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23
Coinductive Axiomatization of Recursive Type Equality and Subtyping
, 1998
"... e present new sound and complete axiomatizations of type equality and subtype inequality for a firstorder type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The mai ..."
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Cited by 65 (2 self)
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e present new sound and complete axiomatizations of type equality and subtype inequality for a firstorder type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle), which has the form A; P ` P A ` P (Fix) where P is either a type equality = 0 or type containment 0 and the proof of the premise must be contractive in a formal sense. In particular, a proof of A; P ` P using the assumption axiom is not contractive. The fixpoint rule embodies a finitary coinduction principle and thus allows us to capture a coinductive relation in the fundamentally inductive framework of inference systems. The new axiomatizations are more concise than previous axiomatizations, particularly so for type containment since no separate axiomatization of type equality is required, as in A...
TypePreserving Compilation of Featherweight Java
, 2001
"... We present an efficient encoding of core Java constructs in a simple, implementable typed intermediate language. The encoding, after type erasure, has the same operational behavior as a standard implementation using vtables and selfapplication for method invocation. Classes inherit superclass metho ..."
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Cited by 34 (8 self)
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We present an efficient encoding of core Java constructs in a simple, implementable typed intermediate language. The encoding, after type erasure, has the same operational behavior as a standard implementation using vtables and selfapplication for method invocation. Classes inherit superclass methods with no overhead. We support mutually recursive classes while preserving separate compilation. Our strategy extends naturally to a significant subset of Java, including interfaces and privacy. The formal translation using Featherweight Java allows comprehensible typepreservation proofs and serves as a starting point for extending the translation to new features.
Logical StepIndexed Logical Relations
"... We show how to reason about “stepindexed ” logical relations in an abstract way, avoiding the tedious, errorprone, and proofobscuring stepindex arithmetic that seems superficially to be an essential element of the method. Specifically, we define a logic LSLR, which is inspired by Plotkin and Aba ..."
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Cited by 15 (6 self)
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We show how to reason about “stepindexed ” logical relations in an abstract way, avoiding the tedious, errorprone, and proofobscuring stepindex arithmetic that seems superficially to be an essential element of the method. Specifically, we define a logic LSLR, which is inspired by Plotkin and Abadi’s logic for parametricity, but also supports recursively defined relations by means of the modal “later ” operator from Appel et al.’s “very modal model” paper. We encode in LSLR a logical relation for reasoning (in)equationally about programs in callbyvalue System F extended with recursive types. Using this logical relation, we derive a useful set of rules with which we can prove contextual (in)equivalences without mentioning step indices. 1
A Relational Account of CallbyValue Sequentiality
 IN: PROC. 12TH SYMP. LOGIC IN COMPUTER SCIENCE
, 1999
"... We construct a model for FPC, a purely functional, sequential, callbyvalue language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract. ..."
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Cited by 13 (2 self)
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We construct a model for FPC, a purely functional, sequential, callbyvalue language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract.
Numbering matters: Firstorder canonical forms for secondorder recursive types
 In Proceedings of the 2004 ACM SIGPLAN International Conference on Functional Programming (ICFP’04
, 2004
"... We study a type system equipped with universal types and equirecursive types, which we refer to as Fµ. We show that type equality may be decided in time O(n log n), an improvement over the previous known bound of O(n 2). In fact, we show that two more general problems, namely entailment of type equa ..."
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Cited by 12 (1 self)
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We study a type system equipped with universal types and equirecursive types, which we refer to as Fµ. We show that type equality may be decided in time O(n log n), an improvement over the previous known bound of O(n 2). In fact, we show that two more general problems, namely entailment of type equations and type unification, may be decided in time O(n log n), a new result. To achieve this bound, we associate, with every Fµ type, a firstorder canonical form, which may be computed in time O(n log n). By exploiting this notion, we reduce all three problems to equality and unification of firstorder recursive terms, for which efficient algorithms are known. 1
Subtyping Recursive Types modulo Associative Commutative Products
 Seventh International Conference on Typed Lambda Calculi and Applications (TLCA ’05
, 2003
"... We study subtyping of recursive types in the presence of associative and commutative productsthat is, subtyping modulo a restricted form of type isomorphisms. We show that this relation, which we claim is useful in practice, is a composition of the usual subtyping relation with the recently propo ..."
