A unifying type-theory for higher-order (amortized) cost analysis

This paper presents λ-amor, a new type-theoretic framework for amortized cost analysis of higher-order functional programs and shows that existing type systems can be embedded in it. λ-amor introduces modal representing potentials – costs have been accounted for, but not yet incurred, which are central to analysis. Additionally, relies on standard concepts like affineness, refinement types an indexed monad. is proved sound using rather simple logical relation. We embed two showing that, despite its simplicity, simulate different evaluation strategies (call-by-name call-by-value), styles (effect-based coeffect-based), with or without amortization. One the embeddings also implies relatively complete all terminating PCF programs.