SISO Output Affine Feedback Transformation Group and Its Faa di Bruno Hopf Algebra

The general goal of this paper is to identify a transformation group that can be used to describe a class of feedback interconnections involving subsystems which are modeled solely in terms of Chen-Fliess functional expansions or Fliess operators and are independent of the existence of any state space models. This interconnection, called an output affine feedback connection, is distinguished from conventional output feedback by the presence of a multiplier in an outer loop. Once this transformation group is established, three basic questions are addressed. How can this transformation group be used to provide an explicit Fliess operator representation of such a closed-loop system? Is it possible to use this feedback scheme to do system inversion purely in an input-output setting? In particular, can feedback input-output linearization be posed and solved entirely in this framework, i.e., without the need for any state space realization? Lastly, what can be said about feedback invariants under this transformation group? A final objective of the paper is to describe the Lie algebra of infinitesimal characters associated with the group in terms of a pre-Lie product.Comment: revised manuscript; title and abstract changed; new material adde

JEff: objects for effect

Effect handling is a way to structure and scope side-effects which is gaining popularity as an alternative to monads in purely functional programming languages. Languages with support for effect handling allow the programmer to define idioms for state, exception handling, asynchrony, backtrack-ing, etc. from within the language. Functional programming languages, however, prohibit certain patterns of modular-ity well-known from object-oriented languages. In this paper we introduce JEff, an object-oriented programming language with native support for effect handling, to provide first answers to the question what it would mean to integrate object-oriented programming with effect handling. We illustrate how user-defined effects could benefit from interface polymorphism, and present its runtime semantics and type system

Rule and Meaning in the Teaching of Grammar

While the construct of rule as a manipulation of purely formal properties of language has been widely abandoned in both formal and functional linguistics, it persists, though with diminished importance, in the field of Second Language Acquisition (SLA). This is true even in Form-Focused Instruction (FFI), including Focus-on-Form (FonF), which emphasizes meaning as both classroom focus and element of language structure. This paper illustrates the meaningfulness of grammar, even where treatment has often appealed to such rules; identifies areas of overlap between what is identified by the term rule and what is identified by the terms meaning (semantics) and form (morphology), and points out the lack of descriptive adequacy of some familiar rules. The author offers research- and practice-based recommendations for pursuing a fully meaning-based communicative approach to teaching grammar even while suitable and comprehensive resource materials for such methods in language education are lacking

Conceptual role semantics and the reference of moral concepts

This paper examines the prospects for a conceptual or functional role theory of moral concepts. It is argued that such an account is well-placed to explain both the irreducibility and practicality of moral concepts. Several versions of conceptual role semantics for moral concepts are distinguished, depending on whether the concept-constitutive conceptual roles are wide or narrow normative or non-normative and purely doxastic or conative. It is argued that the most plausible version of conceptual role semantics for moral concepts involves only ‘narrow’ conceptual roles, where these include connections to motivational, desire-like, states. In the penultimate section it is argued, contrary to what Wedgwood, Enoch and others have claimed, that such an account of moral concepts cannot plausibly be combined with the claim that moral concepts refer to robust properties

‘Something extra’: In defence of an uncanny humanism

This article proposes literature and psychoanalysis as forms of critical education, putting in urgent question the market-driven, instrumental models of learning that currently dominate higher education policy. In psychoanalytic terms, it argues, the primary mechanism at work in such a policy is what psychoanalysis calls splitting, which involves above all a kind of banishment of doubt and a rigid assurance in the rightness of the status quo that precludes meaningful change or transformation in the self and the world. The article goes on to identify in psychoanalysis and literature more ‘unsplit’ modes of thinking that refuse the reduction of the human being to a purely functional value. It ends with a reading of Kazuo Ishiguro’s Never Let Me Go as a critical meditation on this reductive tendency

Shape Analysis in the Absence of Pointers and Structure

discover properties of dynamic and/or mutable structures. We ask, “Is there an equivalent to shape analysis for purely functional programs, and if so, what ‘shapes ’ does it discover? ” By treating binding environments as dynamically allocated structures, by treating bindings as addresses, and by treating value environments as heaps, we argue that we can analyze the “shape ” of higher-order functions. To demonstrate this, we enrich an abstract-interpretive control-flow analysis with principles from shape analysis. In particular, we promote “anodization ” as a way to generalize both singleton abstraction and the notion of focusing, and we promote “binding invariants ” as the analog of shape predicates. Our analysis enables two optimizations known to be beyond the reach of control-flow analysis (globalization and super-β inlining) and one previously unknown optimization (higher-order rematerialization).

Artificial Brains and Hybrid Minds

The paper develops two related thought experiments exploring variations on an ‘animat’ theme. Animats are hybrid devices with both artificial and biological components. Traditionally, ‘components’ have been construed in concrete terms, as physical parts or constituent material structures. Many fascinating issues arise within this context of hybrid physical organization. However, within the context of functional/computational theories of mentality, demarcations based purely on material structure are unduly narrow. It is abstract functional structure which does the key work in characterizing the respective ‘components’ of thinking systems, while the ‘stuff’ of material implementation is of secondary importance. Thus the paper extends the received animat paradigm, and investigates some intriguing consequences of expanding the conception of bio-machine hybrids to include abstract functional and semantic structure. In particular, the thought experiments consider cases of mind-machine merger where there is no physical Brain-Machine Interface: indeed, the material human body and brain have been removed from the picture altogether. The first experiment illustrates some intrinsic theoretical difficulties in attempting to replicate the human mind in an alternative material medium, while the second reveals some deep conceptual problems in attempting to create a form of truly Artificial General Intelligence