Incrementalization speeds up computations by avoiding unnecessary recomputations and by efficiently reusing previous results. While domain-specific techniques achieve impressive speedups, e.g., in the context of database queries, they are difficult to generalize. Meanwhile, general approaches offer little support for incrementalizing domain-specific operations. In this work, we present DeCo , a novel core calculus for incremental functional programming with support for a wide range of user-defined data types. Despite its generic nature, our approach statically incrementalizes domain-specific operations on user-defined data types. It is, hence, more fine-grained than other generic techniques which resort to treating domain-specific operations as black boxes. We mechanized our work in Lean and proved it sound, meaning incrementalized execution computes the same result as full reevaluation. We also provide an executable implementation with case studies featuring examples from linear algebra, relational algebra, dictionaries, trees, and conflict-free replicated data types, plus a brief performance evaluation on linear and relational algebra and on trees.

Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time access and bulk operations. To bridge this gap, some languages represent arrays as (eager) functions instead of lists. In this paper, we connect this idea to a formal logical foundation by interpreting functions as the usual negative types from polarized type theory, and arrays as the corresponding dual positive version of the function type. Positive types are defined to have a single elimination form whose computational interpretation is pattern matching. Just like (positive) product types bind two variables during pattern matching, (positive) array types bind variables with multiplicity during pattern matching. We follow a similar approach for Booleans by introducing conditionally-defined variables. The positive formulation for the array type enables us to combine typed partial evaluation and common subexpression elimination into an elegant algorithm whose result enjoys a property we call maximal fission, which we argue can be beneficial for further optimizations. For this purpose, we present the novel intermediate representation indexed administrative normal form (A_{i}NF), which relies on the formal logical foundation of the positive formulation for the array type to facilitate maximal loop fission and subsequent optimizations. A_{i}NF is normal with regard to commuting conversion for both let-bindings and for-loops, leading to flat and maximally fissioned terms. We mechanize the translation and normalization from a simple surface language to A_{i}NF, establishing that the process terminates, preserves types, and produces maximally fissioned terms.

Incremental computing promises to lead to faster and more efficient programs by avoiding unnecessary recomputations, but existing approaches are often ad-hoc. We consider a more generic approach to incrementality using the idea of data types as polynomial functors and investigate how this approach can lead to constructions of changes and incrementalizations.

Modeling sequential and parallel composition of effectful computations has been investigated in a variety of languages for a long time. In particular, the popular do-notation provides a lightweight effect embedding for any instance of a monad. Idiom bracket notation, on the other hand, provides an embedding for applicatives. First, while monads force effects to be executed sequentially, ignoring potential for parallelism, applicatives do not support sequential effects. Composing sequential with parallel effects remains an open problem. This is even more of an issue as real programs consist of a combination of both sequential and parallel segments. Second, common notations do not support invoking effects in direct-style, instead forcing a rigid structure upon the code. In this paper, we propose a mixed applicative/monadic notation that retains parallelism where possible, but allows sequentiality where necessary. We leverage a direct-style notation where sequentiality or parallelism is derived from the structure of the code. We provide a mechanisation of our effectful language in Coq and prove that our compilation approach retains the parallelism of the source program.

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.

Decentralized applications (dApps) consist of smart contracts that run on blockchains and clients that model collaborating parties. dApps are used to model financial and legal business functionality. Today, contracts and clients are written as separate programs—in different programming languages—communicating via send and receive operations. This makes distributed program flow awkward to express and reason about, increasing the potential for mismatches in the client-contract interface, which can be exploited by malicious clients, potentially leading to huge financial losses. In this article, we present Prisma , a language for tierless decentralized applications, where the contract and its clients are defined in one unit and pairs of send and receive actions that “belong together” are encapsulated into a single direct-style operation, which is executed differently by sending and receiving parties. This enables expressing distributed program flow via standard control flow and renders mismatching communication impossible. We prove formally that our compiler preserves program behavior in presence of an attacker controlling the client code. We systematically compare Prisma with mainstream and advanced programming models for dApps and provide empirical evidence for its expressiveness and performance.

Decentralized applications (dApps) consist of smart contracts that run on blockchains and clients that model collaborating parties. dApps are used to model financial and legal business functionality. Today, contracts and clients are written as separate programs-in different programming languages-communicating via send and receive operations. This makes distributed program flow awkward to express and reason about, increasing the potential for mismatches in the client-contract interface, which can be exploited by malicious clients, potentially leading to huge financial losses. In this paper, we present Prisma, a language for tierless decentralized applications, where the contract and its clients are defined in one unit. Pairs of send and receive actions that "belong together" are encapsulated into a single direct-style operation, which is executed differently by sending and receiving parties. This enables expressing distributed program flow via standard control flow and renders mismatching communication impossible. We prove formally that our compiler preserves program behavior in presence of an attacker controlling the client code. We systematically compare Prisma with mainstream and advanced programming models for dApps and provide empirical evidence for its expressiveness and performance. The design space of dApp programming and other multi-party languages depends on one major choice: a local model versus a global model. In a local model, parties are defined in separate programs and their interactions are encoded via send and receive effects. In a global language, parties are defined within one shared program and interactions are encoded via combined sendand-receive operations with no effects visible to the outside world. The global model is followed by tierless and choreographic languages. However, known approaches to dApp programming follow the local model, thus rely on explicitly specifying the client-contract interaction protocol. Moreover, the contract and clients are implemented in different languages, hence, developers have to master two technology stacks. The dominating approach in industry is Solidity for the contract and JavaScript for clients. Solidity relies on expressing the protocol using assertions in the contract code, which are checked at run time. Failing to insert the correct assertions may give parties illegal access to monetary values to the detriment of others. In research, contract languages have been proposed that rely on advanced type systems such as session types, type states, and linear types. The global model has not been explored for dApp programming. This is unfortunate given the potential to get by with a standard typing discipline and to avoid intricacies and potential mismatches of a two-language stack. Our work fills this gap by proposing Prisma-the first language that features a global programming model for Ethereum dApps. While we focus on the Ethereum blockchain, we believe our techniques

Choreographic languages aim to express multiparty communication protocols, by providing primitives that make interaction manifest. Multitier languages enable programming computation that spans across several tiers of a distributed system, by supporting primitives that allow computation to change the location of execution. Rooted into different theoretical underpinnings - respectively process calculi and lambda calculus - the two paradigms have been investigated independently by different research communities with little or no contact. As a result, the link between the two paradigms has remained hidden for long. In this paper, we show that choreographic languages and multitier languages are surprisingly similar. We substantiate our claim by isolating the core abstractions that differentiate the two approaches and by providing algorithms that translate one into the other in a straightforward way. We believe that this work paves the way for joint research and cross-fertilisation among the two communities.