Lambda: The Ultimate Sublanguage (experience report)

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

Code Generation for Higher Inductive Types

Higher inductive types are inductive types that include nontrivial higher-dimensional structure, represented as identifications that are not reflexivity. While work proceeds on type theories with a computational interpretation of univalence and higher inductive types, it is convenient to encode these structures in more traditional type theories with mature implementations. However, these encodings involve a great deal of error-prone additional syntax. We present a library that uses Agda's metaprogramming facilities to automate this process, allowing higher inductive types to be specified with minimal additional syntax.Comment: 16 pages, Accepted for presentation in WFLP 201

Constrained Type Families

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type families in Haskell provide a powerful, modular means of defining type-level computation. However, their current design implicitly assumes that type families are total, introducing nonsensical types and significantly complicating the metatheory of type families and their extensions. We propose an alternative design, using qualified types to pair type-level computations with predicates that capture their domains. Our approach naturally captures the intuitive partiality of type families, simplifying their metatheory. As evidence, we present the first complete proof of consistency for a language with closed type families.Comment: Originally presented at ICFP 2017; extended editio

Generic Programming with Extensible Data Types; Or, Making Ad Hoc Extensible Data Types Less Ad Hoc

We present a novel approach to generic programming over extensible data types. Row types capture the structure of records and variants, and can be used to express record and variant subtyping, record extension, and modular composition of case branches. We extend row typing to capture generic programming over rows themselves, capturing patterns including lifting operations to records and variations from their component types, and the duality between cases blocks over variants and records of labeled functions, without placing specific requirements on the fields or constructors present in the records and variants. We formalize our approach in System R{\omega}, an extension of F{\omega} with row types, and give a denotational semantics for (stratified) R{\omega} in Agda.Comment: To appear at: International Conference on Functional Programming 2023 Corrected citations from previous versio

Versatile event correlation with algebraic effects

We present the first language design to uniformly express variants of n -way joins over asynchronous event streams from different domains, e.g., stream-relational algebra, event processing, reactive and concurrent programming. We model asynchronous reactive programs and joins in direct style, on top of algebraic effects and handlers. Effect handlers act as modular interpreters of event notifications, enabling fine-grained control abstractions and customizable event matching. Join variants can be considered as cartesian product computations with ”degenerate” control flow, such that unnecessary tuples are not materialized a priori. Based on this computational interpretation, we decompose joins into a generic, naive enumeration procedure of the cartesian product, plus variant-specific extensions, represented in terms of user-supplied effect handlers. Our microbenchmarks validate that this extensible design avoids needless materialization. Alongside a formal semantics for joining and prototypes in Koka and multicore OCaml, we contribute a systematic comparison of the covered domains and features. ERC, Advanced Grant No. 321217 ERC, Consolidator Grant No. 617805 DFG, SFB 1053 DFG, SA 2918/2-

A completely unique account of enumeration

How can we enumerate the inhabitants of an algebraic datatype? This paper explores a datatype generic solution that works for all regular types and indexed families. The enumerators presented here are provably both complete and unique—they will eventually produce every value exactly once—and fair—they avoid bias when composing enumerators. Finally, these enumerators memoise previously enumerated values whenever possible, thereby avoiding repeatedly recomputing recursive results

A type- and scope-safe universe of syntaxes with binding: their semantics and proofs

Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of alpha-equivalence, capture-avoiding substitution, typing contexts, runtime environments, and so on. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. Modern programming languages include features that enable constraints like scope safety to be expressed in types. Nevertheless, the programmer is still forced to write the same boilerplate over again for each new implementation of a scope safe operation (e.g., renaming, substitution, desugaring, printing, etc.), and then again for correctness proofs. We present an expressive universe of syntaxes with binding and demonstrate how to (1) implement scope safe traversals once and for all by generic programming; and (2) how to derive properties of these traversals by generic proving. Our universe description, generic traversals and proofs, and our examples have all been formalised in Agda and are available in the accompanying material available online at https://github.com/gallais/generic-syntax

Abstracting Extensible Data Types: Or, Rows by Any Other Name

We present a novel typed language for extensible data types, generalizing and abstracting existing systems of row types and row polymorphism. Extensible data types are a powerful addition to traditional functional programming languages, capturing ideas from OOP-like record extension and polymorphism to modular compositional interpreters. We introduce row theories, a monoidal generalization of row types, giving a general account of record concatenation and projection (dually, variant injection and branching). We realize them via qualified types, abstracting the interpretation of records and variants over different row theories. Our approach naturally types terms untypable in other systems of extensible data types, while maintaining strong metatheoretic properties, such as coherence and principal types. Evidence for type qualifiers has computational content, determining the implementation of record and variant operations; we demonstrate this in giving a modular translation from our calculus, instantiated with various row theories, to polymorphic λ -calculus

LMS-Verify: abstraction without regret for verified systems programming

Performance critical software is almost always developed in C, as programmers do not trust high-level languages to deliver the same reliable performance. This is bad because low-level code in unsafe languages attracts security vulnerabilities and because development is far less productive, with PL advances mostly lost on programmers operating under tight performance constraints. High-level languages provide memory safety out of the box, but they are deemed too slow and unpredictable for serious system software. Recent years have seen a surge in staging and generative programming: the key idea is to use high-level languages and their abstraction power as glorified macro systems to compose code fragments in first-order, potentially domain-specific, intermediate languages, from which fast C can be emitted. But what about security? Since the end result is still C code, the safety guarantees of the high-level host language are lost. In this paper, we extend this generative approach to emit ACSL specifications along with C code. We demonstrate that staging achieves ``abstraction without regret'' for verification: we show how high-level programming models, in particular higher-order composable contracts from dynamic languages, can be used at generation time to compose and generate first-order specifications that can be statically checked by existing tools. We also show how type classes can automatically attach invariants to data types, reducing the need for repetitive manual annotations. We evaluate our system on several case studies that varyingly exercise verification of memory safety, overflow safety, and functional correctness. We feature an HTTP parser that is (1) fast (2) high-level: implemented using staged parser combinators (3) secure: with verified memory safety. This result is significant, as input parsing is a key attack vector, and vulnerabilities related to HTTP parsing have been documented in all widely-used web servers.</jats:p