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The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government, or any other entity. Abstract In a typical application storing some data, if the memory representations of the internal data(More)
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)
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)
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)
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)
A rooted planar map is a connected graph embedded in the plane, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be (β-)normal if it is fully reduced, and planar if it uses all of its variables exactly once and in last-in, first-out order. We exhibit a bijection between rooted planar maps and normal planar(More)