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Programming Languages: Design, Analysis, and Semantics
, 2000
"... This thesis contains three parts. The first part presents contributions in the fields of domainspecific language design, runtime system design, and static program analysis, the second part presents contributions in the field of control synthesis, and finally the third part presents contributions in ..."
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This thesis contains three parts. The first part presents contributions in the fields of domainspecific language design, runtime system design, and static program analysis, the second part presents contributions in the field of control synthesis, and finally the third part presents contributions in the field of denotational semantics.
On sequential functionals of type 3
 Math. Structures Comput. Sci
, 2006
"... We show that the extensional ordering of the sequential functionals of pure type 3, e.g. as defined via game semantics [2, 4], is not cpoenriched. This shows that this model does not equal Milner’s [9] fully abstract model for P CF. 1 ..."
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We show that the extensional ordering of the sequential functionals of pure type 3, e.g. as defined via game semantics [2, 4], is not cpoenriched. This shows that this model does not equal Milner’s [9] fully abstract model for P CF. 1
Operational and Axiomatic Semantics of PCF
 In Proceedings of the LISP and Functional Programming Conference
, 1990
"... PCF, as considered in this paper, is a lazy typed lambda calculus with functions, pairing, fixedpoint operators and arbitrary algebraic data types. The natural equational axioms for PCF include jequivalence and the socalled "surjective pairing" axiom for pairs. However, the reduction system pcf j ..."
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PCF, as considered in this paper, is a lazy typed lambda calculus with functions, pairing, fixedpoint operators and arbitrary algebraic data types. The natural equational axioms for PCF include jequivalence and the socalled "surjective pairing" axiom for pairs. However, the reduction system pcf j;sp defined by directing each equational axiom is not confluent, for virtually any choice of algebraic data types. Moreover, neither jreduction nor surjective pairing seems to have a counterpart in ordinary execution. Therefore, we consider a smaller reduction system pcf without j reduction or surjective pairing. The system pcf is confluent when combined with any linear, confluent algebraic rewrite rules. The system is also computationally adequate, in the sense that whenever a closed term of "observable" type has a pcf j;sp normal form, this is also the unique pcf normal form. Moreover, the equational axioms for PCF, including (j) and surjective pairing, are sound for pcf observational e...
LCF Should Be Lifted
, 1988
"... : When observing termination of closed terms at all types in Plotkin's interpreter for PCF [11], the standard cpo model A V is not adequate. We define a new model, A Y , with lifted functional types and prove its adequacy for this notion of observation. We prove that with the addition of a parallel ..."
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: When observing termination of closed terms at all types in Plotkin's interpreter for PCF [11], the standard cpo model A V is not adequate. We define a new model, A Y , with lifted functional types and prove its adequacy for this notion of observation. We prove that with the addition of a parallel conditional and a convergence testing operator to the language, the model becomes fully abstract; with the addition of an existentiallike operator, the language becomes universal. Using the model as a guide, we develop a sound logic for the language. 1 Introduction The denotational semantics most appropriate for a programming language depends crucially upon the observations one makes about computations. In general, an observation is some important behavior of the interpreter [8]. For example, in the arithmetic, higherorder programming language PCF [11, 13], one usually chooses to observe the results of arithmetic expressionsthat a term of integer type reduces to a numeral. One may also...
Knowledge and Data Fusion in Probabilistic Networks
, 2003
"... Intelligent systems use internal representations to mediate the transformation from percepts to goaldirected actions. Intelligent learning agents use environmental feedback to modify their internal representations to improve performance over time and adapt to changing circumstances. All learning in ..."
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Intelligent systems use internal representations to mediate the transformation from percepts to goaldirected actions. Intelligent learning agents use environmental feedback to modify their internal representations to improve performance over time and adapt to changing circumstances. All learning involves knowledgedata fusion to some degree. Bayesian learning, the focus of this paper, is specifically designed to incorporate both expert knowledge and observations. We use the term "data" to refer both to collections of cases and to statements about the domain provided by experts and knowledge engineers and used to construct internal representations. The term "knowledge" refers to the internal representation itself, which we take to be a collection of Bayesian network fragments. We describe a prequential learning agent architecture for bounded rational action and learning under uncertainty. We describe recent extensions to Bayesian networks that provide sufficient representation power for expressing general prequential learning agent models. We describe tools and techniques to support a process in which models are constructed and refined using a combination of inputs from experts and environmental feedback. KEY WORDS: Bayesian Networks, Bayesian Learning, Graphical Probabilistic Models, Knowledge Elicitation, Object Oriented Bayesian Networks, Prequential Probability Machine Learning MCMC Issue 1 7/1/01 1.
