Lambda the Ultimate

We present Haskell libraries that statically ensure the safe use of resources such as file handles. We statically prevent accessing an already closed handle or forgetting to close it. The libraries can be trivially extended to other resources such as database connections and graphic contexts...

Region annotations are part of an expression's inferred type. Our new Haskell encoding of monadic regions as monad transformers needs no witness terms. It assures timely deallocation even when resources have markedly different lifetimes and the identity of the longest-living resource is determined only dynamically.

For contrast, we also implement a Haskell library for manual resource management, where deallocation is explicit and safety is assured by a form of linear types. We implement the linear typing in Haskell with the help of phantom types and a parameterized monad to statically track the type-state of resources.

I am starting to think we need a department for effect systems and related topics (though we managed without a monads department!)...

You'll probably want to read the code, so go ahead. The code makes it plain which features of the type system are needed to achieve the end result.

An ancient paper (July 1978: 30 years ago) from the long gone Lisp Bulletin by Harald Wertz.

The system describes attempts to improve incompletely specified Lisp programs, without however resorting to more information, in the form of specifications, test cases or the like.

A second paper on the system is Stereotyped Program Debugging: an Aid for Novice Programmers.

Partial vectorisation of Haskell programs. Manuel M. T. Chakravarty, Roman Leshchinskiy, Simon Peyton Jones, and Gabriele Keller, Proc ACM Workshop on Declarative Aspects of Multicore Programming, San Francisco, Jan 2008.

Vectorisation for functional programs, also called the flattening transformation, relies on drastically reordering computations and restructuring the representation of data types. As a result, it only applies to the purely functional core of a fully-fledged functional language, such as Haskell or ML. A concrete implementation needs to apply vectorisation selectively and integrate vectorised with unvectorised code. This is challenging, as vectorisation alters the data representation, which must be suitably converted between vectorised and unvectorised code. In this paper, we present an approach to partial vectorisation that selectively vectorises sub-expressions and data types, and also, enables linking vectorised with unvectorised modules.

The idea is fairly simple, and utilizes conversion between vectorized and unvectorized representations of the datatypes. A formal translation scheme is provided.

Data Parallel Haskell papers are here.

Catch me if you can: Towards type-safe, hierarchical, lightweight, polymorphic and efficient error management in OCaml, by David Teller, Arnaud Spiwack, Till Varoquaux:

This is the year 2008 and ML-style exceptions are everywhere. Most modern languages, whether academic or industrial, feature some variant of this mechanism. Languages such as Java even have a degree of out-of-the-box static coverage-checking for such exceptions, which is currently not available for ML languages, at least not without resorting to external tools.

In this document, we demonstrate a design principle and a tiny library for managing errors in a functional manner, with static coverage-checking, automatically-inferred, structurally typed and hierarchical exceptional cases, all of this for what we believe is a reasonable run-time cost. Our work is based on OCaml and features simple uses of higher-order programming, low-level exceptions, phantom types, polymorphic variants and compile-time code
rewriting.

Exhaustively checked, user-friendly exception handling was a bit of an open problem for awhile. As the paper details, languages supported either cumbersome, exhaustively checked polymorphic exceptions, as in Haskell, or we had unchecked easily extensible monomorphic exceptions, as in ML, or we had checked, extensible exceptions using a universal type as in Java.

Supporting exhaustively checked, easily extensible polymorphic exceptions seemed quite a challenge, which this paper solves using monadic error handling and nested polymorphic variants. The paper also gives a good overview of current techniques of exception checking in OCaml, ie. ocamlexc.

The performance of such exceptions is understandably lower than native exceptions, given all the thunking and indirection that monads entail. The authors attempt various implementations and test their performance against native exceptions. Ultimately, monadic error management seems acceptable for actual error handling, but not for control flow as native exceptions are sometimes used in OCaml.

One interesting extension is to consider how efficient the implementations would be given more sophisticated control flow operators, such as continuations, coroutines, or delimited continuations, or whether native exceptions can be salvaged using a type and effects system in place of monads.

Functional Netlists, Sungwoo Park, Jinha Kim, Hyeonseung Im. ICFP 2008.

In efforts to overcome the complexity of the syntax and the lack of formal semantics of conventional hardware description languages, a number of functional hardware description languages have been developed. Like conventional hardware description languages, however, functional hardware description languages eventually convert all source programs into netlists, which describe wire connections in hardware circuits at the lowest level and conceal all high-level descriptions written into source programs.

We develop a variant of the lambda calculus, called l-lambda (linear lambda), which may serve as a high-level substitute for netlists. In order to support higher-order functions, l-lambda uses a linear type system which enforces the linear use of variables of function type. The translation of l-lambda into structural descriptions of hardware circuits is sound and complete in the sense that it maps expressions only to realizable hardware circuits and that every realizable hardware circuit has a corresponding expression in l-lambda. To illustrate the use of l-lambda as a high-level substitute for netlists, we design a simple hardware description language that extends l with polymorphism, and use it to implement a Fast Fourier Transform circuit.