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Cited by 8 (0 self)
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We study subtyping of recursive types in the presence of associative and commutative productsthat is, subtyping modulo a restricted form of type isomorphisms. We show that this relation, which we claim is useful in practice, is a composition of the usual subtyping relation with the recently proposed notion of equality up to associativity and commutativity of products, and we propose an efficient decision algorithm for it. We also provide an automatic way of constructing coercions between related types.
Subtyping Recursive Types in Kernel Fun
 In IEEE Symposium on Logic in Computer Science (LICS
, 1999
"... The problem of defining and checking a subtype relation between recursive types was studied in [3] for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known [17]. ..."
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Cited by 6 (1 self)
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The problem of defining and checking a subtype relation between recursive types was studied in [3] for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known [17].
A Game Semantics of Linearly Used Continuations
 FoSSaCs’03, LNCS 2620, 313–327
, 2002
"... We present an analysis of the \linearly used continuationpassing interpretation" of functional languages, based on game semantics. ..."
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Cited by 6 (0 self)
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We present an analysis of the \linearly used continuationpassing interpretation" of functional languages, based on game semantics.
Linear ContinuationPassing
 in the 2001 ACM SIGPLAN Workshop on Continuations (CW'01
, 2002
"... Continuations can be used to explain a wide variety of control behaviours, including calling/returning (procedures), raising/handling (exceptions), labelled jumping (goto statements), process switching (coroutines), and backtracking. However, continuations are often manipulated in a highly stylised ..."
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Cited by 3 (1 self)
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Continuations can be used to explain a wide variety of control behaviours, including calling/returning (procedures), raising/handling (exceptions), labelled jumping (goto statements), process switching (coroutines), and backtracking. However, continuations are often manipulated in a highly stylised way, and we show that all of these, bar backtracking, in fact use their continuations linearly ; this is formalised by taking a target language for cps transforms that has both intuitionistic and linear function types.
A Formal Semantics for Isorecursive and Equirecursive State Abstractions
"... Most methodologies for static program verification support recursivelydefined predicates in specifications, in order to reason about recursive data structures. Intuitively, a predicate instance represents the complete unrolling of its definition; this is the equirecursive interpretation. However, t ..."
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Cited by 3 (0 self)
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Most methodologies for static program verification support recursivelydefined predicates in specifications, in order to reason about recursive data structures. Intuitively, a predicate instance represents the complete unrolling of its definition; this is the equirecursive interpretation. However, this semantics is unsuitable for static verification, when the recursion becomes unbounded. For this reason, most static verifiers supporting recursive definitions employ explicit folding and unfolding of recursive definitions (specified using ghost commands, or inferred). Such a semantics differentiates between, e.g., a predicate instance and its corresponding body, while providing a facility to map between the two; this is the isorecursive semantics. While this latter interpretation is usually implemented in practice, only the equirecursive semantics is typically treated in theoretical work. In this paper we provide both an isorecursive and an equirecursive formal semantics for recursive definitions in the context of Chalice, a verification methodology based on implicit dynamic frames. We extend these assertion semantics to appropriate Hoare Logics, and prove the soundness of our definitions. The development of such formalisations requires addressing several subtle issues, regarding both the possibility of infinitelyrecursive definitions and the need for the isorecursive semantics to correctly reflect the restrictions that make it readily implementable. These questions are made more challenging still in the context of implicit dynamic frames, where the use of heapdependent expressions provides further pitfalls for a correct formal treatment.