Theory

A Tutorial on Proof Theoretic Foundations of Logic Programming

A Tutorial on Proof Theoretic Foundations of Logic Programming. Paola Bruscoli and Alessio Guglielmi. ICLP'03.

I just glanced through this tutorial, but since I know quite a few LtU readers are into proof theory, I thought I'd share the link.

The POPLmark Challenge

(via TYPES)

How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machine-checked proofs? To gauge progress in this area, we issue here a set of challenge problems, dubbed the POPLmark Challenge, chosen to exercise many aspects of programming languages that are known to be difficult to formalize.

A valid solution to the challenge will consist of appropriate software tools, a language representation strategy, and a demonstration that this infrastructure is sufficient to formalize the challenge problems.

The POPLmark team explains,

We are not ourselves automated reasoning experts but rather potential users; our impression is that current tools are almost at the point where they can be used routinely. It's time to bring mechanized metatheory to the masses - go to it!

A New Approach to Abstract Syntax with Variable Binding

Pitts and Gabbay, A New Approach to Abstract Syntax with Variable Binding, FAC 2001.

In the lambda calculus, the particular choice of variable names - even free variables - is irrelevant. Names serve two purposes:

  • as mnemonics to help human readers understand their role, and
  • to distinguish variables that are meant to be different and unify variables that are meant to be the same.

In a theory of binders, only the latter purpose is relevant. This is why it's so annoying to have to deal with capture-avoiding substitution, the Barendregt variable convention, gensym, and the like. These are all ways of getting around the fact that we've committed to a particular name when we really shouldn't have cared what the name was.

There are several standard ways to deal with this. Generating fresh names with gensym is awkward and forces the implementer to reimplement binding and substitution from scratch for each new object language; not to mention its violation of referential transparency. de Bruijn indices remove the variable names but are hard to read and understand. Higher-order abstract syntax implements binders in the object language as functions in the metalanguage, in order to reuse the built-in mechanisms of binding and substitution; but by mixing higher-order values in algebraic datatypes, structural induction is hard to recover.

This paper introduces a theory of fresh names that restores algebraic reasoning, referential transparency, and structural induction to algebraic datatypes with a HOAS-like notation for introducing binders into an abstract syntax. This is the set-theoretical basis for the authors' work on FreshML and FreshO'Caml, which we've discussed a little bit on LtU in the past.

Linear Forwarders

Linear forwarders are actually the basic mechanism of an earlier implementation of the pi calculus called the fusion machine. We modify the fusion machine, replacing fusions by forwarders. The result is more robust in the presence of failures, and more fundamental.

And also:

The point of this paper is to solve the problem of input capability with a language that is “just right” – it neither disallows more features than necessary (as does the join calculus), nor adds more implementation work than is necessary (as does the fusion machine).

Yes, these are the same capabilities as in capability-based security. I am looking forward to read the complete paper, as it seems to confirm my unclear ideas of how capabilities and various pi calculi are related.

μABC: A Minimal Aspect Calculus

Aspect-oriented programming is emerging as a powerful tool for system design and development. In this paper, we study aspects as primitive computational entities on par with objects, functions and horn-clauses. To this end, we introduce μABC, a name-based calculus, that incorporates aspects as primitive. In contrast to earlier work on aspects in the context of object-oriented and functional programming, the only computational entities in μABC are aspects. We establish a compositional translations into μABC from a functional language with aspects and higher-order functions. Further, we delineate the features required to support an aspect-oriented style by presenting a translation of μABC into an extended π-calculus.

Proof and Counterexample

Greg Restall is
writing a book, entitled Proof and Counterexample (or PnC for short). It's on logic viewed through the lens of proof theory. In particular, it covers natural deduction, sequent calculus, normalisation and cut-elimination. It's designed to both be state-of-the-art reseearch on these topics, together with an introduction appropriate for an advanced undergraduate. (We'll see how that works. I'll be test-driving the material with honours students from February to June in 2005.)

These pages will contain all sorts of different material about the book: comments, discussion, pointers to related material, and anything else that the community behind this site sees fit to write.

Newcomers to the field might wonder why this is relevant to programming languages, and some readers would regard this as pointless theory...

But if you are one of us guys excited by Curry-Howard, you might enjoy this wiki a lot.

The Kell Calculus

The Kell Calculus: A Family of Higher-Order Distributed Process Calculi
This paper presents the Kell calculus, a family of distributed process calculi, parameterized by languages for input patterns, that is intended as a basis for studying component-based distributed programming. The Kell calculus is built around a pi-calculus core, and follows five design principles which are essential for a foundational model of distributed and mobile programming: hierarchical localities, local actions, higher-order communication, programmable membranes, and dynamic binding. The paper discusses these principles, and defines the syntax and operational semantics common to all calculi in the Kell calculus family. The paper provides a co-inductive characterization of contextual equivalence for Kell calculi, under sufficient conditions on pattern languages, by means of a form of higher-order bisimulation called strong context bisimulation. The paper also contains several examples that illustrate the expressive power of Kell calculi.

NB: a family of calculi, parameterized by languages

See also: The Kell Calculus

In this page you will find information about the current state of the Kell calculus, links to published papers and drafts, information about where the Kell calculus is going[...]

Comparing the Expressive Power of the Synchronous and the Asynchronous pi-calculus

Comparing the Expressive Power of the Synchronous and the Asynchronous pi-calculus
The Asynchronous pi-calculus, as recently proposed by Boudol and, independently, by Honda and Tokoro, is a subset of the pi-calculus which contains no explicit operators for choice and output-prefixing. The communication mechanism of this calculus, however, is powerful enough to simulate output-prefixing, as shown by Boudol, and input-guarded choice, as shown recently by Nestmann and Pierce. A natural question arises, then, whether or not it is possible to embed in it the full pi-calculus. We show that this is not possible, i.e. there does not exist any uniform, parallel-preserving, translation from the pi-calculus into the asynchronous pi-calculus, up to any “reasonable” notion of equivalence. This result is based on the incapablity of the asynchronous pi-calculus of breaking certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the pi-calculus and CCS.
Quite an important result for those who care about pi.

The others may just enjoy the use of symmetry in the proof.

As CiteSeer is down this weekend, I used a link to CiteBase.

[on edit: CiteSeer is back]

Principles of Program Analysis

To coincide with the reprinting of Principles of Program Analysis by Flemming Nielson, Hanne Riis Nielson and Chris Hankin the authors launched a new web page containing lecture slides and other supplementary material.

The lecture slides cover things like data flow analysis, control flow analysis and abstract interpretation.

Non-determinism in functional languages

Non-determinism in functional languages. Sondergaard and Sestoft. The Computer Journal, Volume 35, Issue 5, pp. 514-523. 1992

The introduction of a non-deterministic operator in even an very simple functional programming language gives rise to a plethora of semantic questions. These questions are not only concerned with the choice operator itself. A surprisingly large number of different parameter passing mechanisms are made possible by the introduction of bounded non-determinism. The diversity of semantic possibilities is examined systematically...
A very useful paper if you are interested in this sort of thing. Thinking of non-determinism helps calrify muddled thinking about properties such as referential transparency.

The version I found online, alas, is a set of tiff image files, one for each page...

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