Transient gradual typing imposes run-time type tests that typically cause a linear slowdown in programs' performance. This performance impact discourages the use of type annotations because adding types to a program makes the program slower. A virtual machine can employ standard just-in-time optimizations to reduce the overhead of transient checks to near zero. These optimizations can give gradually-typed languages performance comparable to state-of-the-art dynamic languages, so programmers can add types to their code without affecting their programs' performance.
The diversity of semantics and language designs incorporating gradual typing has been captured recently via surveys incorporating formal models of different design options. Chung et al. present an object-oriented model covering optional semantics (erasure), transient semantics, concrete semantics (from Thorn @cite_11 ), and behavioural semantics (from Typed Racket), and give a series of programs to clarify the semantics of a particular language. Greenman et al. take a more functional approach, again modelling erasure, transient ( first order''), and behavioural ( higher order'') semantics @cite_23 , and also present performance information based on Typed Racket. Wilson et al. take a rather different approach, employing questionnaires to investigate the semantics programmers expect of a gradual typing system @cite_25 .
@cite_25 @cite_23 @cite_11
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There are several different gradual typing semantics, reflecting different trade-offs between performance and type soundness guarantees. Notably absent, however, are any data on which of these semantics developers actually prefer. We begin to rectify this shortcoming by surveying professional developers, computer science students, and Mechanical Turk workers on their preferences between three gradual typing semantics. These semantics reflect important points in the design space, corresponding to the behaviors of Typed Racket, TypeScript, and Reticulated Python. Our most important finding is that our respondents prefer a runtime semantics that fully enforces statically declared types. Gradual typing combines static and dynamic typing in the same program. One would hope that the performance in a gradually typed language would range between that of a dynamically typed language and a statically typed language. Existing implementations of gradually typed languages have not achieved this goal due to overheads associated with runtime casts. (2016) report up to 100 @math slowdowns for partially typed programs. In this paper we present a compiler, named Grift, for evaluating implementation techniques for gradual typing. We take a straightforward but surprisingly unexplored implementation approach for gradual typing, that is, ahead-of-time compilation to native assembly code with carefully chosen runtime representations and space-efficient coercions. Our experiments show that this approach achieves performance on par with OCaml on statically typed programs and performance between that of Gambit and Racket on untyped programs. On partially typed code, the geometric mean ranges from 0.42 @math to 2.36 @math that of (untyped) Racket across the benchmarks. We implement casts using the coercions of Siek, Thiemann, and Wadler (2015). This technique eliminates all catastrophic slowdowns without introducing significant overhead. Across the benchmarks, coercions range from 15 slower (fft) to almost 2 @math faster (matmult) than regular casts. We also implement the monotonic references of (2015). Monotonic references eliminate all overhead in statically typed code, and for partially typed code, they are faster than proxied references, sometimes up to 1.48 @math . Combining static and dynamic typing within the same language offers clear benefits to programmers. It provides dynamic typing in situations that require rapid prototyping, heterogeneous data structures, and reflection, while supporting static typing when safety, modularity, and efficiency are primary concerns. Siek and Taha (2006) introduced an approach to combining static and dynamic typing in a fine-grained manner through the notion of type consistency in the static semantics and run-time casts in the dynamic semantics. However, many open questions remain regarding the semantics of gradually typed languages. In this paper we present Reticulated Python, a system for experimenting with gradual-typed dialects of Python. The dialects are syntactically identical to Python 3 but give static and dynamic semantics to the type annotations already present in Python 3. Reticulated Python consists of a typechecker and a source-to-source translator from Reticulated Python to Python 3. Using Reticulated Python, we evaluate a gradual type system and three approaches to the dynamic semantics of mutable objects: the traditional semantics based on Siek and Taha (2007) and (2007) and two new designs. We evaluate these designs in the context of several third-party Python programs. Logic programming with the stable model semantics is put forward as a novel constraint programming paradigm. This paradigm is interesting because it bring advantages of logic programming based knowledge representation techniques to constraint programming and because implementation methods for the stable model semantics for ground (variabledfree) programs have advanced significantly in recent years. For a program with variables these methods need a grounding procedure for generating a variabledfree program. As a practical approach to handling the grounding problem a subclass of logic programs, domain restricted programs, is proposed. This subclass enables efficient grounding procedures and serves as a basis for integrating builtdin predicates and functions often needed in applications. It is shown that the novel paradigm embeds classical