A dependently typed framework for static analysis of program execution costs

This paper considers the use of dependent types to capture information about dynamic resource usage in a static type system. Dependent types allow us to give (explicit) proofs of properties with a program; we present a dependently typed core language TT, and define a framework within this language for representing size metrics and their properties. We give several examples of size bounded programs within this framework and show that we can construct proofs of their size bounds within TT. We further show how the framework handles recursive higher order functions and sum types, and contrast our system with previous work based on sized types