Lambda the Ultimate

Latent Effects for Reusable Language Components, by Birthe van den Berg, Tom Schrijvers, Casper Bach Poulsen, Nicolas Wu:

The development of programming languages can be quite complicated and costly. Hence, much effort has been devoted to the modular definition of language features that can be reused in various combinations to define new languages and experiment with their semantics. A notable outcome of these efforts is the algebra-based “datatypes "a la carte" (DTC) approach. When combined with algebraic effects, DTC can model a wide range of common language features. Unfortunately, the
current state of the art does not cover modular definitions of advanced control-flow mechanisms that defer execution to an appropriate point, such as call-by-name and call-by-need evaluation, as well as (multi-)staging. This paper defines latent effects, a generic class of such control-flow mechanisms. We demonstrate how function abstractions, lazy computations and a MetaML-like staging can all be expressed in a modular fashion using latent effects, and how they can be combined in various ways to obtain complex semantics. We provide a full Haskell implementation of our effects and handlers with a range of examples.

Looks like a nice generalization of the basic approach taken by algebraic effects to more subtle contexts. Algebraic effects have been discussed here on LtU many times. I think this description from section 2.3 is a pretty good overview of their approach:

LE&H is based on a different, more sophisticated structure than AE&H’s free monad. This structure supports non-atomic operations (e.g., function abstraction, thunking, quoting) that contain or delimit computations whose execution may be deferred. Also, the layered handling is different. The idea is still the same, to replace bit by bit the structure of the tree by its meaning. Yet, while AE&H grows the meaning around the shrinking tree, LE&H grows little “pockets of meaning” around the individual nodes remaining in the tree, and not just around the root. The latter supports deferred effects because later handlers can still re-arrange the semantic pockets created by earlier handlers.

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.

The Syntax and Semantics of Quantitative Type Theory by Robert Atkey:

Type Theory offers a tantalising promise: that we can program and reason within a single unified system. However, this promise slips away when we try to produce efficient programs. Type Theory offers little control over the intensional aspect of programs: how are computational resources used, and when can they be reused. Tracking resource usage via types has a long history, starting with Girard's Linear Logic and culminating with recent work in contextual effects, coeffects, and quantitative type theories. However, there is conflict with full dependent Type Theory when accounting for the difference between usages in types and terms. Recently, McBride has proposed a system that resolves this conflict by treating usage in types as a zero usage, so that it doesn't affect the usage in terms. This leads to a simple expressive system, which we have named Quantitative Type Theory (QTT).

McBride presented a syntax and typing rules for the system, as well as an erasure property that exploits the difference between “not used” and “used”, but does not do anything with the finer usage information. In this paper, we present present a semantic interpretation of a variant of McBride's system, where we fully exploit the usage information. We interpret terms simultaneously as having extensional (compile-time) content and intensional (runtime) content. In our example models, extensional content is set-theoretic functions, representing the compile-time or type-level content of a type-theoretic construction. Intensional content is given by realisers for the extensional content. We use Abramsky et al.'s Linear Combinatory Algebras as realisers, yield a large range of potential models from Geometry of Interaction, graph models, and syntactic models. Read constructively, our models provide a resource sensitive compilation method for QTT.

To rigorously define the structure required for models of QTT, we introduce the concept of a Quantitative Category with Families, a generalisation of the standard Category with Families class of models of Type Theory, and show that this class of models soundly interprets Quantitative Type Theory.

Resource-aware programming is a hot topic these days, with Rust exploiting affine and ownership types to scope and track resource usage, and with Ethereum requiring programs to spend "gas" to execute. Combining linear and dependent types has proven difficult though, so making it easier to track and reason about resource usage in dependent type theories would then be a huge benefit to making verification more practical in domains where resources are limited.

Co-hygiene and quantum gravity. Some light weekend reading by John Shutt.

The post starts with a dazzling proposition:

Gravity corresponds to pure function-application, and the other fundamental forces correspond to side-effects. ... quantum non-locality ("spooky action at a distance") is part of the analog to side-effects ...

I can't do it justice here, so if you're interested in John's fascinating take on the relationship between lambda calculus and quantum physics, hop on over!

Fully Abstract Compilation via Universal Embedding by Max S. New, William J. Bowman, and Amal Ahmed:

A fully abstract compiler guarantees that two source components are observationally equivalent in the source language if and only if their translations are observationally equivalent in the target. Full abstraction implies the translation is secure: target-language attackers can make no more observations of a compiled component than a source-language attacker interacting with the original source component. Proving full abstraction for realistic compilers is challenging because realistic target languages contain features (such as control effects) unavailable in the source, while proofs of full abstraction require showing that every target context to which a compiled component may be linked can be back-translated to a behaviorally equivalent source context.

We prove the first full abstraction result for a translation whose target language contains exceptions, but the source does not. Our translation—specifically, closure conversion of simply typed λ-calculus with recursive types—uses types at the target level to ensure that a compiled component is never linked with attackers that have more distinguishing power than source-level attackers. We present a new back-translation technique based on a deep embedding of the target language into the source language at a dynamic type. Then boundaries are inserted that mediate terms between the untyped embedding and the strongly-typed source. This technique allows back-translating non-terminating programs, target features that are untypeable in the source, and well-bracketed effects.

Potentially a promising step forward to secure multilanguage runtimes. We've previously discussed security vulnerabilities caused by full abstraction failures here and here. The paper also provides a comprehensive review of associated literature, like various means of protection, back translations, embeddings, etc.

Simon Peyton Jones has been elected as a Fellow of the Royal Society. The Royal Society biography reads:

Simon's main research interest is in functional programming languages, their implementation, and their application. He was a key contributor to the design of the now-standard functional language Haskell, and is the lead designer of the widely-used Glasgow Haskell Compiler (GHC). He has written two textbooks about the implementation of functional languages.

More generally, Simon is interested in language design, rich type systems, compiler technology, code generation, runtime systems, virtual machines, and garbage collection. He is particularly motivated by direct use of principled theory to practical language design and implementation -- that is one reason he loves functional programming so much.

Simon is also chair of Computing at School, the grass-roots organisation that was at the epicentre of the 2014 reform of the English computing curriculum.

Congratulations SPJ!

Type Checking Modular Multiple Dispatch with Parametric Polymorphism and Multiple Inheritance by Eric Allen, Justin Hilburn, Scott Kilpatrick, Victor Luchangco, Sukyoung Ryu, David Chase, Guy L. Steele Jr.:

In previous work, we presented rules for defining overloaded functions that ensure type safety under symmetric multiple dispatch in an object-oriented language with multiple inheritance, and we showed how to check these rules without requiring the entire type hierarchy to be known, thus supporting modularity and extensibility. In this work, we extend these rules to a language that supports parametric polymorphism on both classes and functions.

In a multiple-inheritance language in which any type may be extended by types in other modules, some overloaded functions that might seem valid are correctly rejected by our rules. We explain how these functions can be permitted in a language that additionally supports an exclusion relation among types, allowing programmers to declare “nominal exclusions” and also implicitly imposing exclusion among different instances of each polymorphic type. We give rules for computing the exclusion relation, deriving many type exclusions from declared and implicit ones.

We also show how to check our rules for ensuring the safety of overloaded functions. In particular, we reduce the problem of handling parametric polymorphism to one of determining subtyping relationships among universal and existential types. Our system has been implemented as part of the open-source Fortress compiler.

Fortress was briefly covered here a couple of times, as were multimethods and multiple dispatch, but this paper really generalizes and nicely summarizes previous work on statically typed modular multimethods, and does a good job explaining the typing rules in an accessible way. The integration with parametric polymorphism I think is key to applying multimethods in other domains which may want modular multimethods, but not multiple inheritance.

The Formalization in COQ might also be of interest to some.

