This paper describes Brack, which is a new verified compiler for Scheme. Brack compiles a substantial subset of Scheme, including first-class continuations, recursive bindings, first-class functions, mutable local variables, and lists, to CakeML, from where programs can be compiled to machine code. Compilation from Scheme to CakeML is based around a continuation-passing-style (CPS) transformation that naturally arises from Scheme’s small-step semantics. We have formally established the correctness of Brack in the HOL4 theorem prover.

Over the last three decades, multi-stage programming has been used to write high-level, type-safe, optimising code generators for a wide variety of domains, from database queries and stream processing to geometry, parsing, and differentiable programming.

Metaprogramming and effect handlers interact in unexpected, and sometimes undesirable, ways. One example is scope extrusion: the generation of ill-scoped code. Scope extrusion can either be preemptively prevented, via static type systems, or retroactively detected, via dynamic checks. Static type systems exist in theory, but struggle with a range of implementation and usability problems in practice. In contrast, dynamic checks exist in practice (e.g. in MetaOCaml), but are understudied in theory. Designers of metaprogramming languages are thus given little guidance regarding the design and implementation of checks. We present the first formal study of dynamic scope extrusion checks, introducing a calculus ( λ ⟨ ⟨ o p ⟩ ⟩ ) for describing and evaluating checks. Further, we introduce a novel dynamic check - the "Cause-for-Concern" check - which we prove correct, characterise without reference to its implementation, and argue combines the advantages of existing dynamic checks. Finally, we extend our framework with refined environment classifiers, which statically prevent scope extrusion, and compare their expressivity with the dynamic checks.

Multi-stage programming (MSP) languages such as MetaML have subtle semantics, in which familiar properties often fail to hold and hazardous interactions with other language features such as state or polymorphism abound. The ongoing incorporation of MSP features into general purpose languages makes the need to establish confidence in their design increasingly pressing. Taking inspiration from existing MSP systems, we present a Rocq mechanisation of a core calculus for compile-time and run-time MSP with effects, λ run $ , formally establishing key properties such as type and elaboration soundness and phase distinction. We hope that our mechanised semantics will be a useful basis for formal study of other designs, easing the extension of existing languages with support for MSP.

We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library’s dependently typed interface guarantees that both built-in and user-defined simplification modules are terminating, sound, and complete with respect to a well-specified class of equations. We have implemented the design in the Idris 2 and Agda dependently typed programming languages and shown that it supports modular extension to new theories, proof extraction and certification, goal extraction via reflection, and interactive development.

We propose a new language feature for ML-family languages, the ability to selectively unbox certain data constructors, so that their runtime representation gets compiled away to just the identity on their argument. Unboxing must be statically rejected when it could introduce confusion, that is, distinct values with the same representation. We discuss the use-case of big numbers, where unboxing allows to write code that is both efficient and safe, replacing either a safe but slow version or a fast but unsafe version. We explain the static analysis necessary to reject incorrect unboxing requests. We present our prototype implementation of this feature for the OCaml programming language, discuss several design choices and the interaction with advanced features such as Guarded Algebraic Datatypes. Our static analysis requires expanding type definitions in type expressions, which is not necessarily normalizing in presence of recursive type definitions. In other words, we must decide normalization of terms in the first-order λ -calculus with recursion. We provide an algorithm to detect non-termination on-the-fly during reduction, with proofs of correctness and completeness. Our algorithm turns out to be closely related to the normalization strategy for macro expansion in the cpp preprocessor.

Multi-stage programming has been used in a wide variety of domains to eliminate the tension between abstraction and performance. However, the interaction of multi-stage programming features with features for programming-in-the-large remains understudied, hindering the full integration of multi-stage programming support into existing languages, and limiting the effective use of staging in large programs. We take steps to remedy the situation by studying the extension of MacoCaml, a recent OCaml extension that supports compile-time code generation via macros and quotations , with module functors, the key mechanism in OCaml for assembling program components into larger units. We discuss design choices related to evaluation order, formalize our calculus via elaboration, and show that the design enjoys key metatheoretical properties: syntactic type soundness, elaboration soundness, and phase distinction. We believe that this study lays a foundation for the continued exploration and implementation of the OCaml macro system.

The defunctionalization translation that eliminates higher-order functions from programs forms a key part of many compilers. However, defunctionalization for dependently-typed languages has not been formally studied. We present the first formally-specified defunctionalization translation for a dependently-typed language and establish key metatheoretical properties such as soundness and type preservation. The translation is suitable for incorporation into type-preserving compilers for dependently-typed languages

We introduce MacoCaml, a new design and implementation of compile-time code generation for the OCaml language. MacoCaml features a novel combination of macros with phase separation and quotation-based staging, where macros are considered as compile-time bindings, expression cross evaluation phases using staging annotations, and compile-time evaluation happens inside top-level splices. We provide a theoretical foundation for MacoCaml by formalizing a typed source calculus maco that supports interleaving typing and compile-time code generation, references with explicit compile-time heaps, and modules. We study various crucial properties including soundness and phase distinction. We have implemented MacoCaml in the OCaml compiler, and ported two substantial existing libraries to validate our implementation.

