Inductive Definition and Domain Theoretic Properties of Fully Abstract

A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF + "parallel conditional function"), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is new, in that it is given level-by-level in the finite type hierarchy. To prove full abstraction and non-dcpo domain theoretic properties of these models, a theory of computational strategies is developed. This is also an alternative and, in a sense, an analogue to the later game strategy semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong; and Nickau. In both cases of PCF and PCF^+ there are definable universal (surjective) functionals from numerical functions to any given type, respectively, which also makes each of these models unique up to isomorphism. Although such models are non-omega-complete and therefore not continuous in the traditional terminology, they are also proved to be sequentially complete (a weakened form of omega-completeness), "naturally" continuous (with respect to existing directed "pointwise", or "natural" lubs) and also "naturally" omega-algebraic and "naturally" bounded complete -- appropriate generalisation of the ordinary notions of domain theory to the case of non-dcpos.Comment: 50 page

A 2007 Model Curriculum for a Liberal Arts Degree in Computer Science

In 1986, guidelines for a computer science major degree program offered in the context of the liberal arts were developed by the Liberal Arts Computer Science Consortium (LACS) [4]. In 1996 the same group offered a revised curriculum reflecting advances in the discipline, the accompanying technology, and teaching pedagogy [6]. In each case, the LACS models represented, at least in part, a response to the recommendations of the ACM/IEEE-CS [1][2]. Continuing change in the discipline, technology, and pedagogy coupled with the appearance of Computing Curriculum 2001 [3] have led to the 2007 Model Curriculum described here. This report begins by considering just what computer science is and what goals are appropriate for the study of computer science in the landscape of the liberal arts. A curricular model for this setting follows, updating the 1996 revision. As in previous LACS curricula, [4] and [6], the model is practical; that is, students can schedule it, it can be taught with a relatively small size faculty, and it contributes to the foundation of an excellent liberal arts education. Finally, this 2007 Model Curriculum is compared with the recommendations of CC2001 [3]

On the Semantics of Intensionality and Intensional Recursion

Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality. This is a familiar setting for computer scientists, who often study different programs or processes that are interchangeable, i.e. extensionally equal, even though they are not implemented in the same way, so intensionally distinct. Concomitant with intensionality is the phenomenon of intensional recursion, which refers to the ability of a program to have access to its own code. In computability theory, intensional recursion is enabled by Kleene's Second Recursion Theorem. This thesis is concerned with the crafting of a logical toolkit through which these phenomena can be studied. Our main contribution is a framework in which mathematical and computational constructions can be considered either extensionally, i.e. as abstract values, or intensionally, i.e. as fine-grained descriptions of their construction. Once this is achieved, it may be used to analyse intensional recursion.Comment: DPhil thesis, Department of Computer Science & St John's College, University of Oxfor

Classical, quantum and biological randomness as relative unpredictability

International audienceWe propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness — its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity. Abstract We propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness—its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity