Lambda the Ultimate

There's an interesting Q&A on Stack Overflow.

I previously wrote about a brand of research by Guy Blelloch on the Cost semantics for functional languages, which let us make precise claim about the complexity of functional programs without leaving their usual and comfortable programming models (beta-reduction).

While the complexity behavior of weak reduction strategies, such as call-by-value and call-by-name, is by now relatively well-understood, the lambda-calculus has a much richer range of reduction strategies, in particular those that can reduce under lambda-abstractions, whose complexity behavior is sensibly more subtle and was, until recently, not very well understood. (This has become a practical concern since the rise in usage of proof assistants that must implement reduction under binders and are very concerned about the complexity of their reduction strategy, which consumes a lot of time during type/proof-checking.)

Beniamino Accatoli, who has been co-authoring a lot of work in that area, recently published on arXiv a new paper that has survey quality, and is a good introduction to this area of work and other pointers from the literature.

The Complexity of Abstract Machines

Beniamino Accatoli, 2017

The lambda-calculus is a peculiar computational model whose definition does not come with a notion of machine. Unsurprisingly, implementations of the lambda-calculus have been studied for decades. Abstract machines are implementations schema for fixed evaluation strategies that are a compromise between theory and practice: they are concrete enough to provide a notion of machine and abstract enough to avoid the many intricacies of actual implementations. There is an extensive literature about abstract machines for the lambda-calculus, and yet -- quite mysteriously -- the efficiency of these machines with respect to the strategy that they implement has almost never been studied.

This paper provides an unusual introduction to abstract machines, based on the complexity of their overhead with respect to the length of the implemented strategies. It is conceived to be a tutorial, focusing on the case study of implementing the weak head (call-by-name) strategy, and yet it is an original re-elaboration of known results. Moreover, some of the observation contained here never appeared in print before.

Dave Herman is the voice of the oppressed: syntax is important, contrary to what you have been told!

To illustrate he discusses what he calls Stroustrup's Rule:

• For new features, people insist on LOUD explicit syntax.
• For established features, people want terse notation.

Monads and algebraic effects are general concepts that give a definition of what a "side-effect" can be: an instance of monad, or an instance of algebraic effect, is a specific realization of a side-effect. While most programming languages provide a fixed family of built-in side-effects, monads or algebraic effects give a structured way to introduce a new notion of effect as a library.

A recent avenue of programming language research is how to locally define several realizations of the same effect interface/signature. There may be several valid notions of "state" or "non-determinism" or "probabilistic choice", and different parts of a program may not require the same realization of those -- a typical use-case would be mocking an interaction with the outside world, for example. Can we let users locally define a new interpretation of an effect, or write code that is generic over the specific interpretation? There are several existing approaches, such as monad transformer stacks, free monads interpreters, monad reification and, lately, effect handlers, as proposed in the programming language Eff.

Frank, presented in the publication below, is a new language with user-defined effects that makes effect handling a natural part of basic functional programming, instead of a separate, advanced feature. It is a significant advance in language design, simplifying effectful programming. Functions, called operators, do not just start computing a result from the value of their arguments, they interact with the computation of those arguments by having the opportunity to handle any side-effects arising during their evaluation. It feels like a new programming style, a new calling convention that blends call-by-value and effect handling -- Sam Lindley suggested the name call-by-handling.

Frank also proposes a new type-and-effect system that corresponds to this new programming style. Operators handle some of the effects raised by their arguments, and silently forward the rest to the computation context; their argument types indicate which effects they handle. In other words, the static information carried by an argument types is the delta/increment between the effects permitted by the ambient computation and the effects of evaluating this argument. Frank calls this an adjustment over the ambient ability. This delta/increment style results in lightweight types for operators that can be used in different contexts (a form of effect polymorphism) without explicit quantification over effect variables. This design takes part in a research conversation on how to make type-and-effect systems usable, which is the major roadblock for their wider adoption -- Koka and Links are also promising in that regard, and had to explore elaborate conventions to elide their polymorphic variables.

