A cost-aware logical framework

We present calf , a c ost- ware l ogical f ramework for studying quantitative aspects of functional programs. Taking inspiration from recent work that reconstructs traditional programming languages in terms modal account phase distinctions we argue the cost structure programs motivates distinction between intension and extension . Armed with this technology, contribute synthetic as computational effect which cost-aware enjoy an internal noninterference property: input/output behavior cannot depend on cost. As full-spectrum dependent type theory, presents unified language specification both can be integrated smoothly existing mathematical libraries available theoretic proof assistants. evaluate general framework analysis by implementing two fundamental techniques algorithm analysis: method recurrence relations physicist’s amortized deploy these variety case studies: prove tight, closed bound Euclid’s algorithm, verify complexity batched queues, derive bounds sequential parallel merge sort, all fully mechanized Agda assistant. Lastly substantiate soundness reasoning means model construction.