Using an embedded, interpreted language to control a complicated application can have significant software-engineering benefits. But existing interpreters are designed for embedding into C code. To embed an interpreter into a different language requires an API suited to that language. This paper presents Lua-ML, a new API that is suited to languages that provide higher-order functions and types. The API exploits higher-order functions and types to reduce the amount of glue code needed to use an embedded interpreter. Where embedding in C requires a special-purpose “glue function” for every function to be embedded, embedding in Lua-ML requires only a description of each function's type. Lua-ML also makes it easy to define a Lua function whose behavior depends on the number and types of its arguments.

First-generation heap profilers for lazy functional languages have proved to be effective tools for locating some kinds of space faults, but in other cases they cannot provide sufficient information to solve the problem. This paper describes the design, implementation and use of a new profiler that goes beyond the two-dimensional ‘who produces what’ view of heap cells to provide information about their more dynamic and structural attributes. Specifically, the new profiler can distinguish between cells according to their eventual lifetime, or on the basis of the closure retainers by virtue of which they remain part of the live heap. A bootstrapping Haskell compiler (nhc) hosts the implementation: among examples of the profiler's use we include self-application to nhc. Another example is the original heap-profiling case study clausify, which now consumes even less memory and is much faster.

We give a direct type-theoretic characterization of the basic mechanisms of object-oriented programming, including objects, methods, message passing, and subtyping, by introducing an explicit constructor for object types and suitable introduction, elimination, and equality rules. The resulting abstract framework provides a basis for justifying and comparing previous encodings of objects based on recursive record types (Cardelli, 1984; Cardelli, 1992; Bruce, 1994; Cook et al., 1990; Mitchell, 1990a) and encodings based on existential types (Pierce & Turner, 1994).

Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation. This paper tries to answer questions like: How many terms of a given size are there? What is a ‘typical’ structure of a simply typable term? Despite their ostensible simplicity, these questions still remain unanswered, whereas solutions to such problems are essential for testing compilers and optimizing programs whose expected efficiency depends on the size of terms. Our approach toward the aforementioned problems may be later extended to any language with bound variables, i.e., with scopes and declarations. This paper presents two complementary approaches: one, theoretical, uses complex analysis and generating functions, the other, experimental, is based on a generator of lambda terms. Thanks to de Bruijn indices (de Bruijn, N. (1972) Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indagat. Math.34(5), 381–392), we provide three families of formulas for the number of closed lambda terms of a given size and we give four relations between these numbers which have interesting combinatorial interpretations. As a by-product of the counting formulas, we design an algorithm for generating λ-terms. Performed tests provide us with experimental data, like the average depth of bound variables and the average number of head lambdas. We also create random generators for various sorts of terms. Thereafter, we conduct experiments that answer questions like: What is the ratio of simply typable terms among all terms? (Very small!) How are simply typable lambda terms distributed among all lambda terms? (A typable term almost always starts with an abstraction.) In this paper, abstractions and applications have size 1 and variables have size 0.

We report on an experience using the Coq proof assistant to develop a program verification tool with a machine-checked proof of full correctness. The verifier is able to prove memory safety of x86 machine code programs compiled from code that uses algebraic datatypes. The tool's soundness theorem is expressed in terms of the bit-level semantics of x86 programs, so its correctness depends on very few assumptions. We take advantage of Coq's support for programming with dependent types and modules in the structure of the development. The approach is based on developing a library of reusable functors for transforming a verifier at one level of abstraction into a verifier at a lower level. Using this library, it is possible to prototype a verifier based on a new type system with a minimal amount of work, while obtaining a very strong soundness theorem about the final product.

