Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-p...
ID-logic uses ideas from the field of logic programming to extend second order logic with non-monotone inductive defintions. In this work, we reformulate the semantics of this lo...
In 1973, Parikh proved a speed-up theorem conjectured by G¨odel 37 years before: there exist arithmetical formulæ that are provable in first order arithmetic, but whose shorter ...
Abstract. This paper reports on the Mizar formalization of the theory of continuous lattices as presented in A Compendium of Continuous Lattices, [25]. By the Mizar formalization w...
Abstract: Optimizations in compilers are the most error-prone phases in the compilation process. Since correct compilers are a vital precondition for software correctness, it is ne...