No Arabic abstract
Language-integrated query is a popular and powerful programming construct allowing database queries and ordinary program code to interoperate seamlessly and safely. Language-integrated query techniques rely on classical results about the nested relational calculus stating that its queries can be algorithmically translated to SQL, as long as their result type is a flat relation. Cooper and others advocated higher-order nested relational calculi as a basis for language-integrated queries in functional languages such as Links and F#. However, the translation of higher-order relational queries to SQL relies on a rewrite system for which no strong normalization proof has been published: a previous proof attempt does not deal correctly with rewrite rules that duplicate subterms. This paper fills the gap in the literature, explaining the difficulty with the previous attempt, and showing how to extend the $toptop$-lifting approach of Lindley and Stark to accommodate duplicating rewrites. We also show how to extend the proof to a recently-introduced calculus for heterogeneous queries mixing set and multiset semantics.
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kocks synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for plain expressions and for DAGs and determine the complexity of corresponding unification problems.
We present a unification of refinement and Hoare-style reasoning in a foundational mechanized higher-order distributed separation logic. This unification enables us to prove formally in the Coq proof assistant that concrete implementations of challenging distributed systems refine more abstract models and to combine refinement-style reasoning with Hoare-style program verification. We use our logic to prove correctness of concrete implementations of two-phase commit and single-decree Paxos by showing that they refine their abstract TLA+ specifications. We further use our notion of refinement to transfer fairness assumptions on program executions to model traces and then transfer liveness properties of fair model traces back to program executions, which enables us to prove liveness properties such as strong eventual consistency of a concrete implementation of a Conflict-Free Replicated Data Type and fair termination of a concurrent program.
Scilla is a higher-order polymorphic typed intermediate level language for implementing smart contracts. In this talk, we describe a Scilla compiler targeting LLVM, with a focus on mapping Scilla types, values, and its functional language constructs to LLVM-IR. The compiled LLVM-IR, when executed with LLVMs JIT framework, achieves a speedup of about 10x over the reference interpreter on a typical Scilla contract. This reduced latency is crucial in the setting of blockchains, where smart contracts are executed as parts of transactions, to achieve peak transactions processed per second. Experiments on the Ackermann function achieved a speedup of more than 45x. This talk abstract is aimed at both programming language researchers looking to implement an LLVM based compiler for their functional language, as well as at LLVM practitioners.
Lenses are a popular approach to bidirectional transformations, a generalisation of the view update problem in databases, in which we wish to make changes to source tables to effect a desired change on a view. However, perhaps surprisingly, lenses have seldom actually been used to implement updatable views in databases. Bohannon, Pierce and Vaughan proposed an approach to updatable views called relational lenses, but to the best of our knowledge this proposal has not been implemented or evaluated to date. We propose incremental relational lenses, that equip relational lenses with change-propagating semantics that map small changes to the view to (potentially) small changes to the source tables. We also present a language-integrated implementation of relational lenses and a detailed experimental evaluation, showing orders of magnitude improvement over the non-incremental approach. Our work shows that relational lenses can be used to support expressive and efficient view updates at the language level, without relying on updatable view support from the underlying database.