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168
Adequacy for algebraic effects
 In 4th FoSSaCS
, 2001
"... We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the acalculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to ..."
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Cited by 30 (16 self)
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We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the acalculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to obtain the logic, which is a classical firstorder multisorted logic with higherorder value and computation types, as in Levy’s callbypushvalue, a principle of induction over computations, a free algebra principle, and predicate fixed points. This logic embraces Moggi’s computational λcalculus, and also, via definable modalities, HennessyMilner logic, and evaluation logic, though Hoare logic presents difficulties. 1
Practical programming with higherorder encodings and dependent types
 In Proceedings of the European Symposium on Programming (ESOP ’08
, 2008
"... Abstract. Higherorder abstract syntax (HOAS) refers to the technique of representing variables of an objectlanguage using variables of a metalanguage. The standard firstorder alternatives force the programmer to deal with superficial concerns such as substitutions, whose implementation is often ..."
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Cited by 27 (2 self)
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Abstract. Higherorder abstract syntax (HOAS) refers to the technique of representing variables of an objectlanguage using variables of a metalanguage. The standard firstorder alternatives force the programmer to deal with superficial concerns such as substitutions, whose implementation is often routine, tedious, and errorprone. In this paper, we describe the underlying calculus of Delphin. Delphin is a fully implemented functionalprogramming language supporting reasoning over higherorder encodings and dependent types, while maintaining the benefits of HOAS. More specifically, just as representations utilizing HOAS free the programmer from concerns of handling explicit contexts and substitutions, our system permits programming over such encodings without making these constructs explicit, leading to concise and elegant programs. To this end our system distinguishes bindings of variables intended for instantiation from those that will remain uninstantiated, utilizing a variation of Miller and Tiu’s ∇quantifier [1]. 1
On a monadic semantics for freshness
 THEORETICAL COMPUTER SCIENCE
, 2005
"... A standard monad of continuations, when constructed with domains in the world of FMsets [4], is shown to provide a model of dynamic allocation of fresh names that is both simple and useful. In particular, it is used to prove that the powerful facilities for manipulating fresh names and binding oper ..."
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Cited by 26 (7 self)
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A standard monad of continuations, when constructed with domains in the world of FMsets [4], is shown to provide a model of dynamic allocation of fresh names that is both simple and useful. In particular, it is used to prove that the powerful facilities for manipulating fresh names and binding operations provided by the “Fresh ” series of metalanguages [15,17,18] respect αequivalence of objectlevel languages up to metalevel contextual equivalence.
Static name control for FreshML
 In IEEE Symposium on Logic in Computer Science (LICS
, 2007
"... 3 A complete example ..."
Domain theory for concurrency
, 2003
"... Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. ..."
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Cited by 23 (6 self)
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Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey.
Nominal logic programming
, 2006
"... Nominal logic is an extension of firstorder logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, αequivalence). This article investigates logic programming based on nominal logic. This technique is especial ..."
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Cited by 23 (8 self)
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Nominal logic is an extension of firstorder logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, αequivalence). This article investigates logic programming based on nominal logic. This technique is especially wellsuited for prototyping type systems, proof theories, operational semantics rules, and other formal systems in which bound names are present. In many cases, nominal logic programs are essentially literal translations of “paper” specifications. As such, nominal logic programming provides an executable specification language for prototyping, communicating, and experimenting with formal systems. We describe some typical nominal logic programs, and develop the modeltheoretic, prooftheoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via two examples.
A Definitional Approach to Primitive Recursion over Higher Order Abstract Syntax
 In Proceedings of the 2003 workshop on Mechanized
, 2003
"... Syntax S. J. Ambler (S.Ambler@mcs.le.ac.uk) R. L. Crole (R.Crole@mcs.le.ac.uk) & A. Momigliano (A.Momigliano@mcs.le.ac.uk) Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, U.K. ..."
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Cited by 22 (5 self)
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Syntax S. J. Ambler (S.Ambler@mcs.le.ac.uk) R. L. Crole (R.Crole@mcs.le.ac.uk) & A. Momigliano (A.Momigliano@mcs.le.ac.uk) Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, U.K.
A Sequent Calculus for Nominal Logic
 In Proc. LICS’04
, 2004
"... Nominal logic is a theory of names and binding based on the primitive concepts of freshness and swapping, with a selfdual N  (or "new")quantifier, originally presented as a Hilbertstyle axiom system extending firstorder logic. We present a sequent calculus for nominal logic called Fresh Logic, ..."
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Cited by 22 (10 self)
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Nominal logic is a theory of names and binding based on the primitive concepts of freshness and swapping, with a selfdual N  (or "new")quantifier, originally presented as a Hilbertstyle axiom system extending firstorder logic. We present a sequent calculus for nominal logic called Fresh Logic, or FL, admitting cutelimination. We use FL to provide a prooftheoretic foundation for nominal logic programming and show how to interpret $FOL^{\Delta abla}$, another logic with a selfdual quantifier, within FL.
The Complexity of Equivariant Unification
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP 2004), volume 3142 of LNCS
"... Nominal logic is a firstorder theory of names and binding based on a primitive operation of swapping rather than substitution. Urban, Pitts, and Gabbay have developed a nominal unification algorithm that unifies terms up to nominal equality. However, because of nominal logic's equivariance principl ..."
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Cited by 21 (7 self)
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Nominal logic is a firstorder theory of names and binding based on a primitive operation of swapping rather than substitution. Urban, Pitts, and Gabbay have developed a nominal unification algorithm that unifies terms up to nominal equality. However, because of nominal logic's equivariance principle, atomic formulas can be provably equivalent without being provably equal as terms, so resolution using nominal unification is sound but incomplete. For complete resolution, a more general form of unification called equivariant unification, or "unification up to a permutation" is required. Similarly, for rewrite rules expressed in nominal logic, a more general form of matching called equivariant matching is necessary. In this paper, we study the complexity of the decision problem for equivariant unification and matching. We show that these problems are NPcomplete in general. However, when one of the terms is essentially firstorder, equivariant and nominal unification coincide. This shows that equivariant unification can be performed efficiently in many interesting common cases: for example, anypurely firstorder logic program or rewrite system can be run efficiently on nominal terms.
A Proof Search Specification of the πCalculus
 IN 3RD WORKSHOP ON THE FOUNDATIONS OF GLOBAL UBIQUITOUS COMPUTING
, 2004
"... We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we ..."
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Cited by 21 (11 self)
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We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we