Breaking the Complexity Barrier of Pure Functional Programs with Impure Data Structures

Breaking the Complexity Barrier of Pure Functional Programs with Impure Data Structures by Pieter Wuille and Tom Schrijvers:

Pure functional programming language offer many advantages over impure languages. Unfortunately, the absence of destructive update, imposes a complexity barrier. In imperative languages, there are algorithms and data structures with better complexity. We present our project for combining existing program transformation techniques to transform inefficient pure data structures into impure ones with better complexity. As a consequence, the programmer is not exposed to the impurity and retains the advantages of purity.

This paper is along the same lines a question I asked a couple of years ago. The idea here is to allow programming using immutable interfaces, and then automatically transform it into a more efficient mutable equivalent.

Apple Introduces Swift

Apple today announced a new programming language for their next version of Mac OS X and iOS called Swift.

The Language Guide has more details about the potpourri of language features.

Functional Geometry and the Traite ́ de Lutherie

Functional Geometry and the Traite ́ de Lutherie by Harry Mairson, Brandeis University.

We describe a functional programming approach to the design of outlines of eighteenth-century string instruments. The approach is based on the research described in Francois Denis’s book, Traite ́ de lutherie. The programming vernacular for Denis’s instructions, which we call functional geometry, is meant to reiterate the historically justified language and techniques of this musical instrument design. The programming metaphor is entirely Euclidean, involving straightedge and compass constructions, with few (if any) numbers, and no Cartesian equations or grid. As such, it is also an interesting approach to teaching programming and mathematics without numerical calculation or equational reasoning.

The advantage of this language-based, functional approach to lutherie is founded in the abstract characterization of common patterns in instrument design. These patterns include not only the abstraction of common straightedge and compass constructions, but of higher-order conceptualization of the instrument design process. We also discuss the role of arithmetic, geometric, harmonic, and subharmonic proportions, and the use of their rational approximants.

The Size-Change Termination Principle for Constructor Based Languages

The Size-Change Termination Principle for Constructor Based Languages, by Pierre Hyvernat:

This paper describes an automatic termination checker for a generic first-order call-by-value language in ML style. We use the fact that value are built from variants and tuples to keep some information about how arguments of recursive call evolve during evaluation. The result is a criterion for termination extending the size-change termination principle of Lee, Jones and Ben-Amram that can detect size changes inside subvalues of arguments. Moreover the corresponding algorithm is easy to implement, making it a good candidate for experimentation.

Looks like a relatively straightforward and complete description of a termination checker based on a notion of 'sized types' limited to first-order programs. LtU has covered this topic before, although this new paper doesn't seem to reference that particular Abel work.

Dependently-Typed Metaprogramming (in Agda)

Conor McBride gave an 8-lecture summer course on Dependently typed metaprogramming (in Agda) at the Cambridge University Computer Laboratory:

Dependently typed functional programming languages such as Agda are capable of expressing very precise types for data. When those data themselves encode types, we gain a powerful mechanism for abstracting generic operations over carefully circumscribed universes. This course will begin with a rapid depedently-typed programming primer in Agda, then explore techniques for and consequences of universe constructions. Of central importance are the “pattern functors” which determine the node structure of inductive and coinductive datatypes. We shall consider syntactic presentations of these functors (allowing operations as useful as symbolic differentiation), and relate them to the more uniform abstract notion of “container”. We shall expose the double-life containers lead as “interaction structures” describing systems of effects. Later, we step up to functors over universes, acquiring the power of inductive-recursive definitions, and we use that power to build universes of dependent types.

The lecture notes, code, and video captures are available online.

As with his previous course, the notes contain many(!) mind expanding exploratory exercises, some of which quite challenging.

Extensible Effects -- An Alternative to Monad Transformers

Extensible Effects -- An Alternative to Monad Transformers, by Oleg Kiselyov, Amr Sabry and Cameron Swords:

We design and implement a library that solves the long-standing problem of combining effects without imposing restrictions on their interactions (such as static ordering). Effects arise from interactions between a client and an effect handler (interpreter); interactions may vary throughout the program and dynamically adapt to execution conditions. Existing code that relies on monad transformers may be used with our library with minor changes, gaining efficiency over long monad stacks. In addition, our library has greater expressiveness, allowing for practical idioms that are inefficient, cumbersome, or outright impossible with monad transformers.

