Type inference with constrained types
Theory and Practice of Object Systems - Special issue on foundations of object-oriented languages
Journal of the ACM (JACM)
Combining programming with theorem proving
Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
A faster PSPACE algorithm for deciding the existential theory of the reals
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Privacy integrated queries: an extensible platform for privacy-preserving data analysis
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
Continuity analysis of programs
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Differential privacy: a survey of results
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Type inference in intuitionistic linear logic
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Airavat: security and privacy for MapReduce
NSDI'10 Proceedings of the 7th USENIX conference on Networked systems design and implementation
Distance makes the types grow stronger: a calculus for differential privacy
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Robust computations with dynamical systems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Proceedings of the 19th ACM SIGSOFT symposium and the 13th European conference on Foundations of software engineering
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Probabilistic relational reasoning for differential privacy
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Semantic subtyping with an smt solver
Journal of Functional Programming
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Linear dependent types for differential privacy
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Function sensitivity --- how much the result of a function can change with respect to linear changes in the input --- is a key concept in many research areas. For instance, in differential privacy, one of the most common mechanisms for turning a (possibly privacy-leaking) query into a differentially private one involves establishing a boundon its sensitivity. One approach to sensitivity analysis is to use a type-based approach, extending the Hindley-Milner type system with functional types capturing statically the sensitivity of a functional expression. This approach --- based on affine logic --- has been used in Fuzz, a language for differentially private queries. We describe an automatic typed-based analysis that infers and checks the sensitivity annotations for simple functional programs. We have implemented a prototype in Fuzz's compiler. The first component of the analysis extends the typechecker to generate nonlinear constraints over the positive real numbers extended with infinity, which are then checked by the Z3 SMT solver; a solution for them will provide an upper bound on the sensitivity annotations and ensure the correctness of the annotations. We also present a simple sensitivity minimization procedure and demonstrate the effectiveness of the approach by analyzing several examples.