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These are the slides and the extended abstract from my MSFP 2008 talk. Apparently, I forgot to publish them online. There is a discussion on the Agda mailing list to which the talk is somewhat relevant, so I am publishing now. Abstract: Realizability is an interpretation of intuitionistic logic which subsumes the Curry-Howard interpretation of propositions as [...] With Iztok Kavkler. Abstract: We formulate a predicative, constructive theory of continuous domains whose realizability interpretation gives a practical implementation of continuous ω-chain complete posets and continuous maps between them. We apply the theory to implementation of the interval domain and exact real [...] With Iztok Kavkler. Abstract: The interval domain was proposed by Dana Scott as a domain-theoretic model for real numbers. It is a successful theoretical idea which also inspired a number of computational models for real numbers. However, current state-of-the-art implementations of real numbers, e.g., Mueller’s iRRAM and Lambov’s RealLib, do not seem to be based on the [...] With Iztok Kavkler. Abstract: RZ is a tool which translates axiomatizations of mathematical structures to program speciï¬cations using the realizability interpretation of logic. This helps programmers correctly implement data structures for computable mathematics. RZ does not prescribe a particular method of implementation, but allows programmers to write efficient code by hand, or to extract trusted code from [...] With Chris Stone. Abstract: How to build specifications for abstract data types using realizability [...] |
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