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Some lambda calculus and type theory formalized
 Journal of Automated Reasoning
, 1999
"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."
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Cited by 52 (7 self)
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Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.
Toward Interactive Statistical Modeling
"... When solving machine learning problems, there is currently little automated support for easily experimenting with alternative statistical models or solution strategies. This is because this activity often requires expertise from several different fields (e.g., statistics, optimization, linear algebr ..."
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When solving machine learning problems, there is currently little automated support for easily experimenting with alternative statistical models or solution strategies. This is because this activity often requires expertise from several different fields (e.g., statistics, optimization, linear algebra), and the level of formalism required for automation is much higher than for a human solving problems on paper. We present a system toward addressing these issues, which we achieve by (1) formalizing a type theory for probability and optimization, and (2) providing an interactive rewrite system for applying problem reformulation theorems. Automating solution strategies this way enables not only manual experimentation but also higherlevel, automated activities, such as autotuning. Keywords: machine learning, algorithm derivation, interactive modeling, type theory
The Implementation of Lisex, a MLS Linux Prototype
"... In this article we describe the design and implementation of a Linux multilevel secure (MLS) file system containing access control lists (ACL). The resulting prototype is called Lisex. We implemented Lisex from model formally written and verified in Coq. We used abstract data types (ADT) to impleme ..."
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In this article we describe the design and implementation of a Linux multilevel secure (MLS) file system containing access control lists (ACL). The resulting prototype is called Lisex. We implemented Lisex from model formally written and verified in Coq. We used abstract data types (ADT) to implement some data structures. Hence, we show the methodology that we have applied to program from formal specifications using ADTs.