MultiMLton is an extension of the MLton compiler and runtime system that targets scalable, multicore architectures. It provides specific support for ACML, a derivative of Concurrent ML that allows for the construction of composable asynchronous events. To effectively manage asynchrony, we require the runtime to efficiently handle potentially large numbers of lightweight, short-lived threads, many of which are created specifically to deal with the implicit concurrency introduced by asynchronous events. Scalability demands also dictate that the runtime minimize global coordination. MultiMLton therefore implements a split-heap memory manager that allows mutators and collectors running on different cores to operate mostly independently. More significantly, MultiMLton exploits the premise that there is a surfeit of available concurrency in ACML programs to realize a new collector design that completely eliminates the need for read barriers, a source of significant overhead in other managed runtimes. These two symbiotic features - a thread design specifically tailored to support asynchronous communication, and a memory manager that exploits lightweight concurrency to greatly reduce barrier overheads - are MultiMLton's key novelties. In this article, we describe the rationale, design, and implementation of these features, and provide experimental results over a range of parallel benchmarks and different multicore architectures including an 864 core Azul Vega 3, and a 48 core non-coherent Intel SCC (Single-Cloud Computer), that justify our design decisions.

Atoms and de Bruijn indices are two well-known representation techniques for data structures that involve names and binders. However, using either technique, it is all too easy to make a programming error that causes one name to be used where another was intended. We propose an abstract interface to names and binders that rules out many of these errors. This interface is implemented as a library in Agda. It allows defining and manipulating term representations in nominal style and in de Bruijn style. The programmer is not forced to choose between these styles: on the contrary, the library allows using both styles in the same program, if desired. Whereas indexing the types of names and terms with a natural number is a well-known technique to better control the use of de Bruijn indices, we index types with worlds. Worlds are at the same time more precise and more abstract than natural numbers. Via logical relations and parametricity, we are able to demonstrate in what sense our library is safe, and to obtain theorems for free about world-polymorphic functions. For instance, we prove that a world-polymorphic term transformation function must commute with any renaming of the free variables. The proof is entirely carried out in Agda.

It is often hard to write programs that are efficient yet reusable. For example, an efficient implementation of Gaussian elimination should be specialized to the structure and known static properties of the input matrix. The most profitable optimizations, such as choosing the best pivoting or memoization, cannot be expected of even an advanced compiler because they are specific to the domain, but expressing these optimizations directly makes for ungainly source code. Instead, a promising and popular way to reconcile efficiency with reusability is for a domain expert to write code generators.

Two pillars of this approach are types and effects. Typed multilevel languages such as MetaOCaml ensure safety and early error reporting: a well-typed code generator neither goes wrong nor generates code that goes wrong. Side effects such as state and control ease correctness and expressivity: An effectful generator can resemble the textbook presentation of an algorithm, as is familiar to domain experts, yet insert let for memoization and if for bounds checking, as is necessary for efficiency. Together, types and effects enable structuring code generators as compositions of modules with well-defined interfaces, and hence scaling to large programs. However, blindly adding effects renders multilevel types unsound.

We introduce the first multilevel calculus with control effects and a sound type system. We give small-step operational semantics as well as a one-pass continuation-passing-style translation. For soundness, our calculus restricts the code generator's effects to the scope of generated binders. Even with this restriction, we can finally write efficient code generators for dynamic programming and numerical methods in direct style, like in algorithm textbooks, rather than in continuation-passing or monadic style.

Over 25 implementations of different functional languages are benchmarked using the same program, a floating-point intensive application taken from molecular biology. The principal aspects studied are compile time and execution time for the various implementations that were benchmarked. An important consideration is how the program can be modified and tuned to obtain maximal performance on each language implementation. With few exceptions, the compilers take a significant amount of time to compile this program, though most compilers were faster than the then current GNU C compiler (GCC version 2.5.8). Compilers that generate C or Lisp are often slower than those that generate native code directly: the cost of compiling the intermediate form is normally a large fraction of the total compilation time. There is no clear distinction between the runtime performance of eager and lazy implementations when appropriate annotations are used: lazy implementations have clearly come of age when it comes to implementing largely strict applications, such as the Pseudoknot program. The speed of C can be approached by some implementations, but to achieve this performance, special measures such as strictness annotations are required by non-strict implementations. The benchmark results have to be interpreted with care. Firstly, a benchmark based on a single program cannot cover a wide spectrum of ‘typical’ applications. Secondly, the compilers vary in the kind and level of optimisations offered, so the effort required to obtain an optimal version of the program is similarly varied.

