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Some domain theory and denotational semantics in Coq
, 2009
"... Abstract. We present a Coq formalization of constructive ωcpos (extending earlier work by PaulinMohring) up to and including the inverselimit construction of solutions to mixedvariance recursive domain equations, and the existence of invariant relations on those solutions. We then define operatio ..."
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Abstract. We present a Coq formalization of constructive ωcpos (extending earlier work by PaulinMohring) up to and including the inverselimit construction of solutions to mixedvariance recursive domain equations, and the existence of invariant relations on those solutions. We then define operational and denotational semantics for both a simplytyped CBV language with recursion and an untyped CBV language, and establish soundness and adequacy results in each case. 1
Operational semantics using the partiality monad
 In: International Conference on Functional Programming 2012, ACM Press
, 2012
"... The operational semantics of a partial, functional language is often given as a relation rather than as a function. The latter approach is arguably more natural: if the language is functional, why not take advantage of this when defining the semantics? One can immediately see that a functional seman ..."
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Cited by 6 (0 self)
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The operational semantics of a partial, functional language is often given as a relation rather than as a function. The latter approach is arguably more natural: if the language is functional, why not take advantage of this when defining the semantics? One can immediately see that a functional semantics is deterministic and, in a constructive setting, computable. This paper shows how one can use the coinductive partiality monad to define bigstep or smallstep operational semantics for lambdacalculi and virtual machines as total, computable functions (total definitional interpreters). To demonstrate that the resulting semantics are useful type soundness and compiler correctness results are also proved. The results have been implemented and checked using Agda, a dependently typed programming language and proof assistant.
Formalizing Domains, Ultrametric Spaces and Semantics of Programming Languages
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... We describe a Coq formalization of constructive ωcpos, ultrametric spaces and ultrametricenriched categories, up to and including the inverselimit construction of solutions to mixedvariance recursive equations in both categories enriched over ωcppos and categories enriched over ultrametric spac ..."
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Cited by 3 (1 self)
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We describe a Coq formalization of constructive ωcpos, ultrametric spaces and ultrametricenriched categories, up to and including the inverselimit construction of solutions to mixedvariance recursive equations in both categories enriched over ωcppos and categories enriched over ultrametric spaces. We show how these mathematical structures may be used in formalizing semantics for three representative programming languages. Specifically, we give operational and denotational semantics for both a simplytyped CBV language with recursion and an untyped CBV language, establishing soundness and adequacy results in each case, and then use a Kripke logical relation over a recursivelydefined metric space of worlds to give an interpretation of types over a stepcounting operational semantics for a language with recursive types and general references.
ProjectTeam Proval Proof of programs
"... c t i v it y e p o r t 2009 Table of contents ..."
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