Lambda the Ultimate

Sequent Calculus as a Compiler Intermediate Language
2016 by Paul Downen, Luke Maurer, Zena M. Ariola, Simon Peyton Jones

The typed λ-calculus arises canonically as the term language for a logic called natural deduction, using the Curry-Howard isomorphism: the pervasive connection between logic and programming languages asserting that propositions are types and proofs are programs. Indeed, for many people, the λ-calculus is the living embodiment of Curry-Howard.

But natural deduction is not the only logic! Conspicuously, natural deduction has a twin, born in the very same paper, called the sequent calculus. Thanks to the Curry-Howard isomorphism, terms of the sequent calculus can also be seen as a programming language with an emphasis on control flow.

How to Write Seemingly Unhygienic and Referentially Opaque Macros with Syntax-rules
By Oleg Kiselyov

This paper details how folklore notions of hygiene and referential transparency of R5RS macros are defeated by a systematic attack. We demonstrate syntax-rules that seem to capture user identifiers and allow their own identifiers to be captured by the closest lexical bindings. In other words, we have written R5RS macros that accomplish what commonly believed to be impossible.

We are nearing the day someone quips that C is an improvement on most of its successors (smirk). So reading this page from the SQLite website is instructive, as is reading the page on the tooling and coding practices that make this approach work.

I think none of this is news, and these approaches have been on the books for quite a bit. But still, as I said: an improvement on most of its successors. Hat tip: HN discussion.

Resource Polymorphism, by Guillaume Munch-Maccagnoni:

We present a resource-management model for ML-style programming languages, designed to be compatible with the OCaml philosophy and runtime model. This is a proposal to extend the OCaml language with destructors, move semantics, and resource polymorphism, to improve its safety, efficiency, interoperability, and expressiveness. It builds on the ownership-and-borrowing models of systems programming languages (Cyclone, C++11, Rust) and on linear types in functional programming (Linear Lisp, Clean, Alms). It continues a synthesis of resources from systems programming and resources in linear logic initiated by Baker.

It is a combination of many known and some new ideas. On the novel side, it highlights the good mathematical structure of Stroustrup's "Resource acquisition is initialisation" (RAII) idiom for resource management based on destructors, a notion sometimes confused with finalizers, and builds on it a notion of resource polymorphism, inspired by polarisation in proof theory, that mixes C++'s RAII and a tracing garbage collector (GC).
The proposal targets a new spot in the design space, with an automatic and predictable resource-management model, at the same time based on lightweight and expressive language abstractions. It is backwards-compatible: current code is expected to run with the same performance, the new abstractions fully combine with the current ones, and it supports a resource-polymorphic extension of libraries. It does so with only a few additions to the runtime, and it integrates with the current GC implementation. It is also compatible with the upcoming multicore extension, and suggests that the Rust model for eliminating data-races applies.

Interesting questions arise for a safe and practical type system, many of which have already been thoroughly investigated in the languages and prototypes Cyclone, Rust, and Alms.

An ambitious goal, and it would be an incredibly useful addition to OCaml. Might even displace Rust in some places, since you can theoretically avoid triggering the GC, but you have the excellent GC available when needed. This is definitely a pain point for Rust.

The Left Hand of Equals, by James Noble, Andrew P. Black, Kim B. Bruce, Michael Homer, Mark S. Miller:

When is one object equal to another object? While object identity is fundamental to object-oriented systems, object equality, although tightly intertwined with identity, is harder to pin down. The distinction between identity and equality is reflected in object-oriented languages, almost all of which provide two variants of “equality”, while some provide many more. Programmers can usually override at least one of these forms of equality, and can always define their own methods to distinguish their own objects.

This essay takes a reflexive journey through fifty years of identity and equality in object-oriented languages, and ends somewhere we did not expect: a “left-handed” equality relying on trust and grace.

This covers a lot of ground, not only historical, but conceptual, like the meaning of equality and objects. For instance, they consider Ralph Johnson on what object oriented programming means:

I explain three views of OO programming. The Scandinavian view is that an OO system is one whose creators realise that programming is modelling. The mystical view is that an OO system is one that is built out of objects that communicate by sending messages to each other, and computation is the messages flying from object to object. The software engineering view is that an OO system is one that supports data abstraction, polymorphism by late-binding of function calls, and inheritance.

And constrast with William Cook's autognosis/procedural-abstraction view, which we've discussed here before.

The paper's goal then becomes clear: "What can we do to provide an equality operator for a pure, autognostic object-oriented language?" They answer this question in the context of the Grace programming language. As you might expect from some of the authors, security and trust are important considerations.

Update: The migration of LtU to new servers is complete.

If you notice any issues with the site, please post in this thread (if you can), or email me at antonvs8 at (gmail domain).

Original announcement appears below:

This evening (Sunday, US Eastern time), Lambda the Ultimate will be migrated to new servers.

The site will be offline for around 30 minutes, while this migration and some database maintenance is in progress.

The new platform is a shiny new Kubernetes cluster, which will enable some long-overdue improvements to the site in 2018.

An update will be posted in this thread once the migration is complete.

Compiling a Subset of APL Into a Typed Intermediate Language

by Martin Elsman, Martin Dybdal

Traditionally, APL is an interpreted language ... In this paper, we present a compiler that compiles a subset of APL into a typed intermediate representation, which should serve as a practical and well-defined intermediate format for targeting parallel-architectures through a large number of existing tools and frameworks. The intermediate language is conceptually close to the language Repa. It supports shape-polymorphic functions and types that classify shapes. The compiler takes a simplified approach to certain aspects of APL. Following other APL compilation approaches, the compiler is based on lexical (i.e., static) identifier scoping and has no support for dynamic compilation (APL execute).

Terseness of APL is legendary, for good or bad. I keep finding more and more papers by Haskell community (and especially GHC contributors) working on efficient (parallel) arrays in Haskell.

There is a growing set of fascinating interviews with PL folks at People of Programming Languages.

Exploiting Vector Instructions with Generalized Stream Fusion

By Geoffrey Mainland, Roman Leshchinskiy, and Simon Peyton Jones.

Our ideas are implemented in modified versions of the GHC compiler and vector library. Benchmarks show that high-level Haskell code written using our compiler and libraries can produce code that is faster than both compiler- and hand-vectorized C.

This paper continues the promising line of research started in 1990 by Wadler (at least, that was how I learned of deforestation). Of course, there was a lot of development since then, but this specific paper introduces an interesting idea of multiple representations - potentially changing the game.

Partial sharing graphs offer a reduction model for the lambda calculus that is optimal in a sense put forward by Jean Jacques Levy. This model has seen interest wax and wane: initially it was thought to offer the most efficient possible technology for implementing the lambda calculus, but then an important result showed that bookkeeping overheads of any such model could be very high (Asperti & Mairson 1998). This result had a chilling effect on the initial wave of excitement over the technology.

Now Stefano Guerrini, one of the early investigators of partial sharing graphs, has an article with Marco Solieri (Guerrini & Solieri 2017) arguing that the gains from optimality can be very high and that partial sharing graphs can be relatively close to the best possible efficiency, within a quadratic factor on a conservative analysis (this is relatively close in terms of elementary recursion). Will the argument and result lead to renewed interest in partial sharing graphs from implementors of functional programming? We'll see...

(Asperti & Mairson 1998) Parallel beta reduction is not elementary recursive.

(Guerrini & Solieri 2017) Is the Optimal Implementation inefficient? Elementarily not.