Computer Theorem Proving and HoTT

Theorem-proving is a one-player game. The history of computer programs being the players goes back to 1956 and the ‘LT’ LOGIC THEORY MACHINE of Newell, Shaw and Simon. In game-playing terms, the ‘initial position’ is the core set of axioms chosen for the particular logic and the ‘moves’ are the rules of inference. Now, the Univalent Foundations Program at IAS Princeton and the resulting ‘HoTT’ book on Homotopy Type Theory have demonstrated the success of a new kind of experimental mathematics using computer theorem proving

Using term rewriting to solve Bit-vector arithmetic problems (Poster Presentation)

Among many theories supported by SMT solvers, the theory of finite-precision bit-vector arithmetic is one of the most useful, for both hardware and software systems verification. This theory is also particularly useful for some specific domains such as cryptography, in which algorithms are naturally expressed in terms of bit-vectors. Cryptol is an example of a domain-specific language (DSL) and toolset for cryptography developed by Galois, Inc.; providing an SMT backend that relies on bit-vector decision procedures to certify the correctness of cryptographic specifications [3]. Most of these decision procedures use bit-blasting to reduce a bit-vector problem into pure propositional SAT. Unfortunately bit-blasting does not scale very well, especially in the presence of operators like multiplication or division.(undefined

Reviews

The Collected Poems of C.S. Lewis: A Critical Edition. Edited by Don W. King. Reviewed by Joe R. Christopher. Tree of Salvation: Yggdrasil and the Cross in the North. G. Ronald Murphy. Reviewed by Jon Garrad. Anglo-Saxon Community in J.R.R. Tolkien\u27s The Lord of the Rings. Deborah A. Higgins. Reviewed by Yvette Kisor. Surprised by the Feminine: A Rereading of C.S. Lewis and Gender. Monika B. Hilder. Reviewed by Laura Lee Smith. Arda Inhabited: Environmental Relationships in The Lord of The Rings. Susan Jeffers. Reviewed by Jeremy Larson. Joy: Poet, Seeker, and the Woman Who Captivated C.S. Lewis. Abigail Santamaria. Reviewed by Crystal Hurd. A Naked Tree: Love Sonnets to C.S. Lewis and Other Poems. Joy Davidman. Ed. Don W. King. Reviewed by Joe R. Christopher. The Hero Enkidu. Lewis Turco. Reviewed by Nicholas Birns. Encyclopedia of Goddesses & Heroines. Patricia Monaghan. Reviewed by Cait Coker. The Oxford Inklings. Colin Duriez. Reviewed by Crystal Hurd. The Fellowship: The Literary Lives of the Inklings. Philip Zaleski and Carol Zaleski. Reviewed by Crystal Hurd. The Pilgrim\u27s Regress: Wade Annotated Edition. C.S. Lewis. Edited and introduced by David C. Downing. Reviewed by Mike Foster. North Wind: A Journal of George MacDonald Studies. Editors John Pennington and Fernando Soto. Reviewed by Janet Brennan Croft. Supernatural Studies. Special Issue: Television and the Supernatural. Editor Leah Richards; Guest editor Marisa C. Hayes. Reviewed by Janet Brennan Croft. Journal of Inklings Studies: Theology, Philosophy, Literature. Special Issue: Inklings and the Bible. Executive editor Judith Wolfe. Reviewed by Janet Brennan Croft

Superposition as a logical glue

The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical discipline. A large part of this background knowledge is expressed in form of equalities and isomorphisms, allowing mathematicians to freely move between different incarnations of the same entity without even mentioning the transformation. Providing ITP-systems with similar capabilities seems to be a major way to improve their intelligence, and to ease the communication between the user and the machine. The present paper discusses our experience of integration of a superposition calculus within the Matita interactive prover, providing in particular a very flexible, "smart" application tactic, and a simple, innovative approach to automation.Comment: In Proceedings TYPES 2009, arXiv:1103.311

A formal approach to probabilistic termination

Abstract. We present a probabilistic version of the while loop, in the context of our mechanized framework for verifying probabilistic programs. The while loop preserves useful program properties of measurability and independence, provided a certain condition is met. This condition is naturally interpreted as “from every starting state, the while loop will terminate with probability 1”, and we compare it to other probabilistic termination conditions in the literature. For illustration, we verify in HOL two example probabilistic algorithms that necessarily rely on probabilistic termination: an algorithm to sample the Bernoulli(p) distribution using coin-flips; and the symmetric simple random walk.