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By Le Bellac M.

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Elsevier Science Publishers (1983) 513–523 18. : Theorems for free! In: 4’th Symposium on Functional Programming Languages and Computer Architecture, ACM, London. (1989) 19. : A Generic Theory of Datatypes. PhD thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology (1997) 20. : Functional programming with bananas, lenses, envelopes and barbed wire. In: FPCA ’91: Functional Programming Languages and Computer Architecture. Number 523 in LNCS, Springer-Verlag (1991) 124–144 21.

The effectiveness of the methodology is demonstrated by an extraordinarily concise proof of the well-foundedness of a datatype-generic occurs-in relation. Keywords: Datatype, generic programming, relation algebra, allegory, programming methodology. 1 Introduction The central issue of computing science is the development of practical programming methodologies. Characteristic of a programming methodology is that it involves a discipline designed to maximise confidence in the reliability of the end product.

With respect to x). It follows that all the operations used by G¨ odel are indeed predicatively acceptable, and even capture what is intuitively predicatively acceptable in the language of RST . However, we believe that one should go beyond firstorder languages in order to capture all the predicatively acceptable means of set construction. In [3] we suggest that an adequate language for this is obtained by adding to the the language of RST an operation T C for transitive closure of binary relations, and then replacing RST by the relation P ZF , which is defined like RST , but with the following extra clause: (T Cx,y ϕ)(x, y) P ZF X if ϕ P ZF X, and {x, y} ∩ X = ∅.

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A short introduction to quantum information and quantum computation: solutions of exercises by Le Bellac M.

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