Given the recent discussion about hardware synthesis languages, the appearance of this paper seems timely. The use of linear types is perhaps unsurprising from a technical point of view, but it's surprising when you consider how frequently and in how many different contexts they appear.

Also, one thing I don't understand: there's apparently a difference between a "hardware description language" and a "hardware synthesis language". If anyone could explain what the difference means, I'd appreciate it. :)

Non-Deterministic Recursive Ascent Parsing, Renee Leermakers. 1991 conference on European chapter of the Association for Computational Linguistics.

A purely functional implementation of LR-parsers is given, together with a simple correctness proof. It is presented as a generalization of the recursive descent parser. For non-LR grammars the time-complexity of our parser is cubic if the functions that constitute the parser are implemented as memo-functions, i.e. functions that memorize the results of previous invocations. Memo-functions also facilitate a simple way to construct a very compact representation of the parse forest. For LR(0) grammars, our algorithm is closely related to the recursive ascent parsers recently discovered by Kruseman Aretz [1] and Roberts [2]. Extended CF grammars (grammars with regular expressions at the right hand side) can be parsed with a simple modification of the LR-parser for normal CF grammars.

How LR parsers worked always confused me until I learned about their presentation in terms of recursive ascent.

Parametric Higher-Order Abstract Syntax for Mechanized Semantics

We present parametric higher-order abstract syntax (PHOAS), a new approach to formalizing the syntax of programming languages in computer proof assistants based on type theory. Like higher-order abstract syntax (HOAS), PHOAS uses the meta language's binding constructs to represent the object language's binding constructs. Unlike HOAS, PHOAS types are definable in general-purpose type theories that support traditional functional programming, like Coq's Calculus of Inductive Constructions. We walk through how Coq can be used to develop certified, executable program transformations over several statically-typed functional programming languages formalized with PHOAS; that is, each transformation has a machine-checked proof of type preservation and semantic preservation. Our examples include CPS translation and closure conversion for simply-typed lambda calculus, CPS translation for System F, and translation from a language with ML-style pattern matching to a simpler language with no variable-arity binding constructs. By avoiding the syntactic hassle associated with first-order representation techniques, we achieve a very high degree of proof automation.

I was aware of this some months ago now, but held back commenting on it at Adam's request until it had been accepted for publication, which it now apparently has. This is (one element of) Adam's continued work on LambdaTamer, his Coq-based environment for building certified compilers. There is a new version of LambdaTamer using this parametric higher-order abstract syntax approach. The new version also works in current and future versions of Coq, unlike the previous version. Finally, Adam is apparently working on a paper regarding "type-theoretic denotational semantics for higher order, impure object languages" and is post-docing with Greg Morrisett. The relationship between Adam's work and the YNot project is a bit unclear to me; perhaps either Adam or Greg could help clarify that.

Update: Whoops. I got ahead of myself and neglected to notice that the paper is not actually yet available, although the new version of LambdaTamer is. So at the moment, this story is merely to note that the paper exists and to provide a link to the new LambdaTamer. My apologies to Adam and the LtU readership.

2nd Update: The paper is now available at the link, in either PostScript or PDF form.

FPH: First-class Polymorphism for Haskell, by Dimitrios Vytiniotis, Stephanie Weirich and Simon Peyton Jones:

Languages supporting polymorphism typically have ad-hoc restrictions on where polymorphic types may occur. Supporting “firstclass” polymorphism, by lifting those restrictions, is obviously desirable, but it is hard to achieve this without sacrificing type inference. We present a new type system for higher-rank and impredicative polymorphism that improves on earlier proposals: it is an extension of Damas-Milner; it relies only on System F types; it has a simple, declarative specification; it is robust to program transformations; and it enjoys a complete and decidable type inference algorithm.

Under Related Work, the authors provide a detailed comparison of their system with ML^F, and HM^F.

Conrad Barski has posted a sneak peak from his upcoming Lisp textbook/comic: Land of Lisp.

The first slides may seem unrelated, but boy does the message sting when you reach the ending...

FPers will be quick to note, of course, that this being April Fools' Day the whole thing is a joke and we can all go back to Haskell...

Disciple is an explicitly lazy dialect of Haskell which includes:

• first class destructive update of arbitrary data.
• computational effects without the need for state monads.
• type directed field projections.

All this and more through the magic of effect typing.

The wiki page has more information, unfortunately there's no paper yet summarizing the ideas and results. Their effect system is quite interesting. Some of the ideas recently discussed here are implemented in Disciple.

via Haskell Cafe