A generic imperative language for polynomial time

The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative programming. We introduce a new approach to ramification which, among other benefits, adapts readily to fully general imperative programming. The novelty is in ramifying finite second-order objects, namely finite structures, rather than ramifying elements of free algebras. In so doing we bridge between Implicit Complexity's type theoretic characterizations of feasibility, and the data-flow approach of Static Analysis.Comment: 18 pages, submitted to a conferenc

Adding imperative programming to the pattern calculus

University of Technology, Sydney. Dept. of Software Engineering.By focusing on data and flow control, imperative languages provide a finely grained and efficient mechanism for directly manipulating state and memory. By focusing on functions, polymorphism increases the modularity and reusability of programs. The pattern calculus gives a new account of polymorphism over arbitrary datatypes which has been used as the foundation for building the functional language FISh2. The power of the new polymorphism is not limited to a functional setting and it can be extended into an imperative setting. The main contribution of this thesis is to expand the pattern calculus with imperative features and implement this within a version of FISh2. Two approaches are developed in expanding the calculus to imperative programming based on two setting: functional and imperative. Based on a functional setting, updatable locations are given separate location types; while based on an imperative setting, locations and their values share the same types. In both approaches, structured locations can be defined in the same way the calculus defines structured data. Hence, generic functions on locations can be defined by pattern-matching on (location) constructors. In that way, the power of the combination exceeds that of the boundary of functional or imperative alone. In particular, with the generic assignment function, we have a new approach on memory management which performs inplace update whenever it is reasonable to do so. Similar ideas could be used to extend the power of parametric polymorphism to parallel programming. To illustrate the approach, a key problem is addressed in detail, namely, distributing a data structure over a network of processors

Strategic polymorphism requires just two combinators!

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies.Comment: A preliminary version of this paper was presented at IFL 2002, and included in the informal preproceedings of the worksho

What Does Aspect-Oriented Programming Mean for Functional Programmers?

Aspect-Oriented Programming (AOP) aims at modularising crosscutting concerns that show up in software. The success of AOP has been almost viral and nearly all areas in Software Engineering and Programming Languages have become "infected" by the AOP bug in one way or another. Interestingly the functional programming community (and, in particular, the pure functional programming community) seems to be resistant to the pandemic. The goal of this paper is to debate the possible causes of the functional programming community's resistance and to raise awareness and interest by showcasing the benefits that could be gained from having a functional AOP language. At the same time, we identify the main challenges and explore the possible design-space

Type Generic Observing

Observing intermediate values helps to understand what is going on when your program runs. Gill presented an observation method for lazy functional languages that preserves the program's semantics. However, users need to define for each type how its values are observed: a laborious task and strictness of the program can easily be affected. Here we define how any value can be observed based on the structure of its type by applying generic programming frameworks. Furthermore we present an extension to specify per observation point how much to observe of a value. We discuss especially functional values and behaviour based on class membership in generic programming frameworks

Reusability in software engineering

This paper surveys recent work concerning reusability in software engineering. The current directions in software reusability are discussed, and the two major approaches of reusable building blocks and reusable patterns studied. An extensive bibliography, parts of which are annotated, is included

Can Computer Algebra be Liberated from its Algebraic Yoke ?

So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming, especially the functional and transformational paradigms, are put forward. In the future, algebraic algorithms could constitute the core of extended symbolic manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure

A principled approach to programming with nested types in Haskell

Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell

The Sketch of a Polymorphic Symphony

In previous work, we have introduced functional strategies, that is, first-class generic functions that can traverse into terms of any type while mixing uniform and type-specific behaviour. In the present paper, we give a detailed description of one particular Haskell-based model of functional strategies. This model is characterised as follows. Firstly, we employ first-class polymorphism as a form of second-order polymorphism as for the mere types of functional strategies. Secondly, we use an encoding scheme of run-time type case for mixing uniform and type-specific behaviour. Thirdly, we base all traversal on a fundamental combinator for folding over constructor applications. Using this model, we capture common strategic traversal schemes in a highly parameterised style. We study two original forms of parameterisation. Firstly, we design parameters for the specific control-flow, data-flow and traversal characteristics of more concrete traversal schemes. Secondly, we use overloading to postpone commitment to a specific type scheme of traversal. The resulting portfolio of traversal schemes can be regarded as a challenging benchmark for setups for typed generic programming. The way we develop the model and the suite of traversal schemes, it becomes clear that parameterised + typed strategic programming is best viewed as a potent combination of certain bits of parametric, intensional, polytypic, and ad-hoc polymorphism