We introduce a λ-calculus notation which enables us to detect in a term, more β-redexes than in the usual notation. On this basis, we define an extended β-reduction which is yet a subrelation of conversion. The Church Rosser property holds for this extended reduction. Moreover, we show that we can transform generalised redexes into usual ones by a process called ‘term reshuffling’.

Concurrent programs require high-level abstractions in order to manage complexity and enable compositional reasoning. In this paper, we introduce a novel concurrency abstraction, dubbed transactional events, which combines first-class synchronous message passing events with all-or-nothing transactions. This combination enables simple solutions to interesting problems in concurrent programming. For example, guarded synchronous receive can be implemented as an abstract transactional event, whereas in other languages it requires a non-abstract, non-modular protocol. As another example, three-way rendezvous can be implemented as an abstract transactional event, which is impossible using first-class events alone. Both solutions are easy to code and easy to reason about.

The expressive power of transactional events arises from a sequencing combinator whose semantics enforces an all-or-nothing transactional property – either both of the constituent events synchronize in sequence or neither of them synchronizes. This sequencing combinator, along with a non-deterministic choice combinator, gives transactional events the compositional structure of a monad-with-plus. We provide a formal semantics for transactional events and give a detailed account of an implementation.

The Third Homomorphism Theorem is a folk theorem of the constructive algorithmics community. It states that a function on lists that can be computed both from left to right and from right to left is necessarily a list homomorphism – it can be computed according to any parenthesization of the list. We formalize and prove the theorem, and use it to improve an O(n2) sorting algorithm to O(n log n).

Correct handling of names and binders is an important issue in meta-programming. This paper presents an embedding of constraint logic programming into the αML functional programming language, which provides a provably correct means of implementing proof search computations over inductive definitions involving names and binders modulo α-equivalence. We show that the execution of proof search in the αML operational semantics is sound and complete with regard to the model-theoretic semantics of formulae, and develop a theory of contextual equivalence for the subclass of αML expressions which correspond to inductive definitions and formulae. In particular, we prove that αML expressions, which denote inductive definitions, are contextually equivalent precisely when those inductive definitions have the same model-theoretic semantics. This paper is a revised and extended version of the conference paper (Lakin, M. R. & Pitts, A. M. (2009) Resolving inductive definitions with binders in higher-order typed functional programming. In Proceedings of the 18th European Symposium on Programming (ESOP 2009), Castagna, G. (ed), Lecture Notes in Computer Science, vol. 5502. Berlin, Germany: Springer-Verlag, pp. 47–61) and draws on material from the first author's PhD thesis (Lakin, M. R. (2010) An Executable Meta-Language for Inductive Definitions with Binders. University of Cambridge, UK).

A constraint programming system combines two essential components: a constraint solver and a search engine. The constraint solver reasons about satisfiability of conjunctions of constraints, and the search engine controls the search for solutions by iteratively exploring a disjunctive search tree defined by the constraint program. In this paper we give a monadic definition of constraint programming in which the solver is defined as a monad threaded through the monadic search tree. We are then able to define search and search strategies as first-class objects that can themselves be built or extended by composable search transformers. Search transformers give a powerful and unifying approach to viewing search in constraint programming, and the resulting constraint programming system is first class and extremely flexible.

This paper presents a purely syntactic account of type generativity and sharing – two key mechanisms in the SML module system – and shows its equivalence with the traditional stamp-based description of these mechanisms. This syntactic description recasts the SML module system in a more abstract, type-theoretic framework.