logical satisfiability and standard (finite domain) constraint satisfaction problems but seems to provide a more expressive framework from a knowledge representation point of view. The first steps towards a programming methodology for the new paradigm are taken by presenting solutions to standard constraint satisfaction problems, combinatorial graph problems and planning problems. An efficient implementation of the paradigm based on domain restricted programs has been developed. This is an extension of a previous implementation of the stable model semantics, the Smodels system, and is publicly available. It contains, e.g., builtdin integer arithmetic integrated to stable model computation. The implementation is described briefly and some test results illustrating the current level of performance are reported. We look at the operational semantics of languages with interactive I O through the glasses of constructive type theory. Following on from our earlier work on coinductive trace-based semantics for While [17], we define several big-step semantics for Whil e with interactive I O, based on resumptions and termination-sensitive weak bisimilarity. These require nesting inductive definitions in coinductive definitions, which is interesting both mathe matically and from the point-of-view of implementation in a proof assistant. After first defining a basic semantics of statements in terms o f resumptions with explicit internal actions (delays), we introduce a semantics in terms of delay-free resumptions that essentially removes finite sequences of delays on the fly from those resumptions th at are responsive. Finally, we also look at a semantics in terms of delay-free resumptions supplemented with a silent divergence option. This semantics hinges on decisions between convergence and divergence and is only equivalent to the basic one classically. We have fully formalized our development in Coq. Part 1 Introduction: model programming languages lambda notation equations, reduction and semantics types and type systems notation and mathematical conventions set-theoretic background syntax and semantics induction. Part 2 The language PCF: syntax of PCF PCF programmes and their semantics PCF reduction and symbolic interpreters PCF programming examples, expressive power and limitations variations and extensions of PCF. Part 3 Universal algebra and algebraic data types: preview of algebraic specification algebras, signatures and terms equations, soundness and completeness homomorphisms and initiality algebraic data types rewrite systems. Part 4 Simply-typed lambda calculus: types terms proof systems Henkin models, soundness and completeness. Part 5 Models of typed lambda calculus: domain-theoretic models and fixed points fixed-point induction computational adequacy and full abstraction recursion-theoretic models partial equivalence relations and recursion. Part 6 Imperative programmes: while programmes operational semantics denotational semantics before-after assertions about while programmes semantics of additional programme constructs. Part 7 Categories and recursive types: Cartesian closed categories Kripke lambda models and functor categories domain models of recursive types. Part 8 Logical relations: introduction to logical relations logical relations over applicative structures proof-theoretic results partial surjections and specific models representation independence generalizations of logical relations. Part 9 Polymorphism and modularity: predicative polymorphic calculus impredicative polymorphism data abstraction and existential types general products, sums and programme modules. Part 10 subtyping and related concepts: simply typed lambda calculus with subtyping records, semantic models of subtyping recursive types and a record model of objects polymorphism with subtype constraints. Part 11 Type inference: introduction to type inference type inference for lambda xxx with type variables type inference with polymorphic declarations. We present a method of translating discrete-time Simulink models to Lustre programs. Our method consists of three steps: type inference, clock inference, and hierarchical bottom-up translation. In the process, we explain and formalize the typing and timing mechanisms of Simulink. The method has been implemented in a prototype tool called S2L, which has been used in the context of a European research project to translate two automotive controller models provided by Audi. The “classical” paradigm for denotational semantics models data types as domains, i.e. structured sets of some kind, and programs as (suitable) functions between domains. The semantic universe in which the denotational modelling is carried out is thus a category with domains as objects, functions as morphisms, and composition of morphisms given by function composition. A sharp distinction is then drawn between denotational and operational semantics. Denotational semantics is often referred to as “mathematical semantics” because it exhibits a high degree of mathematical structure; this is in part achieved by the fact that denotational semantics abstracts away from the dynamics of computation—from time. By contrast, operational semantics is formulated in terms of the syntax of the language being modelled; it is highly intensional in character; and it is capable of expressing the dynamical aspects of computation. The classical denotational paradigm has been very successful, but has some definite limitations. Firstly, fine-structural features of computation, such as sequentiality, computational complexity, and optimality of reduction strategies, have either not been captured at all denotationally, or not in a fully satisfactory fashion. Moreover, once languages with features beyond the purely functional are considered, the appropriateness of modelling programs by functions is increasingly open to question. Neither