Semantics

Conservation laws for free!

In this year's POPL, Bob Atkey made a splash by showing how to get 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, which by Noether’s theorem is 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.

Seemingly impossible programs

In case this one went under the radar, at POPL'12, Martín Escardó gave a tutorial on seemingly impossible functional programs:

Programming language semantics is typically applied to
prove compiler correctness and allow (manual or automatic) program
verification. Certain kinds of semantics can also be applied to
discover programs that one wouldn't have otherwise thought of. This is
the case, in particular, for semantics that incorporate topological
ingredients (limits, continuity, openness, compactness). For example,
it turns out that some function types (X -> Y) with X infinite (but
compact) do have decidable equality, contradicting perhaps popular
belief, but certainly not (higher-type) computability theory. More
generally, one can often check infinitely many cases in finite time.

I will show you such programs, run them fast in surprising instances,
and introduce the theory behind their derivation and working. In
particular, I will study a single (very high type) program that (i)
optimally plays sequential games of unbounded length, (ii) implements
the Tychonoff Theorem from topology (and builds finite-time search
functions for infinite sets), (iii) realizes the double-negation shift
from proof theory (and allows us to extract programs from classical
proofs that use the axiom of countable choice). There will be several
examples in the languages Haskell and Agda.

A shorter version (coded in Haskell) appears in Andrej Bauer's blog.

sml-family.org

In his blog, Bob Harper, in joint effort with Dave MacQueen and Lars Bergstrom, announces the launch of sml-family.org:

The Standard ML Family project provides a home for online versions of various formal definitions of Standard ML, including the "Definition of Standard ML, Revised" (Standard ML 97). The site also supports coordination between different implementations of the Standard ML (SML) programming language by maintaining common resources such as the documentation for the Standard ML Basis Library and standard test suites. The goal is to increase compatibility and resource sharing between Standard ML implementations.

The site includes a history section devoted to the history of ML, and of Standard ML in particular. This section will contain a collection of original source documents relating to the design of the language.

Inferring algebraic effects

Logical methods in computer science just published Matija Pretnar's latest take on algebraic effects and handlers:

We present a complete polymorphic effect inference algorithm for an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references and many others. Our main aim is to offer the programmer a useful insight into the effectful behaviour of programs. Handlers help here by cutting down possible effects and the resulting lengthy output that often plagues precise effect systems. Additionally, we present a set of methods that further simplify the displayed types, some even by deliberately hiding inferred information from the programmer.

Pretnar and Bauer's Eff has made previous appearances here on LtU. Apart from the new fangled polymorphic effect system, this paper also contains an Eff tutorial.

Luca Cardelli Festschrift

Earlier this week Microsoft Research Cambridge organised a Festschrift for Luca Cardelli. The preface from the book:

Luca Cardelli has made exceptional contributions to the world of programming
languages and beyond. Throughout his career, he has re-invented himself every
decade or so, while continuing to make true innovations. His achievements span
many areas: software; language design, including experimental languages;
programming language foundations; and the interaction of programming languages
and biology. These achievements form the basis of his lasting scientific leadership
and his wide impact.
...
Luca is always asking "what is new", and is always looking to
the future. Therefore, we have asked authors to produce short pieces that would
indicate where they are today and where they are going. Some of the resulting
pieces are short scientific papers, or abridged versions of longer papers; others are
less technical, with thoughts on the past and ideas for the future. We hope that
they will all interest Luca.

Hopefully the videos will be posted soon.

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.

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.

Mechanized λ<sub>JS</sub>

Mechanized λJS
The Brown PLT Blog, 2012-06-04

In an earlier post, we introduced λJS, our operational semantics for JavaScript. Unlike many other operational semantics, λJS is no toy, but strives to correctly model JavaScript's messy details. To validate these claims, we test λJS with randomly generated tests and with portions of the Mozilla JavaScript test suite.

Testing is not enough. Despite our work, other researchers found a missing case in λJS. Today, we're introducing Mechanized λJS, which comes with a machine-checked proof of correctness, using the Coq proof assistant.

More work on mechanizing the actual, implemented semantics of a real language, rather than a toy.

Tool Demo: Scala-Virtualized

Tool Demo: Scala-Virtualized

This paper describes Scala-Virtualized, which extends the Scala language and compiler with a small number of features that enable combining the benefits of shallow and deep embeddings of DSLs. We demonstrate our approach by showing how to embed three different domain-specific languages in Scala. Moreover, we summarize how others have been using our extended compiler in their own research and teaching. Supporting artifacts of our tool include web-based tutorials, nightly builds, and an Eclipse update site hosting an up-to-date version of the Scala IDE for Eclipse based on the Virtualized Scala compiler and standard library.

Scala has always had a quite good EDSL story thanks to implicits, dot- and paren-inference, and methods-as-operators. Lately there are proposals to provide it with both macros-in-the-camlp4-sense and support for multi-stage programming. This paper goes into some depth on the foundations of the latter subject.

Vellvm: Formalizing the LLVM Intermediate Representation for Verified Program Transformations

Vellvm: Formalizing the LLVM Intermediate Representation for Verified Program Transformations by Jianzhou Zhao, Santosh Nagarakatte, Milo M. K. Martin, and Steve Zdancewic, POPL 2012

This paper presents Vellvm (verified LLVM), a framework for reasoning about programs expressed in LLVM's intermediate representation and transformations that operate on it. Vellvm provides a mechanized formal semantics of LLVM's intermediate representation, its type system, and properties of its SSA form. The framework is built using the Coq interactive theorem prover. It includes multiple operational semantics and proves relations among them to facilitate different reasoning styles and proof techniques.

To validate Vellvm's design, we extract an interpreter from the Coq formal semantics that can execute programs from LLVM test suite and thus be compared against LLVM reference implementations. To demonstrate Vellvm's practicality, we formalize and verify a previously proposed transformation that hardens C programs against spatial memory safety violations. Vellvm's tools allow us to extract a new, verified implementation of the transformation pass that plugs into the real LLVM infrastructure; its performance is competitive with the non-verified, ad-hoc original.

This obviously represents huge progress in marrying the theoretical benefits of tools like Coq with the practical benefits of tools like LLVM. We can only hope that this spurs further development in practical certified software development.

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