts will provide new perspectives and insights for many program manipulation tasks.