concurrency nor “advanced” imperative features such as local references have been captured denotationally in a fully convincing fashion. This analysis suggests a desideratum of Intensional Semantics, interpolating between denotational and operational semantics as traditionally conceived. This should combine the good mathematical structural properties of denotational semantics with the ability to capture dynamical aspects and to embody computational intuitions of operational semantics. Thus we may think of Intensional semantics as “Denotational semantics + time (dynamics)”, or as “Syntax-free operational semantics”. A number of recent developments (and, with hindsight, some older ones) can be seen as contributing to this goal of Intensional Semantics. We will focus on the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages ( 1995) (Abramsky and McCusker 1995) (Hyland and Ong 1995) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless We introduce the stable model semantics fordisjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., non-disjunctive) programs. Depending on whether only total (2-valued) or all partial (3-valued) models are used we obtain thedisjunctive stable semantics or thepartial disjunctive stable semantics, respectively. The proposed semantics are shown to have the following properties: • For normal programs, the disjunctive (respectively, partial disjunctive) stable semantics coincides with thestable (respectively,partial stable) semantics. • For normal programs, the partial disjunctive stable semantics also coincides with thewell-founded semantics. • For locally stratified disjunctive programs both (total and partial) disjunctive stable semantics coincide with theperfect model semantics. • The partial disjunctive stable semantics can be generalized to the class ofall disjunctive logic programs. • Both (total and partial) disjunctive stable semantics can be naturally extended to a broader class of disjunctive programs that permit the use ofclassical negation. • After translation of the programP into a suitable autoepistemic theory ( P ) the disjunctive (respectively, partial disjunctive) stable semantics ofP coincides with the autoepistemic (respectively, 3-valued autoepistemic) semantics of ( P ) . Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model. The literature on gradual typing presents three fundamentally different ways of thinking about the integrity of programs that combine statically typed and dynamically typed code. This paper systematically compares the theory of these approaches, their logical implications for the developer, and their performance. Gradual typing systems ensure type soundness by transforming static type annotations into run-time checks. These checks provide semantic guarantees, but may come at a large cost in performance. In particular, recent work by suggests that enforcing a conventional form of type soundness may slow a program by two orders of magnitude. Since different gradual typing systems satisfy different notions of soundness, the question then arises: what is the cost of such varying notions of soundness? This paper answers an instance of this question by applying 's evaluation method to Reticulated Python, which satisfies a notion of type-tag soundness. We find that the cost of soundness in Reticulated is at most one order of magnitude, and increases linearly with the number of type annotations. Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary first-order sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in first-order logic, providing a way to apply first-order theorem provers to reasoning about non-Herbrand stable models. Current proposals for adding gradual typing to JavaScript, such as Closure, TypeScript and Dart, forgo soundness to deal with issues of scale, code reuse, and popular programming patterns. We show how to address these issues in practice while retaining soundness. We design and implement a new gradual type system, prototyped for expediency as a 'Safe' compilation mode for TypeScript. Our compiler achieves soundness by enforcing stricter static checks and embedding residual runtime checks in compiled code. It emits plain JavaScript that runs on stock virtual machines. Our main theorem is a simulation that ensures that the checks introduced by Safe TypeScript (1) catch any dynamic type error, and (2) do not alter the semantics of type-safe TypeScript code. Safe TypeScript is carefully designed to minimize the performance overhead of runtime checks. At its core, we rely on two new ideas: differential subtyping, a new form of coercive subtyping that computes the minimum amount of runtime type information that must be added to each object; and an erasure modality, which we use to safely and selectively erase type information. This allows us to scale our design to full-fledged TypeScript, including arrays, maps, classes, inheritance, overloading, and generic types. We validate the usability and performance of Safe TypeScript empirically by type-checking and compiling around 120,000 lines of existing TypeScript source code. Although runtime checks can be expensive, the end-to-end overhead is small for code bases that already have type annotations. For instance, we bootstrap the Safe TypeScript compiler (90,000 lines including the base TypeScript compiler): we measure a 15 runtime overhead for type safety, and also uncover programming errors as type safety violations. We conclude that, at least during development and testing, subjecting JavaScript TypeScript programs to safe gradual typing adds significant value to source type annotations at a modest cost. We study syntax-free models for name-passing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual π-calculus operations, defining Indexed Labelled Transition Systems. For non-interleaving causal semantics we define Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi. In each case we relate a denotational semantics to an operational view, for bisimulation and causal bisimulation respectively. We establish completeness properties of, and adjunctions between, categories of the two models. Alternative indexing structures and possible applications are also discussed. These are first steps towards a uniform understanding of the semantics and operations of name-passing calculi. We present an approach to semantics-based statistical machine translation that uses synchronous hyperedge replacement grammars to translate into and from graph-shaped intermediate meaning representations, to our knowledge the first work in NLP to make use of synchronous context free graph grammars. We present algorithms for each step of the semantics-based translation pipeline, including a novel graph-to-word alignment algorithm and two algorithms for synchronous grammar rule extraction. We investigate the influence of syntactic annotations on semantics-based translation by presenting two alternative rule extraction algorithms, one that requires only semantic annotations and another that additionally relies on syntactic annotations, and explore the effect of syntax and language bias in meaning representation structures by running experiments with two different meaning representations, one biased toward an English syntax-like structure and another that is language neutral. While preliminary work, these experiments show promise for semantically-informed machine translation. We present a novel combination of disjunctive programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a well-balanced interface between disjunctive programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also define the well-founded semantics for the normal case, where normal programs are combined with tractable description logics, and we explore its semantic and computational properties. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for the problems of consistency checking and literal entailment under the well-founded semantics, and we give a precise picture of their computational complexity. As a crucial property, in the normal case, consistency checking and literal entailment under the well-founded semantics are both tractable in the data complexity, and even first-order rewritable (and thus can be done in LogSpace in the data complexity) in a special case that is especially useful for representing mappings between ontologies. Static and dynamic type systems have well-known strengths and weaknesses. In previous work we developed a gradual type system for a functional calculus named @math . Gradual typing provides the benefits of both static and dynamic checking in a single language by allowing the programmer to control whether a portion of the program is type checked at compile-time or run-time by adding or removing type annotations on variables. Several object-oriented scripting languages are preparing to add static checking. To support that work this paper develops @math , a gradual type system for object-based languages, extending the Ob < : calculus of Abadi and Cardelli. Our primary contribution is to show that gradual typing and subtyping are orthogonal and can be combined in a principled fashion. We also develop a small-step semantics, provide a machine-checked proof of type safety, and improve the space efficiency of higher-order casts. Programmers in dynamic languages wishing to constrain and understand the behavior of their programs may turn to gradually-typed languages, which allow types to be specified optionally and check values at the boundary between dynamic and static code. Unfortunately, the performance cost of these run-time checks can be severe, slowing down execution by at least 10x when checks are present. Modern virtual machines (VMs) for dynamic languages use speculative techniques to improve performance: If a particular value was seen once, it is likely that similar values will be seen in the future. They combine optimization-relevant properties of values into cacheable “shapes”, then use a single shape check to subsume checks for each property. Values with the same memory layout or the same field types have the same shape. This greatly reduces the amount of type checking that needs to be performed at run-time to execute dynamic code. While very valuable to the VM’s optimization, these checks do little to benefit the programmer aside from improving performance. We present in this paper a design for intrinsic object contracts, which makes the obligations of gradually-typed languages’ type checks an intrinsic part of object shapes, and thus can subsume run-time type checks into existing shape checks, eliminating redundant checks entirely. With an implementation on a VM for JavaScript used as a target for SafeTypeScript’s soundness guarantees, we demonstrate slowdown averaging 7 in fully-typed code relative to unchecked code, and no more than 45 in pessimal configurations. Modeling crisp logical regularities is crucial in semantic parsing, making it difficult for neural models with no task-specific prior knowledge to achieve good results. In this paper, we introduce data recombination, a novel framework for injecting such prior knowledge into a model. From the training data, we induce a high-precision synchronous context-free grammar, which captures important conditional independence properties commonly found in semantic parsing. We then train a sequence-to-sequence recurrent network (RNN) model with a novel attention-based copying mechanism on datapoints sampled from this grammar, thereby teaching the model about these structural properties. Data recombination improves the accuracy of our RNN model on three semantic parsing datasets, leading to new state-of-the-art performance on the standard GeoQuery dataset for models with comparable supervision.