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Establishing quantitative bounds on the execution cost of programs is essential in many areas of computer science such as complexity analysis, compiler optimizations, security and privacy. Techniques based on program analysis, type systems and abstract interpretation are well-studied, but methods for analyzing how the execution costs of two programs compare to each other have not received attention. Naively combining the worst and best case execution costs of the two programs does not work well in many cases because such analysis forgets the similarities between the programs or the inputs.

In this work, we propose a relational cost analysis technique that is capable of establishing precise bounds on the difference in the execution cost of two programs by making use of relational properties of programs and inputs. We develop , a refinement type and effect system for a higher-order functional language with …