Set Theory for Verification: I. From Foundations to Functions

Details Set Theory for Verification: I. From Foundations to Functions Set Theory for Verification: I. From Foundations to Functions

2000-10-31

arxiv.org/abs/cs/9311103v1

published in Journal of Journal of Automated Reasoning 11 (1993), 353-389

Computer Science

Logic in Computer Science

Scientific paper

A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higher-order syntax supports the definition of new binding operators. Unknowns in subgoals can be instantiated incrementally. The paper describes the derivation of rules for descriptions, relations and functions, and discusses interactive proofs of Cantor's Theorem, the Composition of Homomorphisms challenge [9], and Ramsey's Theorem [5]. A generic proof assistant can stand up against provers dedicated to particular logics.

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