Simple Parsimonious Types and Logarithmic Space

We present a functional characterization of deterministic logspace-computable predicates based on a variant (although not a subsystem) of propositional linear logic, which we call parsimonious logic. The resulting calculus is simply-typed and contains no primitive besides those provided by the underlying logical system, which makes it one of the simplest higher-order languages capturing logspace currently known. Completeness of the calculus uses the descriptive complexity characterization of logspace (we encode first-order logic with deterministic closure), whereas soundness is established by executing terms on a token machine (using the geometry of interaction). 1998 ACM Subject Classification F.4.1 Mathematical Logic, F.1.3 Complexity Measures and Classes