We apply the categorical properties of polymorphic functions to compile-time analysis, specifically projection-based strictness analysis. First we interpret parameterised types as functors in a suitable category, and show that they preserve monics and epics. Then we define “strong” and “weak” polymorphism, the latter admitting certain projections that are not polymorphic in the usual sense. We prove that, under the right conditions, a weakly polymorphic function is characterised by a single instance. It follows that the strictness analysis of one simple instance of a polymorphic function yields results that apply to all. We show how this theory may be applied. In comparison with earlier polymorphic strictness analysis methods, ours can apply polymorphic information to a particular instance very simply. The categorical approach simplifies our proofs, enabling them to be carried out at a higher level, and making them independent of the precise form of the programming language to be analysed. The major limitation of our results is that they apply only to first-order functions.

We formulate a typed version of call-by-value λ-calculus containing variants of Felleisen's control operators A and C that provide explicit access to continuations and logically extend the propositions-as-types correspondence to classical propositional logic. We give an equational theory for this calculus, which is shown to be sound and complete with respect to a class of categorical models based on continuation-passing-style semantics.

This paper gives some sufficient conditions for admissible rules to be derivable in intuitionistic propositional calculus. For example, if the premises are Harrop formulas, the rule is admissible only if it is derivable.

In deriving the results, a particular class of substitutes is introduced, which are also useful when dealing with other questions of admissibility.

Unfold/fold transformations have been used in logic programming for some years to transform programs into more efficient ones. We describe recent work on the extent to which these transformations produce programs which are equivalent to the original one. Various notions of equivalence are considered: same success set; finite failure set; least Herbrand model; completion. This is used to illustrate the rather unsatisfactory relationship between logic programming and logic shown by the wide variety of different declarative semantics proposed for logic programs.

Using the well-known categorical notion of ‘functor’, one may define the concept of datatype (algebra) without being forced to introduce a signature (that is, names and typings for the individual sorts (types) and operations involved). This has proved to be advantageous for those theory developments where one is not interested in the syntactic appearance of an algebra.

The categorical notion of ‘transformer’ developed in this paper allows the same approach to laws: without using signatures one can define the concept of law for datatypes (lawful algebras), and investigate the equational specification of datatypes in a syntax-free manner. A transformer is a special kind of functor and also a natural transformation on the level of dialgebras. Transformers are quite expressive, satisfy several closure properties, and are related to naturality and Wadler'' Theorems For Free Theorem. In fact, any colimit is an initial lawful algebra.

It is shown that the category of fuzzy relations with values in a ∗-autonomous poset gives a ∗-autonomous category. It is also shown that this construction can be generalized by replacing the ∗-autonomous poset by a ∗-autonomous category. In both cases, cofree coalgebras exist so that there is a natural! operation.

We present an algebraic approach to the syntax and semantics of Martin-Löf type theory and the calculus of constructions developed by T. Coquand and G. Huet. In our approach, models of this theory and this calculus are treated as three-sorted partial algebras, called ITSΠ-structures, described by essentially algebraic theories. We give a proof that derived statements of Martin-Löf type theory hold in appropriate ITSΠ-structures. In this proof, a formal translation from the language of terms and types into the language of terms of an appropriate essentially algebraic theory of ITSΠ-structures is used. A straightforward set-theoretic construction of ITSΠ-structures that are models of Martin-Löf type theory is demonstrated. We present a construction of a recursive ITSΠ-structure (i.e. its partial and total operations are recursive functions over some alphabet) that is a model of the calculus of constructions and demonstrates the decidability of this calculus.

A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. Using the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. Using the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having “invertible” proofs between the two terms. Work of Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.

We examine the problem of finding fully abstract translations between programming languages, i.e., translations that preserve code equivalence and nonequivalence. We present three examples of fully abstract translations: one from call-by-value to lazy PCF, one from call-by-name to call-by-value PCF, and one from lazy to call-by-value PCF. The translations yield lower bounds on decision procedures for proving equivalences of code. We define a notion of ‘functional translation’ that captures the essence of the proofs of full abstraction, and show that some languages cannot be translated into others.

Motivated by a desire to treat non-termination directly in the semantics of computation, the notion of approximation between programs is studied in the context of categories of partial maps. In particular, contextual approximation and specialisation are considered and shown to coincide. Moreover, after exhibiting the approximation between total maps as a primitive notion, from an arbitrary (or axiomatic) approximation order on total maps a computationally natural approximation order on partial maps is derived. The main technical contribution is a characterisation of when this approximation order between partial maps is domain-theoretic (in the sense that the category of partial maps Cpo-enriches) provided that the approximation order between total maps is also.

Snake robots have the potential to make substantial contributions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10–15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed.

Mobile robots are used to operate in urban environments, for surveillance, reconnaissance, and inspection, as well as for military operations and in hazardous environments. Some are intended for exploration of only natural terrains, but others also for artificial environments, including stairways. This paper presents a mobile robot design that achieves autonomous climbing and descending of stairs. The robot uses sensors and embedded intelligence to achieve the task. The robot is a reconfigurable tracked mobile robot that has the ability to traverse obstacles by changing its track configuration. Algorithms have been further developed for conditions under which the mobile robot would halt its motion during the climbing process when at risk of flipping over. Technical problems related to the implementation of some of the robot functional attributes are presented, and proposed solutions are validated and experimentally tested. The experiments illustrate the effectiveness of the proposed approach to autonomous climbing and descending of stairs.

Consider the following one-player game. Starting with the empty graph on n vertices, in every step a new edge is drawn uniformly at random and inserted into the current graph. This edge has to be coloured immediately with one of r available colours. The player's goal is to avoid creating a monochromatic copy of some fixed graph F for as long as possible. We prove a lower bound of nβ(F,r) on the typical duration of this game, where β(F,r) is a function that is strictly increasing in r and satisfies limr→∞ β(F,r) = 2 − 1/m2(F), where n2−1/m2(F) is the threshold of the corresponding offline colouring problem.

In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification “we have many things, in no way do we mention one thing that is the many taken together”. Instead, in the mereological case: “we have many things, we do mention one thing that is the many taken together, but this one thing is nothing different from the many” (Lewis, 1991, p. 87). The aim of the paper is to argue that—for a certain use of mereology, weaker than Lewis’ one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of individuals is played by plural choices of atoms.

Mobile olfactory robots can be used in a number of relevant application areas where a better understanding of a gas distribution is needed, such as environmental monitoring and safety and security related fields. In this paper, we present a method to integrate the classification of odours together with gas distribution mapping. The resulting odour map is then correlated with the spatial information collected from a laser range scanner to form a combined map. Experiments are performed using a mobile robot in large and unmodified indoor and outdoor environments. Multiple odour sources are used and are identified using only transient information from the gas sensor response. The resulting multi-level map can be used as a representation of the collected odour data.