Computing with functionals  computability theory or computer science
 Bulletin of Symbolic Logic
, 2006
"... We review some of the history of the computability theory of functionals of higher types, and we will demonstrate how contributions from logic and theoretical computer science have shaped this still active subject. ..."
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We review some of the history of the computability theory of functionals of higher types, and we will demonstrate how contributions from logic and theoretical computer science have shaped this still active subject.
Constraint Databases and Program Analysis using Abstract Interpretation
"... Interpretation David Toman Department of Computer Science, University of Toronto Toronto, Ontario, Canada M5S 1A4 david@cs.toronto.edu Abstract. In this paper we discuss a connection between two seemingly distant research areas in computer science: constraint databases and abstract interpretation. ..."
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Interpretation David Toman Department of Computer Science, University of Toronto Toronto, Ontario, Canada M5S 1A4 david@cs.toronto.edu Abstract. In this paper we discuss a connection between two seemingly distant research areas in computer science: constraint databases and abstract interpretation. We show that while the goals of research in the respective communities are different, the used techniques are often based on similar common foundations. We substantiate this claim by showing that abstract interpretation of a standard (Algollike) programming language with respect to its natural semantics can be equivalently thought of as querying a constraint deductive database. On the other hand the constraint database community can often benefit from the sophisticated techniques developed for computing abstract properties of programs, e.g., for query termination analysis or approximate query evaluation. 1 Introduction Abstract Interpretation provides a canonical approach to the analysis ...
Algebraic Reasoning and Completeness in Typed Languages
 In Proc. 20th ACM Symposium on Principles of Programming Languages
, 1992
"... : We consider the following problem in proving observational congruences in functional languages: given a callbyname language based on the simplytyped calculus with algebraic operations axiomatized by algebraic equations E, is the set of observational congruences between terms exactly those prov ..."
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: We consider the following problem in proving observational congruences in functional languages: given a callbyname language based on the simplytyped calculus with algebraic operations axiomatized by algebraic equations E, is the set of observational congruences between terms exactly those provable from (fi), (j), and E? We find conditions for determining whether fijEequational reasoning is complete for proving the observational congruences between such terms. We demonstrate the power and generality of the theorems by presenting a number of easy corollaries for particular algebras. 1 Introduction The (fi) and (j) axioms form the basis for proving equations in callbyname functional languages. In these languages, (fi) and (j) yield sound program optimizations. For example, consider a version of the callbyname language PCF [11, 15] which is described in Appendix A. Our version of PCF includes simplytyped calculus, numerals 0; 1; 2; : : :, successor and predecessor, addition, ...
Thirteen puzzles in programming logic
 Proceedings of the Workshop on Formal Software Development: Combining Specification Methods, Lecture
"... Very abstract concepts underlie the design of modern programming languages— higherorder functions, abstract data types, types as values, names of names. These concepts arise naturally in the course of program design; with an intuitive explanation, programmers generally understand and use them effec ..."
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Very abstract concepts underlie the design of modern programming languages— higherorder functions, abstract data types, types as values, names of names. These concepts arise naturally in the course of program design; with an intuitive explanation, programmers generally understand and use them effectively. Nevertheless, intuition has its limits. Situations arise repeatedly where firmer guidelines are needed to resolve confusions and inconsistency. This note illustrates some of the places where intuitive programming concepts are not adequate. Some specific puzzling cases are collected below which highlight areas where more guidance would be valuable. The statements of the puzzles are, I hope, almost all accessible to novice programmers, though they vary in difficulty as well as significance. My emphasis is on puzzles which come up in most programming languages, not on problems reflecting the idiosyncrasies of some particular language. “Solutions ” for the puzzles are supplied, but they are really brief hints about the current state of the theoretical answers. Simple as the puzzles appear, several of them currently lack satisfactory solutions. The puzzles are intended to make the point that reasoning about program behavior raises challenges with a significant mathematical component. One aim of programming concepts in programming. Software engineering, in common with other design disciplines, deals with the organization and management of large systems interacting with complex environments. At the same time it contrasts with other design disciplines: programs, like essays or