The Revised6 Report on the Algorithmic Language Scheme added a mechanism to the Scheme programming language for creating new record types procedurally. While many programming languages support user defined, structured data types, these are usually handled syntactically, so that the compiler can make choices at compile time about the memory layout of these data types. The procedural record types in Scheme, however, can be constructed at run time, making the efficient run-time representation of record types important to ensure good run-time performance. The run-time representation used in our implementation provides an extended model for record types allowing record types to represent foreign scalar data types, e.g., machine word integers, and allows the base record type to be extended to create non-R6RS record-type systems. This article describes our run-time representation for record types, how the garbage collector handles foreign scalar data types, and includes extended record type systems both for an object-oriented programming model and a representation of foreign structured data types.

Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Lévy to internalise substitutions into λ-calculus and to propose a mechanism for computing on substitutions. λν is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. It favours simplicity and preservation of strong normalisation. This way, another important property is missed, namely confluence on open terms. In spirit, λν is closely related to another calculus of explicit substitutions proposed by de Bruijn and called CλξΦ. In this paper, we introduce λν, we present CλξΦ in the same framework as λν and we compare both calculi. Moreover, we prove properties of λν; namely λν correctly implements β reduction, λν is confluent on closed terms, i.e. on terms of classical λ-calculus and on all terms that are derived from those terms, and finally λν preserves strong normalisation in the following sense: strongly β normalising terms are strongly λν normalising.

We present natural semantics for acyclic as well as cyclic call-by-need lambda calculi, which are proved equivalent to the reduction semantics given by Ariola and Felleisen (J. Funct. Program., vol. 7, no. 3, 1997). The natural semantics are big-step and use global heaps, where evaluation is suspended and memorized. The reduction semantics are small-step, and evaluation is suspended and memorized locally in let-bindings. Thus two styles of formalization describe the call-by-need strategy from different angles. The natural semantics for the acyclic calculus is revised from the previous presentation by Maraist et al. (J. Funct. Program., vol. 8, no. 3, 1998), and its adequacy is ascribed to its correspondence with the reduction semantics, which has been proved equivalent to call-by-name by Ariola and Felleisen. The natural semantics for the cyclic calculus is inspired by that of Launchbury (1993) and Sestoft (1997), and we state its adequacy using a denotational semantics in the style of Launchbury; adequacy of the reduction semantics for the cyclic calculus is in turn ascribed to its correspondence with the natural semantics.

Commercial Users of Functional Programming (CUFP) is an annual workshop that is aimed at the community of software developers who use functional programming in real-world settings. This scribe report covers the talks that were delivered at the 2012 workshop, which was held in association with International Conference on Functional Programming (ICFP) in Copenhagen, Denmark. The goal of the report is to give the reader a sense of what went on, rather than to reproduce the full details of the talks. Videos and slides from all the talks are available online at http://cufp.org.

We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To demonstrate the technique and support our claim, we transform the CEK machine of Felleisen and Friedman (Proc. of the 14th ACM SIGACT-SIGPLAN Symp. Prin. Program. Langs, 1987, pp. 314–325), a lazy variant of Krivine's machine (Higher-Order Symb. Comput. Vol 20, 2007, pp. 199–207), and the stack-inspecting CM machine of Clements and Felleisen (ACM Trans. Program. Lang. Syst. Vol 26, 2004, pp. 1029–1052) into abstract interpretations of themselves. The resulting analyses bound temporal ordering of program events; predict return-flow and stack-inspection behavior; and approximate the flow and evaluation of by-need parameters. For all of these machines, we find that a series of well-known concrete machine refactorings, plus a technique of store-allocated continuations, leads to machines that abstract into static analyses simply by bounding their stores. These machines are parameterized by allocation functions that tune performance and precision and substantially expand the space of analyses that this framework can represent. We demonstrate that the technique scales up uniformly to allow static analysis of realistic language features, including tail calls, conditionals, mutation, exceptions, first-class continuations, and even garbage collection. In order to close the gap between formalism and implementation, we provide translations of the mathematics as running Haskell code for the initial development of our method.