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34
Once Upon a Polymorphic Type
, 1998
"... We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approxim ..."
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Cited by 38 (5 self)
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We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approximate, or defined over restricted languages. Our work extends the Once Upon A Type system of Turner, Mossin, and Wadler (FPCA'95). Firstly, we add type polymorphism, an essential feature of typed functional programming languages. Secondly, we include general Haskellstyle userdefined algebraic data types. Thirdly, we explain and solve the `poisoning problem', which causes the earlier analysis to yield poor results. Interesting design choices turn up in each of these areas. Our analysis is sound with respect to a Launchburystyle operational semantics, and it is straightforward to implement. Good results have been obtained from a prototype implementation, and we are currently integrating the system into the Glasgow Haskell Compiler.
CallbyName, CallbyValue, CallbyNeed, and the Linear Lambda Calculus
, 1994
"... Girard described two translations of intuitionistic logic into linear logic, one where A > B maps to (!A) o B, and another where it maps to !(A o B). We detail the action of these translations on terms, and show that the first corresponds to a callbyname calculus, while the second corresponds t ..."
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Cited by 28 (5 self)
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Girard described two translations of intuitionistic logic into linear logic, one where A > B maps to (!A) o B, and another where it maps to !(A o B). We detail the action of these translations on terms, and show that the first corresponds to a callbyname calculus, while the second corresponds to callbyvalue. We further show that if the target of the translation is taken to be an affine calculus, where ! controls contraction but weakening is allowed everywhere, then the second translation corresponds to a callbyneed calculus, as recently defined by Ariola, Felleisen, Maraist, Odersky, and Wadler. Thus the different calling mechanisms can be explained in terms of logical translations, bringing them into the scope of the CurryHoward isomorphism.
A Concurrent Lambda Calculus with Futures
 THEORETICAL COMPUTER SCIENCE
, 2006
"... We introduce a new lambda calculus with futures, λ(fut), to model the operational semantics of concurrent extensions of ML. λ(fut) can safely express a variety of highlevel concurrency constructs, including channels, semaphores, or ports. Safe implementations of these constructs in (fut) cannot be ..."
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Cited by 22 (4 self)
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We introduce a new lambda calculus with futures, λ(fut), to model the operational semantics of concurrent extensions of ML. λ(fut) can safely express a variety of highlevel concurrency constructs, including channels, semaphores, or ports. Safe implementations of these constructs in (fut) cannot be corrupted in any welltyped context. We prove safety on basis of a linear type system.
Functional BackEnds within the LambdaSigma Calculus
, 1996
"... We define a weak calculus, oe w , as a subsystem of the full calculus with explicit substitutions oe * . We claim that oe w could be the archetypal output language of functional compilers, just as the calculus is their universal input language. Furthermore, oe * could be the adequate theory to e ..."
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Cited by 20 (0 self)
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We define a weak calculus, oe w , as a subsystem of the full calculus with explicit substitutions oe * . We claim that oe w could be the archetypal output language of functional compilers, just as the calculus is their universal input language. Furthermore, oe * could be the adequate theory to establish the correctness of simplified functional compilers. Here, we illustrate these claims by proving the correctness of four simplified compilers and runtime systems modeled as abstract machines. The four machines we prove are the Krivine machine, the SECD, the FAM and the CAM. Thereby, we give the first formal proofs of Cardelli's FAM and of its compiler.
An abstract monadic semantics for value recursion
 In Proceeding of the 2003 Workshop on Fixed Points in Computer Science (FICS
, 2003
"... This paper proposes an operational semantics for value recursion in the context of monadic metalanguages. Our technique for combining value recursion with computational effects works uniformly for all monads. The operational nature of our approach is related to the implementation of recursion in Sch ..."
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Cited by 18 (7 self)
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This paper proposes an operational semantics for value recursion in the context of monadic metalanguages. Our technique for combining value recursion with computational effects works uniformly for all monads. The operational nature of our approach is related to the implementation of recursion in Scheme and its monadic version proposed by Friedman and Sabry, but it defines a different semantics and does not rely on assignments. When contrasted to the axiomatic approach proposed by Erkök and Launchbury, our semantics for the continuation monad invalidates one of the axioms, adding to the evidence that this axiom is problematic in the presence of continuations. 1
A simple rewrite notion for calltime choice semantics
 In Proc. Principles and Practice of Declarative Programming, ACM Press
, 2007
"... Nonconfluent and nonterminating rewrite systems are interesting from the point of view of programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly nonstrict nondeterministic functions. The semantics adopted for nondeterminism is callti ..."