Another important part of Frank's type-system design is the explicit separation between values that are and computations that do. Theoretical works have long made this distinction (for example with Call-By-Push-Value), but programmers are offered the dichotomy of either having only effectful expressions or expressing all computations as values (Haskell's indirect style). Frank puts that distinction in the hands of the user -- this is different from distinguishing pure from impure computations, as done in F* or WhyML.

If you wish to play with the language, a prototype implementation is available.

Do Be Do Be Do (arXiv)
Sam Lindley, Conor McBride, Craig McLaughlin
2017

We explore the design and implementation of Frank, a strict functional programming language with a bidirectional effect type system designed from the ground up around a novel variant of Plotkin and Pretnar’s effect handler abstraction.

Effect handlers provide an abstraction for modular effectful programming: a handler acts as an interpreter for a collection of commands whose interfaces are statically tracked by the type system. However, Frank eliminates the need for an additional effect handling construct by generalising the basic mechanism of functional abstraction itself. A function is simply the special case of a Frank operator that interprets no commands. Moreover, Frank’s operators can be multihandlers which simultaneously interpret commands from several sources at once, without disturbing the direct style of functional programming with values.

Effect typing in Frank employs a novel form of effect polymorphism which avoid mentioning effect variables in source code. This is achieved by propagating an ambient ability inwards, rather than accumulating unions of potential effects outwards.

We introduce Frank by example, and then give a formal account of the Frank type system and its semantics. We introduce Core Frank by elaborating Frank operators into functions, case expressions, and unary handlers, and then give a sound small-step operational semantics for Core Frank.

Programming with effects and handlers is in its infancy. We contribute an exploration of future possibilities, particularly in combination with other forms of rich type system.

Contextual Isomorphisms
Paul Blain Levy
2017

What is the right notion of "isomorphism" between types, in a simple type theory? The traditional answer is: a pair of terms that are inverse, up to a specified congruence. We firstly argue that, in the presence of effects, this answer is too liberal and needs to be restricted, using Führmann’s notion of thunkability in the case of value types (as in call-by-value), or using Munch-Maccagnoni’s notion of linearity in the case of computation types (as in call-by-name). Yet that leaves us with different notions of isomorphism for different kinds of type.

This situation is resolved by means of a new notion of “contextual” isomorphism (or morphism), analogous at the level of types to contextual equivalence of terms. A contextual morphism is a way of replacing one type with the other wherever it may occur in a judgement, in a way that is preserved by the action of any term with holes. For types of pure λ-calculus, we show that a contextual morphism corresponds to a traditional isomorphism. For value types, a contextual morphism corresponds to a thunkable isomorphism, and for computation types, to a linear isomorphism.

This paper is based on a very simple idea that everyone familiar with type-systems can enjoy. It then applies it in a technical setting in which it brings a useful contribution. I suspect that many readers will find that second part too technical, but they may still enjoy the idea itself. To facilitate this, I will rephrase the abstract above in a way that I hope makes it accessible to a larger audience.

The problem that the paper solves is: how do we know what it means for two types to be equivalent? For many languages they are reasonable definitions of equivalence (such that: there exists a bijection between these two types in the language), but for more advanced languages these definitions break down. For example, in presence of hidden mutable state, one can build a pair of functions from the one-element type unit to the two-element type bool and back that are the identity when composed together -- the usual definition of bijection -- while these two types should probably not be considered "the same". Those two functions share some hidden state, so they "cheat". Other, more complex notions of type equivalence have been given in the literature, but how do we know whether they are the "right" notions, or whether they may disappoint us in the same way?

To define what it means for two program fragments to be equivalent, we have a "gold standard", which is contextual equivalence: two program fragments are contextually equivalent if we can replace one for the other in any complete program without changing its behavior. This is simple to state, it is usually clear how to instantiate this definition for a new system, and it gives you a satisfying notion of equivalent. It may not be the most convenient one to work with, so people define others, more specific notions of equivalence (typically beta-eta-equivalence or logical relations); it is fine if they are more sophisticated, and their definiton harder to justify or understand, because they can always be compared to this simple definition to gain confidence.

