26 research outputs found
ProofPeer - A Cloud-based Interactive Theorem Proving System
ProofPeer strives to be a system for cloud-based interactive theorem proving.
After illustrating why such a system is needed, the paper presents some of the
design challenges that ProofPeer needs to meet to succeed. Contexts are
presented as a solution to the problem of sharing proof state among the users
of ProofPeer. Chronicles are introduced as a way to organize and version
contexts
Proving Bounds for Real Linear Programs in Isabelle/HOL
Linear programming is a basic mathematical technique for optimizing a
linear function on a domain that is constrained by linear inequalities.
We restrict ourselves to linear programs on bounded domains that involve only
real variables. In the context of theorem proving, this restriction makes it
possible for any given linear program to obtain certificates from external
linear programming tools that help to prove arbitrarily precise bounds for the
given linear program. To this end, an explicit formalization of matrices
in Isabelle/HOL is presented, and how the concept of lattice-ordered rings
allows for a smooth integration of matrices with the axiomatic type classes of
Isabelle.
As our work is a contribution to the Flyspeck project, we demonstrate that via
reflection and with the above techniques it is now possible to prove bounds
for the linear programs arising in the proof of the Kepler conjecture
sufficiently fast
Abstraction Logic: A New Foundation for (Computer) Mathematics
Abstraction logic is a new logic, serving as a foundation of mathematics. It
combines features of both predicate logic and higher-order logic: abstraction
logic can be viewed both as higher-order logic minus static types as well as
predicate logic plus operators and variable binding. We argue that abstraction
logic is the best foundational logic possible because it maximises both
simplicity and practical expressivity. This argument is supported by the
observation that abstraction logic has simpler terms and a simpler notion of
proof than all other general logics. At the same time, abstraction logic can
formalise both intuitionistic and classical abstraction logic, and is sound and
complete for these logics and all other logics extending deduction logic with
equality
Syntax and Semantics of Babel-17
We present Babel-17, the first programming language for purely functional
structured programming (PFSP). Earlier work illustrated PFSP in the framework
of a toy research language. Babel-17 takes this earlier work to a new level by
showing how PFSP can be combined with pattern matching, object oriented
programming, and features like concurrency, lazy evaluation, memoization and
support for lenses