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- Daniel R. Licata, Noam Zeilberger, Robert Harper
- 2008 23rd Annual IEEE Symposium on Logic in…
- 2008

Variable binding is a prevalent feature of the syntax and proof theory of many logical systems. In this paper, we define a programming language that provides intrinsic support for both representing and computing with binding. This language is extracted as the Curry-Howard interpretation of a focused sequent calculus with two kinds of implication, of… (More)

- Joshua Dunfield, Jonathan Aldrich, +14 authors Noam Zeilberger
- 2007

- Noam Zeilberger
- Ann. Pure Appl. Logic
- 2008

Most type systems are agnostic regarding the evaluation strategy for the underlying languages, with the value restriction for ML which is absent in Haskell as a notable exception. As type systems become more precise, however, detailed properties of the operational semantics may become visible because properties captured by the types may be sound under one… (More)

- Noam Zeilberger
- PLPV
- 2009

One lesson learned painfully over the past twenty years is the perilous interaction of Curry-style typing with evaluation order and side-effects. This led eventually to the value restriction on polymorphism in ML, as well as, more recently, to similar artifacts in type systems for ML with intersection and union refinement types. For example, some of the… (More)

- Noam Zeilberger
- 2009

In previous work, the author gave a higher-order analysis of focusing proofs (in the sense of Andreoli's search strategy), with a role for infinitary rules very similar in structure to Buchholz's Ω-rule. Among other benefits, this " pattern-based " description of focusing simplifies the cut-elimination procedure, allowing cuts to be eliminated in a… (More)

- Noam Zeilberger
- POPL
- 2008

Focusing is a proof-search strategy, originating in linear logic, that elegantly eliminates inessential nondeterminism, with one byproduct being a correspondence between focusing proofs and programs with explicit evaluation order. Higher-order abstract syntax (HOAS) is a technique for representing higher-order programming language constructs (e.g.,… (More)

- Noam Zeilberger
- 2010 25th Annual IEEE Symposium on Logic in…
- 2010

Polarized logic is the logic of values and continuations, and their interaction through continuation-passing style. The main limitations of this logic are the limitations of CPS: that continuations cannot be composed, and that programs are fully sequentialized. Delimited control operators were invented in response to the limitations of classical… (More)

- Noam Zeilberger, Alain Giorgetti
- Logical Methods in Computer Science
- 2014

A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no β-redexes, and planar if it is linear and the use of variables moreover follows a deterministic stack discipline. We… (More)

- Paul-André Melliès, Noam Zeilberger
- POPL
- 2015

The standard reading of type theory through the lens of category theory is based on the idea of viewing a type system as a category of well-typed terms. We propose a basic revision of this reading: rather than interpreting type systems as categories, we describe them as <i>functors</i> from a category of typing derivations to a category of underlying terms.… (More)