The simple idea in the paper above is to use this exact same trick to define what it means for two types to be equivalent. Naively, one could say that two types are equivalent if, in any well-typed program, one can replace some occurrences of the first type by occurrences of the second type, all other things being unchanged. This does not quite work, as changing the types that appear in a program without changing its terms would create ill-typed terms. So instead, the paper proposes that two types are equivalent when we are told how to transform any program using the first type into a program using the second type, in a way that is bijective (invertible) and compositional -- see the paper for details.

Then, the author can validate this definition by showing that, when instantiated to languages (simple or complex) where existing notions of equivalence have been proposed, this new notion of equivalence corresponds to the previous notions.

(Readers may find that even the warmup part of the paper, namely the sections 1 to 4, pages 1 to 6, are rather dense, with a compactly exposed general idea and arguably a lack of concrete examples that would help understanding. Surely this terseness is in large part a consequence of strict page limits -- conference articles are the tweets of computer science research. A nice side-effect (no pun intended) is that you can observe a carefully chosen formal language at work, designed to expose the setting and perform relevant proofs in minimal space: category theory, and in particular the concept of naturality, is the killer space-saving measure here.)

Youtube video (via HN)

By far not the best presentation of Kay's ideas but surely a must watch for fans. Otherwise, skip until the last third of the interview which might add to what most people here already know.

It is interesting that in this talk Kay rather explicitly talks about programming languages as abstraction layers. He also mentions some specifics that may not be as well known as others, yet played a role in his trajectory, such as META.

I fully sympathize with his irritation with the lack of attention to and appreciation of fundamental concepts and theoretical frameworks in CS. On the other hand, I find his allusions to biology unconvincing.
An oh, he is certainly right about Minsky's book (my first introduction to theoretical CS) and in his deep appreciation of John McCarthy.

I am very enthusiastic about the following paper: it brings new ideas and solves a problem that I did not expect to be solvable, namely usable type inference when both polymorphism and subtyping are implicit. (By "usable" here I mean that the inferred types are both compact and principal, while previous work generally had only one of those properties.)

Polymorphism, Subtyping, and Type Inference in MLsub
Stephen Dolan and Alan Mycroft
2017

We present a type system combining subtyping and ML-style parametric polymorphism. Unlike previous work, our system supports type inference and has compact principal types. We demonstrate this system in the minimal language MLsub, which types a strict superset of core ML programs.

This is made possible by keeping a strict separation between the types used to describe inputs and those used to describe outputs, and extending the classical unification algorithm to handle subtyping constraints between these input and output types. Principal types are kept compact by type simplification, which exploits deep connections between subtyping and the algebra of regular languages. An implementation is available online.

The paper is full of interesting ideas. For example, one idea is that adding type variables to the base grammar of types -- instead of defining them by their substitution -- forces us to look at our type systems in ways that are more open to extension with new features. I would recommend looking at this paper even if you are interested in ML and type inference, but not subtyping, or in polymorphism and subtyping, but not type inference, or in subtyping and type inference, but not functional languages.

This paper is also a teaser for the first's author PhD thesis, Algebraic Subtyping. There is also an implementation available.

(If you are looking for interesting work on inference of polymorphism and subtyping in object-oriented languages, I would recommend Getting F-Bounded Polymorphism into Shape by Ben Greenman, Fabian Muehlboeck and Ross Tate, 2014.)

In the first decade of the twenty-first century, the Feyerabend Project organized several workshops to discuss and develop new ways to think of programming languages and computing in general. A new event in this direction is a new workshop that will take place in Brussels, in April, co-located with the new <Programming> conference -- also worth a look.

Salon des Refusés -- Dialectics for new computer science
April 2017, Brussels

Salon des Refusés (“exhibition of rejects”) was an 1863 exhibition of artworks rejected from the official Paris Salon. The jury of Paris Salon required near-photographic realism and classified works according to a strict genre hierarchy. Paintings by many, later famous, modernists such as Édouard Manet were rejected and appeared in what became known as the Salon des Refusés. This workshop aims to be the programming language research equivalent of Salon des Refusés. We provide venue for exploring new ideas and new ways of doing computer science.

