Hidden Markov models (HMMs) are frequently used in areas such as speech recognition and bioinformatics. However, implementing HMM algorithms correctly and efficiently is time-consuming and error-prone. Specifically, using model-specific knowledge to improve performance, such as sparsity in the transition probability matrix, ties the implementation to a particular model, making it harder to modify. Previous work has introduced high-level frameworks for defining HMMs, thus lifting the burden of efficiently implementing HMM algorithms from the user. However, existing tools are ill-suited for sparse HMMs with many states. This paper introduces Trellis, a domain-specific language for succinctly defining sparse HMMs that use GPU acceleration to achieve high performance. We show that Trellis outperforms previous work and is on par with a hand-written CUDA kernel implementation for a particular sparse HMM.

Differential-Algebraic Equations (DAEs) are the foundation of high-level equation-based languages for modeling physical dynamical systems. Simulating models in such languages requires a transformation known as index reduction that involves differentiating individual equations before numerical integration. Commercial and open-source implementations typically perform index reduction by symbolic differentiation (SD) and produce a Jacobian callback function with forward-mode automatic differentiation (AD). The former results in efficient runtime code, and the latter is asymptotically efficient in both runtime and code size. However, AD introduces runtime overhead caused by a non-standard representation of real numbers, and SD is not always applicable in models with general recursion. This work proposes a new approach that uses partial evaluation of AD in the context of numerical DAE solving to combine the strengths of the two differentiation methods while mitigating their weaknesses. Moreover, our approach selectively specializes partial derivatives of the Jacobian by exploiting structural knowledge while respecting a user-defined bound on the code size. Our evaluation shows that the new method both enables expressive modeling from AD and retains the efficiency of SD for many practical applications.

Traditionally, a grammar defining the syntax of a programming language is typically both context free and unambiguous. However, recent work suggests that an attractive alternative is to use ambiguous grammars,thus postponing the task of resolving the ambiguity to the end user. If all programs accepted by an ambiguous grammar can be rewritten unambiguously, then the parser for the grammar is said to be resolvably ambiguous. Guaranteeing resolvable ambiguity statically---for all programs---is hard, where previous work only solves it partially using techniques based on property-based testing. In this paper, we present the first efficient, practical, and proven correct solution to the statically resolvable ambiguity problem. Our approach introduces several key ideas, including splittable productions, operator sequences, and the concept of a grouper that works in tandem with a standard parser. We prove static resolvability using a Coq mechanization and demonstrate its efficiency and practical applicability by implementing and integrating resolvable ambiguity into an essential part of the standard OCaml parser.

When building a new programming language, it can be useful to compose parts of existing languages to avoid repeating implementation work. However, this is problematic already at the syntax level, as composing the grammars of language fragments can easily lead to an ambiguous grammar. State-of-the-art parser tools cannot handle ambiguity truly well: either the grammar cannot be handled at all, or the tools give little help to an end-user who writes an ambiguous program. This composability problem is twofold: (i) how can we detect if the composed grammar is ambiguous, and (ii) if it is ambiguous, how can we help a user resolve an ambiguous program? In this paper, we depart from the traditional view of unambiguous grammar design and enable a language designer to work with an ambiguous grammar, while giving users the tools needed to handle these ambiguities. We introduce the concept of resolvable ambiguity wherein a user can resolve an ambiguous program by editing it, as well as an approach to computing the resolutions of an ambiguous program. Furthermore, we present a method based on property-based testing to identify if a composed grammar is unambiguous, resolvably ambiguous, or unresolvably ambiguous. The method is implemented in Haskell and evaluated on a large set of language fragments selected from different languages. The evaluation shows that (i) the approach can handle significantly more cases of language compositions compared to approaches which ban ambiguity altogether, and (ii) that the approach is fast enough to be used in practice.