Our alternative to a monad transformer stack is a single monad, for the coroutine-like communication of a client with its handler. Its type reflects possible requests, i.e., possible effects of a computation. To support arbitrary effects and their combinations, requests are values of an extensible union type, which allows adding and, notably, subtracting summands. Extending and, upon handling, shrinking of the union of possible requests is reflected in its type, yielding a type-and-effect system for Haskell. The library is lightweight, generalizing the extensible exception handling to other effects and accurately tracking them in types.

A follow-up to Oleg's delimited continuation adaptation of Cartwright and Felleisen's work on Extensible Denotational Language Specifications, which is a promising alternative means of composing effects to the standard monad transformers.

This work embeds a user-extensible effect EDSL in Haskell by encoding all effects into a single effect monad using a novel open union type and the continuation monad. The encoding is very similar to recent work on Algebraic Effects and Handlers, and closely resembles a typed client-server interaction ala coroutines. This seems like a nice convergence of the topics covered in the algebraic effects thread and other recent work on effects, and it's more efficient than monad transformers to boot.

How OCaml type checker works -- or what polymorphism and garbage collection have in common

How OCaml type checker works -- or what polymorphism and garbage collection have in common

There is more to Hindley-Milner type inference than the Algorithm W. In 1988, Didier Rémy was looking to speed up the type inference in Caml and discovered an elegant method of type generalization. Not only it is fast, avoiding the scan of the type environment. It smoothly extends to catching of locally-declared types about to escape, to type-checking of universals and existentials, and to implementing MLF.

Alas, both the algorithm and its implementation in the OCaml type checker are little known and little documented. This page is to explain and popularize Rémy's algorithm, and to decipher a part of the OCaml type checker. The page also aims to preserve the history of Rémy's algorithm.

The attraction of the algorithm is its insight into type generalization as dependency tracking -- the same sort of tracking used in automated memory management such as regions and generational garbage collection. Generalization can be viewed as finding dominators in the type-annotated abstract syntax tree with edges for shared types. Fluet and Morrisett's type system for regions and MetaOCaml environment classifiers use the generalization of a type variable as a criterion of region containment. Uncannily, Rémy's algorithm views the region containment as a test if a type variable is generalizable.

As usual with Oleg, there's a lot going on here. Personally, I see parallels with "lambda with letrec" and "call-by-push-value," although making the connection with the latter takes some squinting through some of Levy's work other than his CBPV thesis. Study this to understand OCaml type inference and/or MLF, or for insights into region typing, or, as the title suggests, for suggestive analogies between polymorphism and garbage collection. comes from David Pollak and aims at revolutionizing building tablet apps, but the main attraction now seems to be in exploring the way data flow and cloud computing can be integrated. The screencast is somewhat underwhelming but at least convinces me that there is a working prototype (I haven't looked further than the website as yet). The vision document has some nice ideas. came up recently in the discussion of the future of spreadsheets.

Milner Symposium 2012

The Milner Symposium 2012 was held in Edinburgh this April in memory of the late Robin Milner.

The Milner Symposium is a celebration of the life and work of one of the world's greatest computer scientists, Robin Milner. The symposium will feature leading researchers whose work is inspired by Robin Milner.

The programme consisted of academic talks by colleagues and past students. The talks and slides are available online.

I particularly liked the interleaving of the personal and human narrative underlying the scientific journey. A particularly good example is Joachim Parrow's talk on the origins of the pi calculus. Of particular interest to LtU members is the panel on the future of functional programming languages, consisting of Phil Wadler, Xavier Leroy, David MacQueen, Martin Odersky, Simon Peyton-Jones, and Don Syme.

CUFP 2012 Tutorials

If you are in Denmark in September you should attend. If not, raise a glass to salute what is now abundantly clear: FPLs are conquering the ("real") world.

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