With growing complexity, distributed software systems become increasingly challenging to maintain and reason about. When implementing a distributed protocol, developers must ensure manually that the different components fit together. Choreographic programming addresses this challenge by specifying global protocols in a single program and projecting them into communicating processes, so-called endpoints. Recent choreographic approaches are designed as programming libraries that embed this paradigm into a host language like Haskell or Rust. In these designs, we observe common cases of partiality: unreachable branches in endpoint projection (EPP) and located-value access can trigger runtime errors or undefined behavior, relying on manual discipline of library maintainers rather than being statically type-checked. Also, some programs require users to write down dummy branches that should not be reachable, for example when branching on sum types. To close this gap, we use the dependently typed Lean programming language to implement a similar choreographic library. We show how we are able to move from a partial EPP to a total EPP function, and also eliminate cases of partiality in user-written code with pattern matching on sum types. ChorLean ensures total EPP and safe value access via proof-carrying located values, passing Lean's totality checker without undefined cases, while supporting the same feature set as libraries like MultiChor.

Choreographic programming is a programming model for developing distributed applications where an entire communication protocol is written as a single program, which a compiler then projects to one process per participant. Choreographic programming abstracts over low-level network communication primitives such as sockets, and provides a high degree of safety guarantees with deadlock freedom ensured by construction. Mechanizing choreographies necessarily deals with both operations specific to distributed programming and standard (local) operations that also occur in non-distributed programs, as well as the typical issues of binding and substitution. We aim to sidestep the latter issues, thereby obtaining a more concise mechanization that focuses on the essential distributed aspects of choreographies. To this end, we use a method recently proposed by Thiemann to elegantly model deadlock-free processes in a dependently typed language: Using state transformers to represent the computations performed by each process. We bring the state transformer model to choreographies, allowing us to reduce the usual mechanization effort around binding and substitution, and to abstract over the details of the "local" aspects of the language. We mechanize in Lean a choreographic language that supports point-to-point communication, broadcasting, recursive procedures, and local stateful methods, allowing each participant to be assigned a different set of methods. We prove soundness and completeness of endpoint projection, establish deadlock freedom for the projected processes, prove confluence, and verify a Hoare logic for choreographies.

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 (AiNF), which relies on the formal logical foundation of the positive formulation for the array type to facilitate maximal loop fission and subsequent optimizations. AiNF 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 AiNF, 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.

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 tomodel 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.

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.

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.