Static and dynamic semantics of NoSQL languages

We present a calculus for processing semistructured data that spans differences of application area among several novel query languages, broadly categorized as "NoSQL". This calculus lets users define their own operators, capturing a wider range of data processing capabilities, whilst providing a typing precision so far typical only of primitive hard-coded operators. The type inference algorithm is based on semantic type checking, resulting in type information that is both precise, and flexible enough to handle structured and semistructured data. We illustrate the use of this calculus by encoding a large fragment of Jaql, including operations and iterators over JSON, embedded SQL expressions, and co-grouping, and show how the encoding directly yields a typing discipline for Jaql as it is, namely without the addition of any type definition or type annotation in the code

A Graph Model for Imperative Computation

Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on the lattice of sets of natural numbers can be represented via their graphs. A graph is a relation mapping finite sets of input values to output values. We consider a similar model based on relations whose input values are finite sequences rather than sets. This alteration means that we are taking into account the order in which observations are made. This new notion of graph gives rise to a model of affine lambda-calculus that admits an interpretation of imperative constructs including variable assignment, dereferencing and allocation. Extending this untyped model, we construct a category that provides a model of typed higher-order imperative computation with an affine type system. An appropriate language of this kind is Reynolds's Syntactic Control of Interference. Our model turns out to be fully abstract for this language. At a concrete level, it is the same as Reddy's object spaces model, which was the first "state-free" model of a higher-order imperative programming language and an important precursor of games models. The graph model can therefore be seen as a universal domain for Reddy's model

Session Communication and Integration

The scenario-based specification of a large distributed system is usually naturally decomposed into various modules. The integration of specification modules contrasts to the parallel composition of program components, and includes various ways such as scenario concatenation, choice, and nesting. The recent development of multiparty session types for process calculi provides useful techniques to accommodate the protocol modularisation, by encoding fragments of communication protocols in the usage of private channels for a class of agents. In this paper, we extend forgoing session type theories by enhancing the session integration mechanism. More specifically, we propose a novel synchronous multiparty session type theory, in which sessions are separated into the communicating and integrating levels. Communicating sessions record the message-based communications between multiple agents, whilst integrating sessions describe the integration of communicating ones. A two-level session type system is developed for pi-calculus with syntactic primitives for session establishment, and several key properties of the type system are studied. Applying the theory to system description, we show that a channel safety property and a session conformance property can be analysed. Also, to improve the utility of the theory, a process slicing method is used to help identify the violated sessions in the type checking.Comment: A short version of this paper is submitted for revie

Principal types for object-oriented languages

Object-oriented languages can he translated into a lambda-calculus with records. Therefore, type inference for record languages is one aspect of the yet unsolved problem of inferring types for object-oriented languages. In order to obtain the necessary flexibility for such a type system, we can either introduce a general subtyping notion or use extensible record types. Subtyping, especially in combination with imperative features, poses many hard problems. Therefore, the second approach is promising. The problem is that, in previous type inference systems that used extensible record types, principal types could not be inferred. We have found that, for an object-oriented language where classes are not first-class citizens, we could greatly simplify the underlying record language. We show that, for our simple record language, there exists a type inference algorithm that infers principal types

Dependent Merges and First-Class Environments

In most programming languages a (runtime) environment stores all the definitions that are available to programmers. Typically, environments are a meta-level notion, used only conceptually or internally in the implementation of programming languages. Only a few programming languages allow environments to be first-class values, which can be manipulated directly in programs. Although there is some research on calculi with first-class environments for statically typed programming languages, these calculi typically have significant restrictions. In this paper we propose a statically typed calculus, called ?_i, with first-class environments. The main novelty of the ?_i calculus is its support for first-class environments, together with an expressive set of operators that manipulate them. Such operators include: reification of the current environment, environment concatenation, environment restriction, and reflection mechanisms for running computations under a given environment. In ?_i any type can act as a context (i.e. an environment type) and contexts are simply types. Furthermore, because ?_i supports subtyping, there is a natural notion of context subtyping. There are two important ideas in ?_i that generalize and are inspired by existing notions in the literature. The ?_i calculus borrows disjoint intersection types and a merge operator, used in ?_i to model contexts and environments, from the ?_i calculus. However, unlike the merges in ?_i, the merges in ?_i can depend on previous components of a merge. From implicit calculi, the ?_i calculus borrows the notion of a query, which allows type-based lookups on environments. In particular, queries are key to the ability of ?_i to reify the current environment, or some parts of it. We prove the determinism and type soundness of ?_i, and show that ?_i can encode all well-typed ?_i programs

Reify Your Collection Queries for Modularity and Speed!

Modularity and efficiency are often contradicting requirements, such that programers have to trade one for the other. We analyze this dilemma in the context of programs operating on collections. Performance-critical code using collections need often to be hand-optimized, leading to non-modular, brittle, and redundant code. In principle, this dilemma could be avoided by automatic collection-specific optimizations, such as fusion of collection traversals, usage of indexing, or reordering of filters. Unfortunately, it is not obvious how to encode such optimizations in terms of ordinary collection APIs, because the program operating on the collections is not reified and hence cannot be analyzed. We propose SQuOpt, the Scala Query Optimizer--a deep embedding of the Scala collections API that allows such analyses and optimizations to be defined and executed within Scala, without relying on external tools or compiler extensions. SQuOpt provides the same "look and feel" (syntax and static typing guarantees) as the standard collections API. We evaluate SQuOpt by re-implementing several code analyses of the Findbugs tool using SQuOpt, show average speedups of 12x with a maximum of 12800x and hence demonstrate that SQuOpt can reconcile modularity and efficiency in real-world applications.Comment: 20 page

Mixin Composition Synthesis based on Intersection Types

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators. We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis. Furthermore, we demonstrate how a translated repository and goal type can be used as input to an existing framework for composition synthesis in bounded combinatory logic via type inhabitation. The computed result is a class typed by the goal type and generated by a mixin composition applied to an existing class

Relational Approach to Logical Query Optimization of XPath

To be able to handle the ever growing volumes of XML documents, effective and efficient data management solutions are needed. Managing XML data in a relational DBMS has great potential. Recently, effective relational storage schemes and index structures have been proposed as well as special-purpose join operators to speed up querying of XML data using XPath/XQuery. In this paper, we address the topic of query plan construction and logical query optimization. The claim of this paper is that standard relational algebra extended with special-purpose join operators suffices for logical query optimization. We focus on the XPath accelerator storage scheme and associated staircase join operators, but the approach can be generalized easily