Also, another interesting point is Fortress' use of second-class intersection and union types to simplify type checking.

Breaking Through the Normalization Barrier: A Self-Interpreter for F-omega, by Matt Brown and Jens Palsberg:

According to conventional wisdom, a self-interpreter for a strongly normalizing λ-calculus is impossible. We call this the normalization barrier. The normalization barrier stems from a theorem in computability theory that says that a total universal function for the total computable functions is impossible. In this paper we break through the normalization barrier and define a self-interpreter for System Fω, a strongly normalizing λ-calculus. After a careful analysis of the classical theorem, we show that static type checking in Fω can exclude the proof’s diagonalization gadget, leaving open the possibility for a self-interpreter. Along with the self-interpreter, we program four other operations in Fω, including a continuation-passing style transformation. Our operations rely on a new approach to program representation that may be useful in theorem provers and compilers.

I haven't gone through the whole paper, but their claims are compelling. They have created self-interpreters in System F, System Fω and System Fω+, which are all strongly normalizing typed languages. Previously, the only instance of this for a typed language was Girard's System U, which is not strongly normalizing. The key lynchpin appears in this paragraph on page 2:

Our result breaks through the normalization barrier. The conventional wisdom underlying the normalization barrier makes an implicit assumption that all representations will behave like their counterpart in the computability theorem, and therefore the theorem must apply to them as well. This assumption excludes other notions of representation, about which the theorem says nothing. Thus, our result does not contradict the theorem, but shows that the theorem is less far-reaching than previously thought.

Pretty cool if this isn't too complicated in any given language. Could let one move some previously non-typesafe runtime features, into type safe libraries.

Dependent Types for Low-Level Programming by Jeremy Condit, Matthew Harren, Zachary Anderson, David Gay, and George C. Necula:

In this paper, we describe the key principles of a dependent type system for low-level imperative languages. The major contributions of this work are (1) a sound type system that combines dependent types and mutation for variables and for heap-allocated structures in a more flexible way than before and (2) a technique for automatically inferring dependent types for local variables. We have applied these general principles to design Deputy, a dependent type system for C that allows the user to describe bounded pointers and tagged unions. Deputy has been used to annotate and check a number of real-world C programs.

A conceptually simple approach to verifying the safety of C programs, which proceeeds in 3 phases: 1. infer locals that hold pointer bounds, 2. flow-insensitive checking introduces runtime assertions using these locals, 3. flow-sensitive optimization that removes the assertions that it can prove always hold.

You're left with a program that ensures runtime safety with as few runtime checks as possible, and the resulting C program is compiled with gcc which can perform its own optimizations.

This work is from 2007, and the project grew into the Ivy language, which is a C dialect that is fully backwards compatible with C if you #include a small header file that includes the extensions.

It's application to C probably won't get much uptake at this point, but I can see this as a useful compiler plugin to verify unsafe Rust code.

Freer Monads, More Extensible Effects, by Oleg Kiselyov and Hiromi Ishii:

We present a rational reconstruction of extensible effects, the recently proposed alternative to monad transformers, as the confluence of efforts to make effectful computations compose. Free monads and then extensible effects emerge from the straightforward term representation of an effectful computation, as more and more boilerplate is abstracted away. The generalization process further leads to freer monads, constructed without the Functor constraint.

The continuation exposed in freer monads can then be represented as an efficient type-aligned data structure. The end result is the algorithmically efficient extensible effects library, which is not only more comprehensible but also faster than earlier implementations. As an illustration of the new library, we show three surprisingly simple applications: non-determinism with committed choice (LogicT), catching IO exceptions in the presence of other effects, and the semi-automatic management of file handles and other resources through monadic regions.

We extensively use and promote the new sort of ‘laziness’, which underlies the left Kan extension: instead of performing an operation, keep its operands and pretend it is done.

This looks very promising, and includes some benchmarks comparing the heavily optimized and special-cased monad transformers against this new formulation of extensible effects using Freer monads.

See also the reddit discussion.