Reasoning about modular datatypes with Mendler induction

In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof assistants that are based on type theory, like Coq. The reason is that it involves type definitions, such as those of type-level fixpoint operators, that are not strictly positive. The known work-around of impredicative encodings is problematic, insofar as it impedes conventional inductive reasoning. Weak induction principles can be used instead, but they considerably complicate proofs. This paper proposes a novel and simpler technique to reason inductively about impredicative encodings, based on Mendler-style induction. This technique involves dispensing with dependent induction, ensuring that datatypes can be lifted to predicates and relying on relational formulations. A case study on proving subject reduction for structural operational semantics illustrates that the approach enables modular proofs, and that these proofs are essentially similar to conventional ones.Comment: In Proceedings FICS 2015, arXiv:1509.0282

An algebraic basis for specifying and enforcing access control in security systems

Security services in a multi-user environment are often based on access control mechanisms. Static aspects of an access control policy can be formalised using abstract algebraic models. We integrate these static aspects into a dynamic framework considering requesting access to resources as a process aiming at the prevention of access control violations when a program is executed. We use another algebraic technique, monads, as a meta-language to integrate access control operations into a functional programming language. The integration of monads and concepts from a denotational model for process algebras provides a framework for programming of access control in security systems

Aspect-Oriented Programming with Type Classes

We consider the problem of adding aspects to a strongly typed language which supports type classes. We show that type classes as supported by the Glasgow Haskell Compiler can model an AOP style of programming via a simple syntax-directed transformation scheme where AOP programming idioms are mapped to type classes. The drawback of this approach is that we cannot easily advise functions in programs which carry type annotations. We sketch a more principled approach which is free of such problems by combining ideas from intentional type analysis with advanced overloading resolution strategies. Our results show that type-directed static weaving is closely related to type class resolution -- the process of typing and translating type class programs

Safe Concurrency Introduction through Slicing

Traditional refactoring is about modifying the structure of existing code without changing its behaviour, but with the aim of making code easier to understand, modify, or reuse. In this paper, we introduce three novel refactorings for retrofitting concurrency to Erlang applications, and demonstrate how the use of program slicing makes the automation of these refactorings possible

Algorithmic Debugging of Real-World Haskell Programs: Deriving Dependencies from the Cost Centre Stack

Existing algorithmic debuggers for Haskell require a transformation of all modules in a program, even libraries that the user does not want to debug and which may use language features not supported by the debugger. This is a pity, because a promising ap- proach to debugging is therefore not applicable to many real-world programs. We use the cost centre stack from the Glasgow Haskell Compiler profiling environment together with runtime value observations as provided by the Haskell Object Observation Debugger (HOOD) to collect enough information for algorithmic debugging. Program annotations are in suspected modules only. With this technique algorithmic debugging is applicable to a much larger set of Haskell programs. This demonstrates that for functional languages in general a simple stack trace extension is useful to support tasks such as profiling and debugging

A framework for point-free program transformation

The subject of this paper is functional program transformation in the so-called point-free style. By this we mean first translating programs to a form consisting only of categorically-inspired combinators, algebraic data types defined as fixed points of functors, and implicit recursion through the use of type-parameterized recursion patterns. This form is appropriate for reasoning about programs equationally, but difficult to actually use in practice for programming. In this paper we present a collection of libraries and tools developed at Minho with the aim of supporting the automatic conversion of programs to point-free (embedded in Haskell), their manipulation and rule-driven simplification, and the (limited) automatic application of fusion for program transformation.Fundação para a Ciência e a Tecnologia (FCT

Bidirectionalization for Free with Runtime Recording: Or, a Light-Weight Approach to the View-Update Problem

A bidirectional transformation is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some laws. Over the years, a lot of effort has been made to offer better language support for programming such transformations. In particular, a technique known as bidirectionalization is able to analyze and transform unidirectional programs written in general purpose languages, and "bidirectionalize" them. Among others, a technique termed as semantic bidirectionalization proposed by Voigtländer stands out in term of user-friendliness. The unidirectional program can be written using arbitrary language constructs, as long as the function is polymorphic and the language constructs respect parametricity. The free theorems that follow from the polymorphic type of the program allow a kind of forensic examination of the transformation, determining its effect without examining its implementation. This is convenient, in the sense that the programmer is not restricted to using a particular syntax; but it does require the transformation to be polymorphic. In this paper, we lift this polymorphism requirement to improve the applicability of semantic bidirectionalization. Concretely, we provide a type class PackM γ α μ, which intuitively reads "a concrete datatype γ is abstracted to a type α, and the 'observations' made by a transformation on values of type γ are recorded by a monad μ". With PackM, we turn monomorphic transformations into polymorphic ones, that are ready to be bidirectionalized. We demonstrate our technique with a case study of standard XML queries, which were considered beyond semantic bidirectionalization because of their monomorphic nature

Down with variables

Techn. Report DI-PURe-05.06.01The subject of this paper is point-free functional programming in Haskell. By this we mean writing programs using categorically-inspired combinators, algebraic data types defined as fixed points of functors, and impicit recursion through the use of type-parameterized recursion patterns. This style of programming is appropriate for program calculation (reasoning about programs equationally), but difficult to actually use in practice - most programmers use a mixture of the above elements with explicit recursion and manipulation of arguments. In this paper we present a mechanism that allows programmers to convert classic point-wise code into point-free style, and a Haskell library that enables the direct execution of the resulting code. Together, they make possible the use of point-free either as a direct programming style or as a domain into which programs can be transformed before being subject to further manipulation