Kamal Aboul-Hosn

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The relationship between theorems and lemmas in mathematical reasoning is often vague. No system exists that formalizes the structure of theorems in a mathematical library. Nevertheless, the decisions we make in creating lemmas provide an inherent hierarchical structure to the statements we prove. In this paper, we develop a formal system that organizes(More)
Tactics and tacticals, programs that represent and execute several steps of deduction, are fundamental to theorem provers providing automated tools for creating proofs quickly and easily. The language used for tactics is usually a full-scale programming language, separate from the language used to represent proofs. Consequently, there is also a separation(More)
The formal analysis of programs with arrays is a notoriously difficult problem due largely to aliasing considerations. In this paper we augment the rules of Kleene algebra with tests (KAT) with rules for the equational manipulation of arrays in the style of schematic KAT. These rules capture and make explicit the essence of subscript aliasing, where two(More)
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