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Cited by 15 (4 self)
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Nonconfluent and nonterminating rewrite systems are interesting from the point of view of programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly nonstrict nondeterministic functions. The semantics adopted for nondeterminism is calltime choice, whose combination with nonstrictness is not a trivial issue that has been addressed from a semantic point of view in the Constructorbased Rewriting Logic (CRWL) framework. We investigate here how to express calltime choice and nonstrict semantics from a point of view closer to classical rewriting. The proposed notion of rewriting uses an explicit representation for sharing with letconstructions and is proved to be equivalent to the CRWL approach. Moreover, we relate this letrewriting relation (and hence CRWL) with ordinary rewriting, providing in particular soundness and completeness of letrewriting with respect to rewriting for a class of programs which are confluent in a certain semantic sense.
Infinite sets that admit fast exhaustive search
 In Proceedings of the 22nd Annual IEEE Symposium on Logic In Computer Science
, 2007
"... Abstract. Perhaps surprisingly, there are infinite sets that admit mechanical exhaustive search in finite time. We investigate three related questions: What kinds of infinite sets admit mechanical exhaustive search in finite time? How do we systematically build such sets? How fast can exhaustive sea ..."
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Cited by 14 (8 self)
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Abstract. Perhaps surprisingly, there are infinite sets that admit mechanical exhaustive search in finite time. We investigate three related questions: What kinds of infinite sets admit mechanical exhaustive search in finite time? How do we systematically build such sets? How fast can exhaustive search over infinite sets be performed? Keywords. Highertype computability and complexity, Kleene–Kreisel functionals, PCF, Haskell, topology. 1.
A nondeterministic callbyneed lambda calculus
 INTERNATIONAL CONFERENCE ON FUNCTIONAL PROGRAMMING
, 1998
"... In this paper we present a nondeterministic callbyneed (untyped) lambda calculus nd with a constant choice and a letsyntax that models sharing. Our main result is that nd has the nice operational properties of the standard lambda calculus: confluence on sets of expressions, and normal order redu ..."
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Cited by 14 (7 self)
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In this paper we present a nondeterministic callbyneed (untyped) lambda calculus nd with a constant choice and a letsyntax that models sharing. Our main result is that nd has the nice operational properties of the standard lambda calculus: confluence on sets of expressions, and normal order reduction is sufficient to reach head normal form. Using a strong contextual equivalence we show correctness of several program transformations. In particular of lambdalifting using deterministic maximal free expressions. These results show that nd is a new and also natural combination of nondeterminism and lambdacalculus, which has a lot of opportunities for parallel evaluation. An intended application of nd is as a foundation for compiling lazy functional programming languages with I/O based on direct calls. The set of correct program transformations can be rigorously distinguished from noncorrect ones. All program transformations are permitted with the slight exception that for transformations like common subexpression elimination and lambdalifting with maximal free expressions the involved subexpressions have to be deterministic ones.
Substructural Operational Semantics as Ordered Logic Programming
"... We describe a substructural logic with ordered, linear, and persistent propositions and then endow a fragment with a committed choice forwardchaining operational interpretation. Exploiting higherorder terms in this metalanguage, we specify the operational semantics of a number of object language f ..."
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Cited by 12 (9 self)
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We describe a substructural logic with ordered, linear, and persistent propositions and then endow a fragment with a committed choice forwardchaining operational interpretation. Exploiting higherorder terms in this metalanguage, we specify the operational semantics of a number of object language features, such as callbyvalue, callbyname, callbyneed, mutable store, parallelism, communication, exceptions and continuations. The specifications exhibit a high degree of uniformity and modularity that allows us to analyze the structural properties required for each feature in isolation. Our substructural framework thereby provides a new methodology for language specification that synthesizes structural operational semantics, abstract machines, and logical approaches. 1
Purely Functional Lazy Nondeterministic Programming
"... Functional logic programming and probabilistic programming have demonstrated the broad benefits of combining laziness (nonstrict evaluation with sharing of the results) with nondeterminism. Yet these benefits are seldom enjoyed in functional programming, because the existing features for nonstric ..."
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Cited by 12 (3 self)
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Functional logic programming and probabilistic programming have demonstrated the broad benefits of combining laziness (nonstrict evaluation with sharing of the results) with nondeterminism. Yet these benefits are seldom enjoyed in functional programming, because the existing features for nonstrictness, sharing, and nondeterminism in functional languages are tricky to combine. We present a practical way to write purely functional lazy nondeterministic programs that are efficient and perspicuous. We achieve this goal by embedding the programs into existing languages (such as Haskell, SML, and OCaml) with highquality implementations, by making choices lazily and representing data with nondeterministic components, by working with custom monadic data types and search strategies, and by providing equational laws for the programmer to reason about their code.