Many interesting ideas about programming might struggle to find space in the modern programming language research community, often because they are difficult to evaluate using established evaluation methods (be it proofs, measurements or controlled user studies). As a result, new ideas are often seen as “unscientific”.

This workshop provides a venue where such interesting and thought provoking ideas can be exposed to critical evaluation. Submissions that provoke interesting discussion among the program committee members will be published together with an attributed review that presents an alternative position, develops additional context or summarizes discussion from the workshop. This means of engaging with papers not just enables explorations of novel programming ideas, but also enourages new ways of doing computer science.

The workshop's webpage also contains descriptions of of some formats that could "make it possible to think about programming in a new way", including: Thought experiments, Experimentation, Paradigms, Metaphors, myths and analogies, and From jokes to science fiction.

For writings on similar questions about formalism, paradigms or method in programming language research, see Richard Gabriel's work, especially The Structure of a Programming Language Revolution (2012) and Writers’ Workshops As Scientific Methodology (?)), Thomas Petricek's work, especially Against a Universal Definition of 'Type' (2015) and Programming language theory Thinking the unthinkable (2016)), and Jonathan Edwards' blog: Alarming Development.

For programs of events of similar inspiration in the past, you may be interested in the Future of Programming workshops: program of 2014, program of September 2015, program of October 2015. Other events that are somewhat similar in spirit -- but maybe less radical in content -- are Onward!, NOOL and OBT.

Proving Programs Correct Using Plain Old Java Types, by Radha Jagadeesan, Alan Jeffrey, Corin Pitcher, James Riely:

Tools for constructing proofs of correctness of programs have a long history of development in the research community, but have often faced difficulty in being widely deployed in software development tools. In this paper, we demonstrate that the off-the-shelf Java type system is already powerful enough to encode non-trivial proofs of correctness using propositional Hoare preconditions and postconditions.

We illustrate the power of this method by adapting Fähndrich and Leino’s work on monotone typestates and Myers and Qi’s closely related work on object initialization. Our approach is expressive enough to address phased initialization protocols and the creation of cyclic data structures, thus allowing for the elimination of null and the special status of constructors. To our knowledge, our system is the first that is able to statically validate standard one-pass traversal algorithms for cyclic graphs, such as those that underlie object deserialization. Our proof of correctness is mechanized using the Java type system, without any extensions to the Java language.

Not a new paper, but it provides a lightweight verification technique for some program properties that you can use right now, without waiting for integrated theorem provers or SMT solvers. Properties that require only monotone typestates can be verified, ie. those that operations can only move the typestate "forwards".

In order to achieve this, they require programmers to follow a few simple rules to avoid Java's pervasive nulls. These are roughly: don't assign null explicitly, be sure to initialize all fields when constructing objects.

Automating Ad hoc Data Representation Transformations by Vlad Ureche, Aggelos Biboudis, Yannis Smaragdakis, and Martin Odersky:

To maximize run-time performance, programmers often specialize their code by hand, replacing library collections and containers by custom objects in which data is restructured for efficient access. However, changing the data representation is a tedious and error-prone process that makes it hard to test, maintain and evolve the source code.

We present an automated and composable mechanism that allows programmers to safely change the data representation in delimited scopes containing anything from expressions to entire class definitions. To achieve this, programmers define a transformation and our mechanism automatically and transparently applies it during compilation, eliminating the need to manually change the source code.

Our technique leverages the type system in order to offer correctness guarantees on the transformation and its interaction with object-oriented language features, such as dynamic dispatch, inheritance and generics.

We have embedded this technique in a Scala compiler plugin and used it in four very different transformations, ranging from improving the data layout and encoding, to
retrofitting specialization and value class status, and all the way to collection deforestation. On our benchmarks, the technique obtained speedups between 1.8x and 24.5x.

This is a realization of an idea that has been briefly discussed here on LtU a few times, whereby a program is written using high-level representations, and the user has the option to provide a lowering to a more efficient representation after the fact.

This contrasts with the typical approach of providing efficient primitives, like primitive unboxed values, and leaving it to the programmer to compose them efficiently up front.