The Environment as an Argument

Context-awareness as defined in the setting of Ubiquitous Computing [3] is all about expressing the dependency of a specific computation upon some implicit piece of information. The manipulation and expression of such dependencies may thus be neatly encapsulated in a language where computations are first-class values. Perhaps surprisingly however, context-aware programming has not been explored in a functional setting, where first-class computations and higher-order functions are commonplace. In this paper we present an embedded domain-specific language (EDSL) for constructing context-aware applications in the functional programming language Haskell. © 2012 Springer-Verlag

Fibrational induction meets effects

This paper provides several induction rules that can be used to prove properties of effectful data types. Our results are semantic in nature and build upon Hermida and Jacobs’ fibrational formulation of induction for polynomial data types and its extension to all inductive data types by Ghani, Johann, and Fumex. An effectful data type μ(TF) is built from a functor F that describes data, and a monad T that computes effects. Our main contribution is to derive induction rules that are generic over all functors F and monads T such that μ(TF) exists. Along the way, we also derive a principle of definition by structural recursion for effectful data types that is similarly generic. Our induction rule is also generic over the kinds of properties to be proved: like the work on which we build, we work in a general fibrational setting and so can accommodate very general notions of properties, rather than just those of particular syntactic forms. We give examples exploiting the generality of our results, and show how our results specialize to those in the literature, particularly those of Filinski and Støvring

Constructing applicative functors

Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of constructing useful functors of this type, just as transformers are used to construct computational monads. For example, coends, familiar to functional programmers as existential types, yield a range of useful applicative functors, including left Kan extensions. Other constructions are final fixed points, a limited sum construction, and a generalization of the semi-direct product of monoids. Implementations in Haskell are included where possible

Session-ocaml: a session-based library with polarities and lenses

We propose session-ocaml, a novel library for session-typed concurrent/distributed programming in OCaml. Our technique solely relies on parametric polymorphism, which can encode core session type structures with strong static guarantees. Our key ideas are: ( ) polarised session types, which give an alternative formulation of duality enabling OCaml to automatically infer an appropriate session type in a session with a reasonable notational overhead; and ( ) a parameterised monad with a data structure called ‘slots’ manipulated with lenses, which can statically enforce session linearity and delegations. We show applications of session-ocaml including a travel agency usecase and an SMTP protocol

From parametricity to conservation laws, via Noether's Theorem

Invariance is of paramount importance in programming languages and in physics. In programming languages, John Reynolds' theory of relational parametricity demonstrates that parametric polymorphic programs are invariant under change of data representation, a property that yields "free" theorems about programs just from their types. In physics, Emmy Noether showed that if the action of a physical system is invariant under change of coordinates, then the physical system has a conserved quantity: a quantity that remains constant for all time. Knowledge of conserved quantities can reveal deep properties of physical systems. For example, the conservation of energy is by Noether's theorem a consequence of a system's invariance under time-shifting. In this paper, we link Reynolds' relational parametricity with Noether's theorem for deriving conserved quantities. We propose an extension of System Fω with new kinds, types and term constants for writing programs that describe classical mechanical systems in terms of their Lagrangians. We show, by constructing a relationally parametric model of our extension of Fω, that relational parametricity is enough to satisfy the hypotheses of Noether's theorem, and so to derive conserved quantities for free, directly from the polymorphic types of Lagrangians expressed in our system

A New Linear Logic for Deadlock-Free Session-Typed Processes

The π -calculus, viewed as a core concurrent programming language, has been used as the target of much research on type systems for concurrency. In this paper we propose a new type system for deadlock-free session-typed π -calculus processes, by integrating two separate lines of work. The first is the propositions-as-types approach by Caires and Pfenning, which provides a linear logic foundation for session types and guarantees deadlock-freedom by forbidding cyclic process connections. The second is Kobayashi’s approach in which types are annotated with priorities so that the type system can check whether or not processes contain genuine cyclic dependencies between communication operations. We combine these two techniques for the first time, and define a new and more expressive variant of classical linear logic with a proof assignment that gives a session type system with Kobayashi-style priorities. This can be seen in three ways: (i) as a new linear logic in which cyclic structures can be derived and a CYCLE -elimination theorem generalises CUT -elimination; (ii) as a logically-based session type system, which is more expressive than Caires and Pfenning’s; (iii) as a logical foundation for Kobayashi’s system, bringing it into the sphere of the propositions-as-types paradigm

Observed communication semantics for classical processes

Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication, and use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences

Refining Inductive Types

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce purpose-specific refinements on an ad hoc basis, developers must anticipate which refinements to include in libraries, and implementations must often store redundant information about data and their refinements. In this paper we show how to generically derive inductive characterisations of refinements of inductive types, and argue that these characterisations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. Our characterisations also ensure that standard techniques for programming with and reasoning about inductive types are applicable to refinements, and that refinements can themselves be further refined

Molecular mechanisms of EGF signaling-dependent regulation of pipe, a gene crucial for dorsoventral axis formation in Drosophila

During Drosophila oogenesis the expression of the sulfotransferase Pipe in ventral follicle cells is crucial for dorsoventral axis formation. Pipe modifies proteins that are incorporated in the ventral eggshell and activate Toll signaling which in turn initiates embryonic dorsoventral patterning. Ventral pipe expression is the result of an oocyte-derived EGF signal which down-regulates pipe in dorsal follicle cells. The analysis of mutant follicle cell clones reveals that none of the transcription factors known to act downstream of EGF signaling in Drosophila is required or sufficient for pipe regulation. However, the pipe cis-regulatory region harbors a 31-bp element which is essential for pipe repression, and ovarian extracts contain a protein that binds this element. Thus, EGF signaling does not act by down-regulating an activator of pipe as previously suggested but rather by activating a repressor. Surprisingly, this repressor acts independent of the common co-repressors Groucho or CtBP