A practical algorithm for exact array dependence analysis
Communications of the ACM
Interpretation of a Mizar-Like Logic in First-Order Logic
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
The Nuprl Open Logical Environment
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
JProver: Integrating Connection-Based Theorem Proving into Interactive Proof Assistants
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Automation for interactive proof: first prototype
Information and Computation - Special issue: Combining logical systems
The design and implementation of VAMPIRE
AI Communications - CASC
Using first-order theorem provers in the Jahob data structure verification system
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Lightweight integration of the Ergo theorem prover inside a proof assistant
Proceedings of the second workshop on Automated formal methods
Extending Sledgehammer with SMT solvers
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Expressing polymorphic types in a many-sorted language
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Hybrid contract checking via symbolic simplification
PEPM '12 Proceedings of the ACM SIGPLAN 2012 workshop on Partial evaluation and program manipulation
A polymorphic intermediate verification language: design and logical encoding
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
CADE'13 Proceedings of the 24th international conference on Automated Deduction
TFF1: the TPTP typed first-order form with rank-1 polymorphism
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Polymorphism has become a common way of designing short and reusable programs by abstracting generic definitions from type-specific ones. Such a convenience is valuable in logic as well, because it unburdens the specifier from writing redundant declarations of logical symbols. However, top shelf automated theorem provers such as Simplify, Yices or other SMT-LIB ones do not handle polymorphism. To this end, we present efficient reductions of polymorphism in both unsorted and many-sorted first order logics. For each encoding, we show that the formulas and their encoded counterparts are logically equivalent in the context of automated theorem proving. The efficiency keynote is to disturb the prover as little as possible, especially the internal decision procedures used for special sorts, e.g. integer linear arithmetic, to which we apply a special treatment. The corresponding implementations are presented in the framework of the Why/Caduceus toolkit.