Lexers and parsers are typically defined separately and connected by a token stream. This separate definition is important for modularity and reduces the potential for parsing ambiguity. However, materializing tokens as data structures and case-switching on tokens comes with a cost. We show how to fuse separately-defined lexers and parsers, drastically improving performance without compromising modularity or increasing ambiguity. We propose a deterministic variant of Greibach Normal Form that ensures deterministic parsing with a single token of lookahead and makes fusion strikingly simple, and prove that normalizing context free expressions into the deterministic normal form is semantics-preserving. Our staged parser combinator library, flap, provides a standard interface, but generates specialized token-free code that runs two to six times faster than ocamlyacc on a range of benchmarks.

Multi-stage programming using typed code quotation is an established technique for writing optimizing code generators with strong type-safety guarantees. Unfortunately, quotation in Haskell interacts poorly with type classes, making it difficult to write robust multi-stage programs. We study this unsound interaction and propose a resolution, staged type class constraints, which we formalize in a source calculus λ ⇒ that elaborates into an explicit core calculus F . We show type soundness of both calculi, establishing that well-typed, well-staged source programs always elaborate to well-typed, well-staged core programs, and prove beta and eta rules for code quotations. Our design allows programmers to incorporate type classes into multi-stage programs with confidence. Although motivated by Haskell, it is also suitable as a foundation for other languages that support both overloading and quotation.

In call-by-value languages, some mutually-recursive definitions can be safely evaluated to build recursive functions or cyclic data structures, but some definitions (let rec x = x + 1) contain vicious circles and their evaluation fails at runtime. We propose a new static analysis to check the absence of such runtime failures. We present a set of declarative inference rules, prove its soundness with respect to the reference source-level semantics of Nordlander, Carlsson, and Gill [2008], and show that it can be directed into an algorithmic backwards analysis check in a surprisingly simple way. Our implementation of this new check replaced the existing check used by the OCaml programming language, a fragile syntactic criterion which let several subtle bugs slip through as the language kept evolving. We document some issues that arise when advanced features of a real-world functional language (exceptions in first-class modules, GADTs, etc.) interact with safety checking for recursive definitions.

In this paper, we recall the definition of the context-free expressions (or µ-regular expressions), an algebraic presentation of the context-free languages. Then, we define a core type system for the context-free expressions which gives a compositional criterion for identifying those context-free expressions which can be parsed unambiguously by predictive algorithms in the style of recursive descent or LL(1).

We describe our experience teaching an advanced typed functional programming course based around the use of System Fω as a programming language.

Partially-static data structures are a well-known technique for improving binding times. However, they are often defined in an ad-hoc manner, without a unifying framework to ensure full use of the equations associated with each operation. We present a foundational view of partially-static data structures as free extensions of algebras for suitable equational theories, i.e. the coproduct of an algebra and a free algebra in the category of algebras and their homomorphisms. By precalculating these free extensions, we construct a high-level library of partially-static data representations for common algebraic structures. We demonstrate our library with common use-cases from the literature: string and list manipulation, linear algebra, and numerical simplification.

Generic programming libraries such as Scrap Your Boilerplate eliminate the need to write repetitive code, but typically introduce significant performance overheads. This leaves programmers with the regrettable choice between writing succinct but slow programs and writing tedious but efficient programs. Applying structured multi-stage programming techniques transforms Scrap Your Boilerplate from an inefficient library into a typed optimising code generator, bringing its performance in line with hand-written code, and so combining high-level programming with uncompromised performance.

Causal commutative arrows (CCA) extend arrows with additional constructs and laws that make them suitable for modelling domains such as functional reactive programming, differential equations and synchronous dataflow.

Generic programming libraries such as Scrap Your Boilerplate eliminate the need to write repetitive code, but typically introduce significant performance overheads. This leaves programmers with the unfortunate choice of writing succinct but slow programs or writing tedious but efficient programs. We show how to systematically transform an implementation of the Scrap Your Boilerplate library in the multi-stage programming language MetaOCaml to eliminate the overhead, making it possible to combine the benefits of high-level abstract programming with the efficiency of low-level code.

Abstract We introduce the arrow calculus, a metalanguage for manipulating Hughes's arrows with close relations both to Moggi's metalanguage for monads and to Paterson's arrow notation. Arrows are classically defined by extending lambda calculus with three constructs satisfying nine (somewhat idiosyncratic) laws; in contrast, the arrow calculus adds four constructs satisfying five laws (which fit two well-known patterns). The five laws were previously known to be sound; we show that they are also complete, and hence that the five laws may replace the nine.

Higher-order abstract syntax provides a convenient way of embedding domain-specific languages, but is awkward to analyse and manipulate directly. We explore the boundaries of higher-order abstract syntax. Our key tool is the unembedding of embedded terms as de Bruijn terms, enabling intensional analysis. As part of our solution we present techniques for separating the definition of an embedded program from its interpretation, giving modular extensions of the embedded language, and different ways to encode the types of the embedded language.

This paper describes a novel system for acquiring adjectival subcategorization frames (SCFs) and associated frequency information from English corpus data. The system incorporates a decision-tree classifier for 30 SCF types which tests for the presence of grammatical relations (GRs) in the output of a robust statistical parser. It uses a powerful pattern-matching language to classify GRs into frames hierarchically in a way that mirrors inheritance-based lexica. The experiments show that the system is able to detect SCF types with 70% precision and 66% recall rate. A new tool for linguistic annotation of SCFs in corpus data is also introduced which can considerably alleviate the process of obtaining training and test data for subcategorization acquisition.