Set theory for verification. I: from foundations to functions
Journal of Automated Reasoning
Handbook of logic in artificial intelligence and logic programming
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
A &kgr;-denotational semantics for map theory in ZFC + SI
Theoretical Computer Science
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Certified Exact Transcendental Real Number Computation in Coq
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
From Bayesian notation to pure racket via discrete measure-theoretic probability in λZFC
IFL'10 Proceedings of the 22nd international conference on Implementation and application of functional languages
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Applied mathematicians increasingly use computers to answer mathematical questions. We want to provide them domain-specific languages. The languages should have exact meanings and computational meanings. Some proof assistants can encode exact mathematics and extract programs, but formalizing the required theorems can take years. As an alternative, we develop λ ZFC , a lambda calculus that contains infinite sets as values, in which to express exact mathematics and gradually change infinite calculations to computable ones. We define it as a conservative extension of set theory, and prove that most contemporary theorems apply directly to λ ZFC terms. We demonstrate λ ZFC 's expressiveness by coding up the real numbers, arithmetic and limits. We demonstrate that it makes deriving computational meaning easier by defining a monad in it for expressing limits, and using standard topological theorems to derive a computable replacement.