Abstract

not be interpreted as representing the o cial policies, either expressed or implied, of NSF or the U.S. Government. This thesis describes the design of a meta-logical framework that supports the representation and veri cation of deductive systems, its implementation as an automated theorem prover, and experimental results related to the areas of programming languages, type theory, and logics. Design: The meta-logical framework extends the logical framework LF [HHP93] by a meta-logic M + 2. This design is novel and unique since it allows higher-order encodings of deductive systems and induction principles to coexist. On the one hand, higher-order representation techniques lead to concise and direct encodings of programming languages and logic calculi. Inductive de nitions on the other hand allow the formalization of properties about deductive systems, such as the proof that an operational semantics preserves types or the proof that a logic is is a proof calculus whose proof terms are recursive functions that may be consistent.M +

Citations