This collection of papers constitutes the refereed proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics, TPHOLs '99, held in Nice, France, in September 1999. The 20 revised full papers presented together with three invited contributions were reviewed and selected from 35 papers submitted. Various aspects of higher order theorem proving, formal verification, and specification are discussed. Among the theorem provers evaluated are COQ, HOL, Isabelle, Isabelle/ZF, and OpenMath.

We've known about algorithms for millennia, but we've only been writing c- puter programs for a few decades. A big di?erence between the Euclidean or Eratosthenes age and ours is that since the middle of the twentieth century, we express the algorithms we conceive using formal languages: programming languages. Computer scientists are not the only ones who use formal languages. - tometrists, for example, prescribe eyeglasses using very technical expressions, ? ? such as "OD: -1.25 (-0.50) 180 OS: -1.00 (-0.25) 180," in which the parent- ses are essential. Many such formal languages have been...