In the Age of Web: Typed Functional-First Programming Revisited

Most programming languages were designed before the age of web. This matters because the web changes many assumptions that typed functional language designers take for granted. For example, programs do not run in a closed world, but must instead interact with (changing and likely unreliable) services and data sources, communication is often asynchronous or event-driven, and programs need to interoperate with untyped environments. In this paper, we present how the F# language and libraries face the challenges posed by the web. Technically, this comprises using type providers for integration with external information sources and for integration with untyped programming environments, using lightweight meta-programming for targeting JavaScript and computation expressions for writing asynchronous code. In this inquiry, the holistic perspective is more important than each of the features in isolation. We use a practical case study as a starting point and look at how F# language and libraries approach the challenges posed by the web. The specific lessons learned are perhaps less interesting than our attempt to uncover hidden assumptions that no longer hold in the age of web.Comment: In Proceedings ML/OCaml 2014, arXiv:1512.0143

Non-linear Pattern Matching with Backtracking for Non-free Data Types

Non-free data types are data types whose data have no canonical forms. For example, multisets are non-free data types because the multiset $\{a,b,b\}$ has two other equivalent but literally different forms $\{b,a,b\}$ and $\{b,b,a\}$. Pattern matching is known to provide a handy tool set to treat such data types. Although many studies on pattern matching and implementations for practical programming languages have been proposed so far, we observe that none of these studies satisfy all the criteria of practical pattern matching, which are as follows: i) efficiency of the backtracking algorithm for non-linear patterns, ii) extensibility of matching process, and iii) polymorphism in patterns. This paper aims to design a new pattern-matching-oriented programming language that satisfies all the above three criteria. The proposed language features clean Scheme-like syntax and efficient and extensible pattern matching semantics. This programming language is especially useful for the processing of complex non-free data types that not only include multisets and sets but also graphs and symbolic mathematical expressions. We discuss the importance of our criteria of practical pattern matching and how our language design naturally arises from the criteria. The proposed language has been already implemented and open-sourced as the Egison programming language

Extending monads with pattern matching

Sequencing of effectful computations can be neatly captured using monads and elegantly written using do notation. In practice such monads often allow additional ways of composing computations, which have to be written explicitly using combinators. We identify joinads, an abstract notion of computation that is stronger than monads and captures many such ad-hoc extensions. In particular, joinads are monads with three additional operations: one of type m a → m b → m (a, b) captures various forms of parallel composition, one of type m a → m a → m a that is inspired by choice and one of type m a → m (m a) that captures aliasing of computations. Algebraically, the first two operations form a near-semiring with commutative multiplication. We introduce docase notation that can be viewed as a monadic version of case. Joinad laws imply various syntactic equivalences of programs written using docase that are analogous to equiva-lences about case. Examples of joinads that benefit from the nota-tion include speculative parallelism, waiting for a combination of user interface events, but also encoding of validation rules using the intersection of parsers

The F# Computation Expression Zoo

Program logic can often be structured using abstract computation types such as monoids, monad transformers or applicative functors. Functional programmers use those abstractions directly while main-stream languages often integrate concrete instances as language features – e.g. generators in Python or asynchronous computations in C# 5.0. The question is, is there a sweet spot between convenient, hardwired language features, and an inconvenient but flexible libraries? F# computation expressions answer this question in the affirmative. Unlike the “do” notation in Haskell, computation expressions are not tied to a single kind of abstraction. They support a wide range of abstractions, depending on what operations are available. F# also provides greater syntactic flexibility leading to a more intuitive syntax, without resorting to full macro-based meta-programming. We present computation expressions in a principled way, developing a type system that captures the semantics of the calculus. We demonstrate how computation expressions structure well-known abstractions including monoidal list comprehensions, monadic parsers, applicative formlets and asynchronous sequences based on monad transformers

Gradients without backpropagation

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

Themes in information-rich functional programming for internet-scale data sources,”

Abstract The F# language includes a feature called "F# 3.0 Type Providers" to support the integration of internet-scale information sources into a strongly typed functional-first programming environment. In this position paper we describe the key themes in information-rich functional programming that we have observed during this work. Our contribution is to document these themes and highlight future challenges and opportunities, in the context of a recently released, practical, open-source system for informationrich functional programming. We believe that this area is rich in excellent opportunities for future language and tooling research, information-space integration and schematization techniques

Initializing Mutually Referential Abstract Objects: The Value Recursion Challenge

AbstractMutual dependencies between objects arise frequently in programs, and programmers must typically solve this value recursion by manually filling “initialization holes” to help construct the corresponding object graphs, i.e. null values and/or explicitly mutable locations. This paper aims to augment ongoing theoretical work on value recursion with a description of a semi-safe mechanism for a generalized form of value recursion in an ML-like language, where initialization corresponds to a graph of lazy computations whose nodes are sequentially forced, requiring runtime checks for soundness during initialization in the style of Russo. Our primary contribution is to use the mechanism to develop compelling examples of how the absence of value recursion leads to real problems in the presence of abstraction boundaries, and give micro-examples that characterize how initialization graphs permit more programs to be expressed in the mutation-free fragment of ML. Finally we argue that in heterogeneous programming environments semi-safe variations on value-recursion may be appropriate for ML-like languages, because initialization effects from external libraries are difficult to characterize, document and control

The early history of F#

This paper describes the genesis and early history of the F# programming language. I start with the origins of strongly-typed functional programming (FP) in the 1970s, 80s and 90s. During the same period, Microsoft was founded and grew to dominate the software industry. In 1997, as a response to Java, Microsoft initiated internal projects which eventually became the .NET programming framework and the C# language. From 1997 the worlds of academic functional programming and industry combined at Microsoft Research, Cambridge. The researchers engaged with the company through Project 7, the initial effort to bring multiple languages to .NET, leading to the initiation of .NET Generics in 1998 and F# in 2002. F# was one of several responses by advocates of strongly-typed functional programming to the "object-oriented tidal wave" of the mid-1990s. The development of the core features of F# 1.0 happened from 2004-2007, and I describe the decision-making process that led to the "productization" of F# by Microsoft in 2007-10 and the release of F# 2.0. The origins of F#'s characteristic features are covered: object programming, quotations, statically resolved type parameters, active patterns, computation expressions, async, units-of-measure and type providers. I describe key developments in F# since 2010, including F# 3.0-4.5, and its evolution as an open source, cross-platform language with multiple delivery channels. I conclude by examining some uses of F# and the influence F# has had on other languages so far.</jats:p