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Register a new userLatent Effects for Reusable Language Components: Extended Version
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Added by
Tom Schrijvers
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The development of programming languages can be quite complicated and costly. Hence, much effort has been devoted to the modular definition of language features that can be reused in various combinations to define new languages and experiment with their semantics. A notable outcome of these efforts is the algebra-based datatypes a la carte (DTC) approach. When combined with algebraic effects, DTC can model a wide range of common language features. Unfortunately, the current state of the art does not cover modular definitions of advanced control-flow mechanisms that defer execution to an appropriate point, such as call-by-name and call-by-need evaluation, as well as (multi-)staging. This paper defines latent effects, a generic class of such control-flow mechanisms. We demonstrate how function abstractions, lazy computations and a MetaML-like staging can all be expressed in a modular fashion using latent effects, and how they can be combined in various ways to obtain complex semantics. We provide a full Haskell implementation of our effects and handlers with a range of examples.
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Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that type-based reasoning is preserved when moving from the fully static setting to a gradual one, these theorems do not imply that correctness of type-based refactorings and optimizations is preserved. Establishing correctness of program transformations is technically difficult, and is often neglected in the metatheory of gradual languages. In this paper, we propose an axiomatic account of program equivalence in a gradual cast calculus, which we formalize in a logic we call gradual type theory (GTT). Based on Levys call-by-push-value, GTT gives an axiomatic account of both call-by-value and call-by-name gradual languages. We then prove theorems that justify optimizations and refactorings in gradually typed languages. For example, uniqueness principles for gradual type connectives show that if the $betaeta$ laws hold for a connective, then casts between that connective must be equivalent to the lazy cast semantics. Contrapositively, this shows that eager cast semantics violates the extensionality of function types. As another example, we show that gradual upcasts are pure and dually, gradual downcasts are strict. We show the consistency and applicability of our theory by proving that an implementation using the lazy cast semantics gives a logical relations model of our type theory, where equivalence in GTT implies contextual equivalence of the programs. Since GTT also axiomatizes the dynamic gradual guarantee, our model also establishes this central theorem of gradual typing. The model is parametrized by the implementation of the dynamic types, and so gives a family of implementations that validate type-based optimization and the gradual guarantee.
Satisfiability modulo theories (SMT) solving has become a critical part of many static analyses, including symbolic execution, refinement type checking, and model checking. We propose Formulog, a domain-specific language that makes it possible to write a range of SMT-based static analyses in a way that is both close to their formal specifications and amenable to high-level optimizations and efficient evaluation. Formulog extends the logic programming language Datalog with a first-order functional language and mechanisms for representing and reasoning about SMT formulas; a novel type system supports the construction of expressive formulas, while ensuring that neither normal evaluation nor SMT solving goes wrong. Our case studies demonstrate that a range of SMT-based analyses can naturally and concisely be encoded in Formulog, and that -- thanks to this encoding -- high-level Datalog-style optimizations can be automatically and advantageously applied to these analyses.
Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the $(hatrho,delta)$-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state $hatrho$ and its distance $delta$ to the ideal state $rho$. This predicate $(hatrho,delta)$ can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the $(hatrho,delta)$-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.
Gradually typed languages allow statically typed and dynamically typed code to interact while maintaining benefits of both styles. The key to reasoning about these mixed programs is Siek-Vitousek-Cimini-Boylands (dynamic) gradual guarantee, which says that giving components of a program more precise types only adds runtime type checking, and does not otherwise change behavior. In this paper, we give a semantic reformulation of the gradual guarantee called graduality. We change the name to promote the analogy that graduality is to gradual typing what parametricity is to polymorphism. Each gives a local-to-global, syntactic-to-semantic reasoning principle that is formulated in terms of a kind of observational approximation. Utilizing the analogy, we develop a novel logical relation for proving graduality. We show that embedding-projection pairs (ep pairs) are to graduality what relations are to parametricity. We argue that casts between two types where one is more dynamic (less precise) than the other necessarily form an ep pair, and we use this to cleanly prove the graduality cases for casts from the ep-pair property. To construct ep pairs, we give an analysis of the type dynamism relation (also known as type precision or naive subtyping) that interprets the rules for type dynamism as compositional constructions on ep pairs, analogous to the coercion interpretation of subtyping.
RacerD is a static race detector that has been proven to be effective in engineering practice: it has seen thousands of data races fixed by developers before reaching production, and has supported the migration of Facebooks Android app rendering infrastructure from a single-threaded to a multi-threaded architecture. We prove a True Positives Theorem stating that, under certain assumptions, an idealized theoretical version of the analysis never reports a false positive. We also provide an empirical evaluation of an implementation of this analysis, versus the original RacerD. The theorem was motivated in the first case by the desire to understand the observation from production that RacerD was providing remarkably accurate signal to developers, and then the theorem guided further analyzer design decisions. Technically, our result can be seen as saying that the analysis computes an under-approximation of an over-approximation, which is the reverse of the more usual (over of under) situation in static analysis. Until now, static analyzers that are effective in practice but unsound have often been regarded as ad hoc; in contrast, we suggest that, in the future, theorems of this variety might be generally useful in understanding, justifying and designing effective static analyses for bug catching.
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