Needed Computations Shortcutting Needed Steps

We define a compilation scheme for a constructor-based, strongly-sequential, graph rewriting system which shortcuts some needed steps. The object code is another constructor-based graph rewriting system. This system is normalizing for the original system when using an innermost strategy. Consequently, the object code can be easily implemented by eager functions in a variety of programming languages. We modify this object code in a way that avoids total or partial construction of the contracta of some needed steps of a computation. When computing normal forms in this way, both memory consumption and execution time are reduced compared to ordinary rewriting computations in the original system.Comment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681

An Investigation of Abadi and Cardelli's Untyped Calculus of Objects

We study the relationship between the natural (big-step) semantics and the reduction (small-step) semantics of Abadi and Cardelli's untyped calculus of objects. By applying Danvy et al.'s functional correspondence to the natural semantics, we derive an abstract machine for this calculus, and by applying Danvy et al.'s syntactic correspondence to the reduction semantics, we also derive an abstract machines for this calculus. These two abstract machines are identical. The fact that the machines are identical, and the fact that they have been derived using meaning-preserving program transformations, entail that the derivation constitutes a proof of equivalence between natural semantics and the reduction semantics. The derivational nature of our proof contrasts with Abadi and Cardelli's soundness proof, which was carried out by pen and paper. We also note that the abstract machine is new. To move closer to actual language implementations, we reformulate the calculus to use explicit substitutions. The reformulated calculus is new. By applying the functional and syntactic correspondences to natural and reduction semantics of this new calculus, we again obtain two abstract machines. These two machines are also identical, and as such, they establish the equivalence of the natural semantics and the reduction semantics of the new calculus. Finally, we prove that the two abstract machines are strongly bisimilar. Therefore, the two calculi are computationally equivalent

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves.In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold:First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable.Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization.Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization.In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization

From Outermost Reduction Semantics to Abstract Machine

Reduction semantics is a popular format for small-step operational semantics of deterministic programming languages with computational effects.Each reduction semantics gives rise to a reduction-based normalization function where the reduction sequence is enumerated.Refocusing is a practical way to transform a reduction-based normalization function into a reduction-free one where the reduction sequence is not enumerated.This reduction-free normalization function takes the form of an abstract machine that navigates from one redex site to the next without systematically detouring via the root of the term to enumerate the reduction sequence, in contrast to the reduction-based normalization function.We have discovered that refocusing does not apply as readily for reduction semantics that use an outermost reduction strategy and have overlapping rules where a contractum can be a proper subpart of a redex.In this article, we consider such an outermost reduction semantics with backward-overlapping rules, and we investigate how to apply refocusing to still obtain a reduction-free normalization function in the form of an abstract machine

Ginnerup Revisited. New Excavations at a Key Neolithic Site on Djursland, Denmark

New excavations of an enclosure-related site at Ginnerup on Djursland, Denmark, in 2020 resulted in the identification of several features containing depositions of marine shells. One of these, A4, is a natural depression with a fill comprised of four consecutively deposited layers, forming an undisturbed stratigraphy, dated by several 14C dates to between c. 3150 and 2950 BC. The oldest layer contained finds from phase MN A Ib of the Funnel Beaker culture, while the remaining three layers yielded finds from the latest Funnel Beaker culture on Djursland (MN A II/III, Ferslev style) with an upwardly increasing content of Pitted Ware culture elements, thereby allowing the emergence of this culture in Denmark to be followed for the first time. Preservation conditions for organic material were excellent due to a content of marine shells, mainly from oysters and mussels, in all layers. In this preliminary account, a survey of the material culture in the four layers is presented, together with 14C dates, zoological investigations of mammal and fish bones, isotope analyses (d13C, d15N and d34S) and aDNA analyses of mammal bones and examinations of plant macro-remains. The abundant bones of wild horses also hold a huge potential for zoological and genetic studies, the results of which can qualify the ongoing debate about the rewilding of horses in present-day Europe