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22
An algorithm for optimal lambda calculus reduction
, 1990
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Cited by 127 (0 self)
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all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.
Inheritance As Implicit Coercion
 Information and Computation
, 1991
"... . We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. ..."
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Cited by 124 (3 self)
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. We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. Our goal is to interpret inheritances in Fun via coercion functions which are definable in the target of the translation. Existing techniques in the theory of semantic domains can be then used to interpret the extended polymorphic lambda calculus, thus providing many models for the original language. This technique makes it possible to model a rich type discipline which includes parametric polymorphism and recursive types as well as inheritance. A central difficulty in providing interpretations for explicit type disciplines featuring inheritance in the sense discussed in this paper arises from the fact that programs can typecheck in more than one way. Since interpretations follow the type...
A Linear Spine Calculus
 Journal of Logic and Computation
, 2003
"... We present the spine calculus S ##&# as an efficient representation for the linear #calculus # ##&# which includes unrestricted functions (#), linear functions (#), additive pairing (&), and additive unit (#). S ##&# enhances the representation of Church's simply typed # ..."
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Cited by 34 (7 self)
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We present the spine calculus S ##&# as an efficient representation for the linear #calculus # ##&# which includes unrestricted functions (#), linear functions (#), additive pairing (&), and additive unit (#). S ##&# enhances the representation of Church's simply typed #calculus by enforcing extensionality and by incorporating linear constructs. This approach permits procedures such as unification to retain the efficient head access that characterizes firstorder term languages without the overhead of performing #conversions at run time. Applications lie in proof search, logic programming, and logical frameworks based on linear type theories. It is also related to foundational work on term assignment calculi for presentations of the sequent calculus. We define the spine calculus, give translations of # ##&# into S ##&# and viceversa, prove their soundness and completeness with respect to typing and reductions, and show that the typable fragment of the spine calculus is strongly normalizing and admits unique canonical, i.e. ##normal, forms.
Maximal causality analysis
 in: Conference on Application of Concurrency to System Design (ACSD
, 2005
"... Perfectly synchronous systems immediately react to the inputs of their environment, which may lead to socalled causality cycles between actions and their trigger conditions. Algorithms to analyze the consistency of such cycles usually extend data types by an additional value to explicitly indicate ..."
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Cited by 17 (17 self)
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Perfectly synchronous systems immediately react to the inputs of their environment, which may lead to socalled causality cycles between actions and their trigger conditions. Algorithms to analyze the consistency of such cycles usually extend data types by an additional value to explicitly indicate unknown values. In particular, Boolean functions are thereby extended to ternary functions. However, a Boolean function usually has several ternary extensions, and the result of the causality analysis depends on the chosen ternary extension. In this paper, we show that there always is a maximal ternary extension that allows one to solve as many causality problems as possible. Moreover, we elaborate the relationship to hazard elimination in hardware circuits, and finally show how the maximal ternary extension of a Boolean function can be efficiently computed by means of binary decision diagrams.
BetaReduction As Unification
, 1996
"... this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of terms in . Quite apart from the new light it sheds on fireduction, such an analysis turns out to have several othe ..."
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Cited by 13 (9 self)
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this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of terms in . Quite apart from the new light it sheds on fireduction, such an analysis turns out to have several other benefits
Lambda! Considered Both as a Paradigmatic Language and as a MetaLanguage
"... Intuitionistic Linear Logic (ILL) is a resourceconscious logic. The CurryHoward Isomorphism (CHI) applied to ILL, generates typed functionallike languages that have primitive constants by means of which the amount of resources (terms), used during the computation, is explicit. \Gamma ! is an u ..."
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Cited by 2 (1 self)
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Intuitionistic Linear Logic (ILL) is a resourceconscious logic. The CurryHoward Isomorphism (CHI) applied to ILL, generates typed functionallike languages that have primitive constants by means of which the amount of resources (terms), used during the computation, is explicit. \Gamma ! is an untyped functionallike language inspired from a typed language joined at ILL by CHI. We want to use the resourceaware language \Gamma ! both as a paradigmatic programming language and as a metalanguage for implementing a fragment of the untyped calculus fi . For using \Gamma ! in the first way we give an algorithm for automatically assigning formulas of ILL as types to terms of \Gamma ! . Concerning the second kind of use, we introduce a onestep translation Tr from the fragment C of fi that can be typed a la Curry to the typable fragment of \Gamma ! in ILL. Tr preserves the linearbehaved terms of C and is both correct and complete, in a reasonable sense, w.r.t. the...
Generalized Finite Developments
"... Abstract. The Finite Development theorem (FD) is a fundamental theorem in the theory of the syntax of the lambdacalculus. It gives sense to parallel reductions by stating that one can contract any given set of (possibly nested) redexes in any lambda term without looping and caring about the order i ..."
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Abstract. The Finite Development theorem (FD) is a fundamental theorem in the theory of the syntax of the lambdacalculus. It gives sense to parallel reductions by stating that one can contract any given set of (possibly nested) redexes in any lambda term without looping and caring about the order in which these redexes are contracted. This theorem can be used to prove the ChurchRosser property, thus insuring determinism of reductions and uniqueness of normal forms. This paper explains how to extend the FD theorem to a finite number of creations of new redexes, i.e. redexes which do not exist in the initial term. This generalized theorem (gFD) also provides a proof technique to show the completeness of various reduction strategies. Finally it gives a natural intuition to the strong normalization property of the standard firstorder typed lambdacalculus. The results in this article are not new, but were often mixed with other arguments; the aim of this paper is to stress on this sole gFD theorem. 1
On modal logics of partial recursive functions
 Studia Logica
"... The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above inter ..."
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The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and nondeterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established.
Lecture Notes on Functional Computation 15816: Linear Logic
, 2012
"... In the linear λcalculus from last lecture, we interpreted proof reductions as term reductions in an underlying language of proof terms. This is the original insight behind the CurryHoward isomorphism [How69], albeit on an natural deduction for (nonlinear) intuitionistic logic and simplytyped (no ..."
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In the linear λcalculus from last lecture, we interpreted proof reductions as term reductions in an underlying language of proof terms. This is the original insight behind the CurryHoward isomorphism [How69], albeit on an natural deduction for (nonlinear) intuitionistic logic and simplytyped (nonlinear) λterms. But there is still a significant step between proof term reduction and an operational semantics. For example, in functional programming languages such as ML or Haskell, we do not evaluate under λabstractions, and we impose a specific order of evaluation for functions such as callbyvalue or callbyname. Finding compelling logical underpinnnings for these is still an active area of research. In this lecture we investigate a specific possibility for analyzing the computational content of linear natural deductions, using two pieces already in place: the translation from natural deduction to sequent calculus, and the interpretation of sequent proofs as concurrent processes. Combining these two will give us a concurrent operational semantics for the linear