Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language with an imperative style and a precise semantics allowing programs to be translatable into efficient imperative languages, to obtain proofs of correctness together with efficient execution. This language is designed to facilitate translations into correct programs in imperative languages with assignment statements, iteration, recursion, arrays, pointers, and side effects. It can also be used in place of a pseudo-programming language to specify algorithms.
There is a perceived trade-off between machine learning code that is easy to write, and machine learning code that is scalable or fast to execute. In machine learning, imperative style libraries like Autograd and PyTorch are easy to write, but suffer from high interpretive overhead and are not easily deployable in production or mobile settings. Graph-based libraries like TensorFlow and Theano benefit from whole-program optimization and can be deployed broadly, but make expressing complex models more cumbersome. We describe how the use of staged programming in Python, via source code transforma…
In this paper, we show a new approach to transformations of an imperative program with function calls and global variables into a logically constrained term rewriting system. The resulting system represents transitions of the whole execution environment with a call stack. More precisely, we prepare a function symbol for the whole environment, which stores values for global variables and a call stack as its arguments. For a function call, we prepare rewrite rules to push the frame to the stack and to pop it after the execution. Any running frame is located at the top of the stack, and statement…
In machine learning (ML), researchers and engineers seem to be at odds. System implementers would prefer models to be declarative, with detailed type information and semantic restrictions that allow models to be optimised, rearranged and parallelised. Yet practitioners show an overwhelming preference for dynamic, imperative languages with mutable state, and much engineering effort is spent bridging the resulting semantic divide. Is there a fundamental conflict? This article explores why imperative and functional styles are used, and how future language designs might get the best of both worlds…
In this paper, we describe an IDE called CAPS (Calculational Assistant for Programming from Specifications) for the interactive, calculational derivation of imperative programs. In building CAPS, our aim has been to make the IDE accessible to non-experts while retaining the overall flavor of the pen-and-paper calculational style. We discuss the overall architecture of the CAPS system, the main features of the IDE, the GUI design, and the trade-offs involved.
Declarative styles such as functional programming (FP) are rapidly gaining ground on their imperative cousins, including procedural and object-oriented programming. The shift is subtle because it is happening within the context of multiparadigm programming languages such as JavaScript. FP is better suited to modern processes like test-driven development (TDD), and architectures like massively parallel, cloud-based computing. This article describes the technical details that characterize the shift from imperative to FP and implications for software quality management, particularly reuse and tes…
Automated software verification is a very active field of research which has made enormous progress both in theoretical and practical aspects. Recently, an important amount of research effort has been put into applying these techniques on top of mainstream programming languages. These languages typically provide powerful features such as reflection, aliasing and polymorphism which are handy for practitioners but, in contrast, make verification a real challenge. In this work we present Pest, a simple experimental, while-style, multiprocedural, imperative programming language which was conceived…
In (Apt et al, TOPLAS 1998) we introduced the imperative programming language Alma-0 that supports declarative programming. In this paper we illustrate the hybrid programming style of Alma-0 by means of various examples that complement those presented in (Apt et al, TOPLAS 1998). The presented Alma-0 programs illustrate the versatility of the language and show that ``don't know'' nondeterminism can be naturally combined with assignment.
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple "core" programming language - an imperative language with bounded loops, and arithmetics limited to addition and multiplication - it was possible to decide precisely whether a program had certain growth-rate properties, namely polynomial (or linear) bounds on computed values, or on the running time. This work emphasized the role of the core language in mitigating the notorious undecidability of program properties, so that one deals with decidable problems. A natural and intriguing problem was whether more elements can be added …
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and side-effects in functional and imperative languages. Another benefit is a better way of modelling computational effects in logical frameworks. With this analogy in mind, we embark on an investigation of inference systems based on considering inference behaviour as a form of computation. We delineate a categorical formalisation of control constructs in inference …
This is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical language automatically incorporates desirable features, such as alpha-equivalence and how it can describe pure computation, imperative store, and control features in a uniform framework. The graph semantics combines some of the best features of structural operational semantics and abstract machines, while offering powerful new methods for reasoning about context…
Static Single Assignment (SSA) is the workhorse of modern optimizing compilers for imperative programming languages. However, functional languages have been slow to adopt SSA and prefer to use intermediate representations based on minimal lambda calculi due to SSA's inability to express higher order constructs. We exploit a new SSA construct -- regions -- in order to express functional optimizations via classical SSA based reasoning. Region optimization currently relies on ad-hoc analyses and transformations on imperative programs. These ad-hoc transformations are sufficient for imperative lan…
Traditionally, semantic models of imperative languages use an auxiliary structure which mimics memory. In this way, ownership and other encapsulation properties need to be reconstructed from the graph structure of such global memory. We present an alternative "syntactic" model where memory is encoded as part of the program rather than as a separate resource. This means that execution can be modelled by just rewriting source code terms, as in semantic models for functional programs. Formally, this is achieved by the block construct, introducing local variable declarations, which play the role o…
Creol is an object-oriented modeling language in which inherently concurrent objects exchange asynchronous method calls. The operational semantics of Creol is written in an actor-based style, formulated in rewriting logic. The operational semantics yields a language interpreter in the Maude system, which can be used to analyze models. Recently, Creol has been applied to the modeling of systems with radio communication, such as sensor systems. With radio communication, messages expire and, if sent simultaneously, they may collide in the air. In order to capture these and other properties of dis…
Intensional sets are sets given by a property rather than by enumerating their elements. In previous work, we have proposed a decision procedure for a first-order logic language which provides Restricted Intensional Sets (RIS), i.e., a sub-class of intensional sets that are guaranteed to denote finite---though unbounded---sets. In this paper we show how RIS can be exploited as a convenient programming tool also in a conventional setting, namely, the imperative O-O language Java. We do this by considering a Java library, called JSetL, that integrates the notions of logical variable, (set) unifi…
