Sidi Ould Biha

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In this paper, we present an approach to describe uniformly iterated “big” operations, like Pn i=0 f(i) or maxi∈I f(i) and to provide lemmas that encapsulate all the commonly used reasoning steps on these constructs. We show that these iterated operations can be handled generically using the syntactic notation and canonical structure facilities provided by(More)
This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a(More)
Programmable logic Controllers (PLC) are embedded systems that are widely used in industry. We propose a formal semantics of the Instruction List (IL) language, one of the five programing languages defined in the IEC 61131-3 standard for PLC programing. This semantics support a significant subset of the IL language that includes on-delay timers. We(More)
Representation theory is a branch of algebra that allows the study of groups through linear applications, i.e. matrices. Thus problems in abstract groups can be reduced to problems on matrices. Representation theory is the basis of character theory. In this paper we present a formalization of finite groups representation theory in the Coq system that(More)
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