Maximal Sharing in the Lambda Calculus with letrec

Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of `maximal compactness' for lambda-letrec-terms among all terms with the same infinite unfolding. Instead of defined purely syntactically, this notion is based on a graph semantics. lambda-letrec-terms are interpreted as first-order term graphs so that unfolding equivalence between terms is preserved and reflected through bisimilarity of the term graph interpretations. Compactness of the term graphs can then be compared via functional bisimulation. We describe practical and efficient methods for the following two problems: transforming a lambda-letrec-term into a maximally compact form; and deciding whether two lambda-letrec-terms are unfolding-equivalent. The transformation of a lambda-letrec-term $L$ into maximally compact form $L_0$ proceeds in three steps: (i) translate L into its term graph $G = [[ L ]]$; (ii) compute the maximally shared form of $G$ as its bisimulation collapse $G_0$; (iii) read back a lambda-letrec-term $L_0$ from the term graph $G_0$ with the property $[[ L_0 ]] = G_0$. This guarantees that $L_0$ and $L$ have the same unfolding, and that $L_0$ exhibits maximal sharing. The procedure for deciding whether two given lambda-letrec-terms $L_1$ and $L_2$ are unfolding-equivalent computes their term graph interpretations $[[ L_1 ]]$ and $[[ L_2 ]]$, and checks whether these term graphs are bisimilar. For illustration, we also provide a readily usable implementation.Comment: 18 pages, plus 19 pages appendi

Action semantics in retrospect

This paper is a themed account of the action semantics project, which Peter Mosses has led since the 1980s. It explains his motivations for developing action semantics, the inspirations behind its design, and the foundations of action semantics based on unified algebras. It goes on to outline some applications of action semantics to describe real programming languages, and some efforts to implement programming languages using action semantics directed compiler generation. It concludes by outlining more recent developments and reflecting on the success of the action semantics project

Type-Directed Weaving of Aspects for Polymorphically Typed Functional Languages

Incorporating aspect-oriented paradigm to a polymorphically typed functional language enables the declaration of type-scoped advice, in which the effect of an aspect can be harnessed by introducing possibly polymorphic type constraints to the aspect. The amalgamation of aspect orientation and functional programming enables quick behavioral adaption of functions, clear separation of concerns and expressive type-directed programming. However, proper static weaving of aspects in polymorphic languages with a type-erasure semantics remains a challenge. In this paper, we describe a type-directed static weaving strategy, as well as its implementation, that supports static type inference and static weaving of programs written in an aspect-oriented polymorphically typed functional language, AspectFun. We show examples of type-scoped advice, identify the challenges faced with compile-time weaving in the presence of type-scoped advice, and demonstrate how various advanced aspect features can be handled by our techniques. Lastly, we prove the correctness of the static weaving strategy with respect to the operational semantics of AspectFun

Trustworthy Refactoring via Decomposition and Schemes: A Complex Case Study

Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true confidence in applying tool-automated refactoring to industrial-scale code. By using our strategic rewriting based refactoring specification language, we present the decomposition of a complex transformation into smaller steps that can be expressed as instances of refactoring schemes, then we demonstrate the semi-automatic formal verification of the components based on a theoretical understanding of the semantics of the programming language. The extensible and verifiable refactoring definitions can be executed in our interpreter built on top of a static analyser framework.Comment: In Proceedings VPT 2017, arXiv:1708.0688

Interactive Simplifier Tracing and Debugging in Isabelle

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not in the form the user expected, or the simplifier fails to apply a rule. We describe a new, interactive tracing facility which offers insight into the hierarchical structure of the simplification with user-defined filtering, memoization and search. The new simplifier trace is integrated into the Isabelle/jEdit Prover IDE.Comment: Conferences on Intelligent Computer Mathematics, 201

Adaptive Online Sequential ELM for Concept Drift Tackling

A machine learning method needs to adapt to over time changes in the environment. Such changes are known as concept drift. In this paper, we propose concept drift tackling method as an enhancement of Online Sequential Extreme Learning Machine (OS-ELM) and Constructive Enhancement OS-ELM (CEOS-ELM) by adding adaptive capability for classification and regression problem. The scheme is named as adaptive OS-ELM (AOS-ELM). It is a single classifier scheme that works well to handle real drift, virtual drift, and hybrid drift. The AOS-ELM also works well for sudden drift and recurrent context change type. The scheme is a simple unified method implemented in simple lines of code. We evaluated AOS-ELM on regression and classification problem by using concept drift public data set (SEA and STAGGER) and other public data sets such as MNIST, USPS, and IDS. Experiments show that our method gives higher kappa value compared to the multiclassifier ELM ensemble. Even though AOS-ELM in practice does not need hidden nodes increase, we address some issues related to the increasing of the hidden nodes such as error condition and rank values. We propose taking the rank of the pseudoinverse matrix as an indicator parameter to detect underfitting condition.Comment: Hindawi Publishing. Computational Intelligence and Neuroscience Volume 2016 (2016), Article ID 8091267, 17 pages Received 29 January 2016, Accepted 17 May 2016. Special Issue on "Advances in Neural Networks and Hybrid-Metaheuristics: Theory, Algorithms, and Novel Engineering Applications". Academic Editor: Stefan Hauf

The Semantics of Graph Programs

GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling low-level data structures. The core of GP consists of four constructs: single-step application of a set of conditional graph-transformation rules, sequential composition, branching and iteration. We present a formal semantics for GP in the style of structural operational semantics. A special feature of our semantics is the use of finitely failing programs to define GP's powerful branching and iteration commands

Modular interpreters with implicit context propagation

Modular interpreters are a crucial first step towards component-based language development: instead of writing language interpreters from scratch, they can be assembled from reusable, semantic building blocks. Unfortunately, traditional language interpreters can be hard to extend because different language constructs may require different interpreter signatures. For instance, arithmetic interpreters produce a value without any context information, whereas binding constructs require an additional environment.In this paper, we present a practical solution to this problem based on implicit context propagation. By structuring denotational-style interpreters as Object Algebras, base interpreters can be retroactively lifted into new interpreters that have an extended signature. The additional parameters are implicitly propagated behind the scenes, through the evaluation of the base interpreter.Interpreter lifting enables a flexible style of modular and extensible language development. The technique works in mainstream object-oriented languages, does not sacrifice type safety or separate compilation, and can be easily automated, for instance using macros in Scala or dynamic proxies in Java. We illustrate implicit context propagation using a modular definition of Featherweight Java and its extension to support side-effects, and an extensible domain-specific language for state machines. We finally investigate the performance overhead of lifting by running the DeltaBlue benchmark program in Javascript on top of a modular implementation of LambdaJS and a dedicated micro-benchmark. The results show that lifting makes interpreters roughly twice as slow because of additional call overhead. Further research is needed to eliminate this performance penalty