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19
Axiomatic constructor classes in Isabelle/HOLCF
 In In Proc. 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs ’05), Volume 3603 of Lecture Notes in Computer Science
, 2005
"... Abstract. We have definitionally extended Isabelle/HOLCF to support axiomatic Haskellstyle constructor classes. We have subsequently defined the functor and monad classes, together with their laws, and implemented state and resumption monad transformers as generic constructor class instances. This ..."
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Abstract. We have definitionally extended Isabelle/HOLCF to support axiomatic Haskellstyle constructor classes. We have subsequently defined the functor and monad classes, together with their laws, and implemented state and resumption monad transformers as generic constructor class instances. This is a step towards our goal of giving modular denotational semantics for concurrent lazy functional programming languages, such as GHC Haskell. 1
Formal verification of monad transformers
 In ICFP’12
, 2012
"... We present techniques for reasoning about constructor classes that (like the monad class) fix polymorphic operations and assert polymorphic axioms. We do not require a logic with firstclass type constructors, firstclass polymorphism, or type quantification; instead, we rely on a domaintheoretic m ..."
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We present techniques for reasoning about constructor classes that (like the monad class) fix polymorphic operations and assert polymorphic axioms. We do not require a logic with firstclass type constructors, firstclass polymorphism, or type quantification; instead, we rely on a domaintheoretic model of the type system in a universal domain to provide these features. These ideas are implemented in the Tycon library for the Isabelle theorem prover, which builds on the HOLCF library of domain theory. The Tycon library provides various axiomatic type constructor classes, including functors and monads. It also provides automation for instantiating those classes, and for defining further subclasses. We use the Tycon library to formalize three Haskell monad transformers: the error transformer, the writer transformer, and the resumption transformer. The error and writer transformers do not universally preserve the monad laws; however, we establish datatype invariants for each, showing that they are valid monads when viewed as abstract datatypes.
Recursion on the partial continuous functionals
 Logic Colloquium ’05
, 2006
"... We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the wellknown abbreviation ..."
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We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the wellknown abbreviation
Two behavioural lambda models
 Types for Proofs and Programs
, 2003
"... Abstract. We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. This is proved by using the finitary logical description of the model obtained by defining a suitable intersection type assign ..."
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Abstract. We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. This is proved by using the finitary logical description of the model obtained by defining a suitable intersection type assignment system.
HOLCF ’11: A Definitional Domain Theory for Verifying Functional Programs
, 2012
"... HOLCF is an interactive theorem proving system that uses the mathematics of domain theory to reason about programs written in functional programming languages. This thesis introduces HOLCF ’11, a thoroughly revised and extended version of HOLCF that advances the state of the art in program verificat ..."
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HOLCF is an interactive theorem proving system that uses the mathematics of domain theory to reason about programs written in functional programming languages. This thesis introduces HOLCF ’11, a thoroughly revised and extended version of HOLCF that advances the state of the art in program verification: HOLCF ’11 can reason about many program definitions that are beyond the scope of other formal proof tools, while providing a high degree of proof automation. The soundness of the system is ensured by adhering to a definitional approach: New constants and types are defined in terms of previous concepts, without introducing new axioms. Major features of HOLCF ’11 include two highlevel definition packages: the Fixrec package for defining recursive functions, and the Domain package for defining recursive datatypes. Each of these uses the domaintheoretic concept of least fixed points to translate usersupplied recursive specifications into safe lowlevel definitions. Together, these tools make it easy for users to translate a wide variety of functional programs into the formalism of HOLCF. Theorems generated by the tools also make it easy for users to reason about their programs, with a very high level of confidence in the soundness of the results. As a case study, we present a fully mechanized verification of a model of concurrency based on powerdomains. The formalization depends on many features unique to HOLCF ’11, and is the first verification of such a model in a formal proof tool. ii ACKNOWLEDGMENTS I would like to thank my advisor, John Matthews, for having continued to devote so much time to working with me, even as a parttime professor; and for motivating me to keep studying domain theory (and enjoying it!) these past years. iii
A Lambda Model Characterizing Computational Behaviours of Terms
 PROCEEDINGS OF THE AND LIKAVEC INTERNATIONAL WORKSHOP REWRITING IN PROOF AND COMPUTATION
, 2001
"... We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. ..."
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We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms.
Probabilistic coherence spaces as a model of higherorder probabilistic computation
, 2011
"... ..."
Lambda and pi calculi, CAM and SECD machines
, 2001
"... We analyse machines that implement the callbyvalue reduction strategy of the λcalculus: two environment machines—CAM and SECD—and two encodings into the πcalculus—due to Milner and Vasconcelos. To establish the relation between the various machines, we setup a notion of reduction machine and two ..."
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We analyse machines that implement the callbyvalue reduction strategy of the λcalculus: two environment machines—CAM and SECD—and two encodings into the πcalculus—due to Milner and Vasconcelos. To establish the relation between the various machines, we setup a notion of reduction machine and two notions of correspondences: operational—in which a reduction step in the source machine is mimicked by a sequence of steps in the target machine—and convergent—where only reduction to normal form is simulated. We show that there are operational correspondences from the λcalculus into CAM, and from CAM and from SECD into the πcalculus. Plotkin completes the picture by showing that there is a convergent correspondence from the λcalculus into SECD. 1
Universality results for models in locally Boolean domains
 IN COMPUTER SCIENCE LOGIC
, 2006
"... In [6] J. Laird has shown that an infinitary sequential extension of PCF has a fully abstract model in his category of locally boolean domains (introduced in [8]). In this paper we introduce an extension SPCF ∞ of his language by recursive types and show that it is universal for its model in locall ..."
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In [6] J. Laird has shown that an infinitary sequential extension of PCF has a fully abstract model in his category of locally boolean domains (introduced in [8]). In this paper we introduce an extension SPCF ∞ of his language by recursive types and show that it is universal for its model in locally boolean domains. Finally we consider an infinitary target language CPS ∞ for (the) CPS translation (of [16]) and show that it is universal for a model in locally boolean domains which is constructed like Dana Scott’s D ∞ where D = 1
Exponentials with infinite multiplicities
"... Given a semiring with unit which satisfies some algebraic conditions, we de ne an exponential functor on the category of sets and relations which allows to define a denotational model of di erential linear logic and of the lambdacalculus with resources. We show that, when the semiring has an ele ..."
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Given a semiring with unit which satisfies some algebraic conditions, we de ne an exponential functor on the category of sets and relations which allows to define a denotational model of di erential linear logic and of the lambdacalculus with resources. We show that, when the semiring has an element which is in nite in the sense that it is equal to its successor, this model does not validate the Taylor formula and that it is possible to build, in the associated Kleisli cartesian closed category, a model of the pure lambdacalculus which is not sensible. This is a quantitative analogue of the standard graph model construction in the