Bridging the GUI gap with reactive values and relations

There are at present two ways to write GUIs for functional code. One is to use standard GUI toolkits, with all the benefits they bring in terms of feature completeness, choice of platform, conformance to platform-specific look-and-feel, long-term viability, etc. However, such GUI APIs mandate an imperative programming style for the GUI and related parts of the application. Alternatively, we can use a functional GUI toolkit. The GUI can then be written in a functional style, but at the cost of foregoing many advantages of standard toolkits that often will be of critical importance. This paper introduces a light-weight framework structured around the notions of reactive values and reactive relations . It allows standard toolkits to be used from functional code written in a functional style. We thus bridge the gap between the two worlds, bringing the advantages of both to the developer. Our framework is available on Hackage and has been been validated through the development of non-trivial applications in a commercial context, and with different standard GUI toolkits

Representations of stream processors using nested fixed points

We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two continuous functions between streams that yields a representation of their composite. In the case of discrete-valued functions, the representatives are well-founded (finite-path) trees of a certain kind. The underlying idea can be traced back to Brouwer's justification of bar-induction, or to Kreisel and Troelstra's elimination of choice-sequences. In the case of stream-valued functions, the representatives are non-wellfounded trees pieced together in a coinductive fashion from well-founded trees. The definition requires an alternating fixpoint construction of some ubiquity

Bridging the GUI gap with reactive values and relations

There are at present two ways to write GUIs for functional code. One is to use standard GUI toolkits, with all the benefits they bring in terms of feature completeness, choice of platform, conformance to platform-specific look-and-feel, long-term viability, etc. However, such GUI APIs mandate an imperative programming style for the GUI and related parts of the application. Alternatively, we can use a functional GUI toolkit. The GUI can then be written in a functional style, but at the cost of foregoing many advantages of standard toolkits that often will be of critical importance. This paper introduces a light-weight framework structured around the notions of reactive values and reactive relations . It allows standard toolkits to be used from functional code written in a functional style. We thus bridge the gap between the two worlds, bringing the advantages of both to the developer. Our framework is available on Hackage and has been been validated through the development of non-trivial applications in a commercial context, and with different standard GUI toolkits

Equivalence of call-by-name and call-by-need for lambda-calculi with letrec

We develop a proof method to show that in a (deterministic) lambda calculus with letrec and equipped with contextual equivalence the call-by-name and the call-by-need evaluation are equivalent, and also that the unrestricted copy-operation is correct. Given a let-binding x = t, the copy-operation replaces an occurrence of the variable x by the expression t, regardless of the form of t. This gives an answer to unresolved problems in several papers, it adds a strong method to the tool set for reasoning about contextual equivalence in higher-order calculi with letrec, and it enables a class of transformations that can be used as optimizations. The method can be used in different kind of lambda calculi with cyclic sharing. Probably it can also be used in non-deterministic lambda calculi if the variable x is "deterministic", i.e., has no interference with non-deterministic executions. The main technical idea is to use a restricted variant of the infinitary lambda-calculus, whose objects are the expressions that are unrolled w.r.t. let, to define the infinite developments as a reduction calculus on the infinite trees and showing a standardization theorem

Program transformation for functional circuit descriptions

We model sequential synchronous circuits on the logical level by signal-processing programs in an extended lambda calculus Lpor with letrec, constructors, case and parallel or (por) employing contextual equivalence. The model describes gates as (parallel) boolean operators, memory using a delay, which in turn is modeled as a shift of the list of signals, and permits also constructive cycles due to the parallel or. It opens the possibility of a large set of program transformations that correctly transform the expressions and thus the represented circuits and provides basic tools for equivalence testing and optimizing circuits. A further application is the correct manipulation by transformations of software components combined with circuits. The main part of our work are proof methods for correct transformations of expressions in the lambda calculus Lpor, and to propose the appropriate program transformations

Closures of may and must convergence for contextual equivalence

We show on an abstract level that contextual equivalence in non-deterministic program calculi defined by may- and must-convergence is maximal in the following sense. Using also all the test predicates generated by the Boolean, forall- and existential closure of may- and must-convergence does not change the contextual equivalence. The situation is different if may- and total must-convergence is used, where an expression totally must-converges if all reductions are finite and terminate with a value: There is an infinite sequence of test-predicates generated by the Boolean, forall- and existential closure of may- and total must-convergence, which also leads to an infinite sequence of different contextual equalities

Constructive interval temporal logic in Alf

This paper gives an implementation of an interval temporal logic in a constructive type theory, using the Alf proof system. After explaining the constructive approach, its relevance to interval temporal logic and potential applications of our work, we explain the fundamentals of the Alf system. We then present the implementation of the logic and give a number of examples of its use. We conclude by exploring how the work can be extended in the future

Composing graphical user interfaces in a purely functional language

This thesis is about building interactive graphical user interfaces in a compositional manner. Graphical user interface application hold out the promise of providing users with an interactive, graphical medium by which they can carry out tasks more effectively and conveniently. The application aids the user to solve some task. Conceptually, the user is in charge of the graphical medium, controlling the order and the rate at which individual actions are performed. This user-centred nature of graphical user interfaces has considerable ramifications for how software is structured. Since the application now services the user rather than the other way around, it has to be capable of responding to the user's actions when and in whatever order they might occur. This transfer of overall control towards the user places heavy burden on programming systems, a burden that many systems don't support too well. Why? Because the application now has to be structured so that it is responsive to whatever action the user may perform at any time. The main contribution of this thesis is to present a compositional approach to constructing graphical user interface applications in a purely functional programming language The thesis is concerned with the software techniques used to program graphical user interface applications, and not directly with their design. A starting point for the work presented here was to examine whether an approach based on functional programming could improve how graphical user interfaces are built. Functional programming languages, and Haskell in particular, contain a number of distinctive features such as higher-order functions, polymorphic type systems, lazy evaluation, and systematic overloading, that together pack quite a punch, at least according to proponents of these languages. A secondary contribution of this thesis is to present a compositional user interface framework called Haggis, which makes good use of current functional programming techniques. The thesis evaluates the properties of this framework by comparing it to existing systems