19 research outputs found
Data Structures and Data Types in Object-Oriented Databases
The possibility of finding a static type system for object-oriented programming languages was initiated by Cardelli [Car88, CW85] who showed that it is possible to express the polymorphic nature of functions such a
Comprehension Syntax
The syntax of comprehensions is very close to the syntax of a number of practical database query languages and is, we believe, a better starting point than first-order logic for the development of database languages. We give an informal account of a language based on comprehension syntax that deals uniformly with a variety of collection types; it also includes pattern matching, variant types and function definition. We show, again informally, how comprehension syntax is a natural fragment of structural recursion, a much more powerful programming paradigm for collection types. We also show that a very small "abstract syntax language" can serve as a basis for the implementation and optimization of comprehension syntax
A query language and optimization techniques for unstructured data
A new kind of data model has recently emerged in which the database is not constrained by a conventional schema. Systems like ACeDB, which has become very popular with biologists, and the recent Tsimmis proposal for data integration organize data in tree-like structures whose components can be used equally well to represent sets and tuples. Such structures allow great flexibility in data representation What query language is appropriate for such structures? Here we propose a simple language UnQL for querying data organized as a rooted, edge-labeled graph. In this model, relational data may be represented as fixed-depth trees, and on such trees UnQL is equivalent to the relational algebra. The novelty of UnQL consists in its programming constructs for arbitrarily deep data and for cyclic structures. While strictly more powerful than query languages with path expressions like XSQL, UnQL can still be efficiently evaluated. We describe new optimization techniques for the deep or "vertical" dimension of UnQL queries. Furthermore, we show that known optimization techniques for operators on flat relations apply to the "horizontal" dimension of UnQL
Semantics of a Typed Algebraic Lambda-Calculus
Algebraic lambda-calculi have been studied in various ways, but their
semantics remain mostly untouched. In this paper we propose a semantic analysis
of a general simply-typed lambda-calculus endowed with a structure of vector
space. We sketch the relation with two established vectorial lambda-calculi.
Then we study the problems arising from the addition of a fixed point
combinator and how to modify the equational theory to solve them. We sketch an
algebraic vectorial PCF and its possible denotational interpretations
Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance
Refinement types sharpen systems of simple and dependent types by offering
expressive means to more precisely classify well-typed terms. We present a
system of refinement types for LF in the style of recent formulations where
only canonical forms are well-typed. Both the usual LF rules and the rules for
type refinements are bidirectional, leading to a straightforward proof of
decidability of typechecking even in the presence of intersection types.
Because we insist on canonical forms, structural rules for subtyping can now be
derived rather than being assumed as primitive. We illustrate the expressive
power of our system with examples and validate its design by demonstrating a
precise correspondence with traditional presentations of subtyping. Proof
irrelevance provides a mechanism for selectively hiding the identities of terms
in type theories. We show that LF refinement types can be interpreted as
predicates using proof irrelevance, establishing a uniform relationship between
two previously studied concepts in type theory. The interpretation and its
correctness proof are surprisingly complex, lending support to the claim that
refinement types are a fundamental construct rather than just a convenient
surface syntax for certain uses of proof irrelevance
Database Programming in Machiavelli - a Polymorphic Language with Static Type Inference
Machiavelli is a polymorphically typed programming language in the spirit of ML, but supports an extended method of type inferencing that makes its polymorphism more general and appropriate for database applications. In particular, a function that selects a field f of a records is polymorphic in the sense that it can be applied to any record which contains a field f with the appropriate type. When combined with a set data type and database operations including join and projection, this provides a natural medium for relational database programming. Moreover, by implementing database objects as reference types and generating the appropriate views â sets of structures with âidentity â â we can achieve a degree of static type checking for object-oriented databases.
Extensional Models for Polymorphism
We present a general method for constructing extensional models for the Girard-Reynolds polymorphic lambda calculus - the polymorphic extensional collapse. The method yields models that satisfy additional, computationally motivated constraints like having only two polymorphic booleans and having only the numerals as polymorphic integers. Moreover, the method can be used to show that any simply typed lambda model can be fully and faithfully embedded into a model of the polymorphic lambda calculus
Database Programming in Machiavelli - a Polymorphic Language with Static Type Inference
Machiavelli is a polymorphically typed programming language in the spirit of ML, but supports an extended method of type inferencing that makes its polymorphism more general and appropriate for database applications. In particular, a function that selects a field f of a records is polymorphic in the sense that it can be applied to any record which contains a field f with the appropriate type. When combined with a set data type and database operations including join and projection, this provides a natural medium for relational database programming. Moreover, by implementing database objects as reference types and generating the appropriate views --- sets of structures with "identity" --- we can achieve a degree of static type checking for object-oriented databases. 1 Introduction The term "impedance mismatch" has been coined [Mai89] to describe the phenomenon that the data types available in a programming language do not usually match the structures provided in a database system. This ..