Atsushi Ohori

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 ƒ of a records is polymorphic in the sense that it can be applied to any record which contains a field ƒ 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.

Using powerdomains to generalize relational databases

Abstract Much of relational algebra and the underlying principles of relational database design have a simple representation in the theory of domains that is traditionally used in the denotational semantics of programming languages. By investigating the possible orderings on powerdomains that are well known in the study of nondeterminism and concurrency it is possible to show that many of the ideas in relational databases apply to structures that are much more general than relations. This also suggests a method of representing database objects as typed objects in programming languages. In this paper we show how operations such as natural join and projection —which are fundamental to relational database design—can be generalized, and we use this generalized framework to give characterizations of several relational database concepts including functional dependencies and universal relations. All of these have a simple-minded semantics in terms of the underlying domains, which can be thought of as domains of partial descriptions of “real-world” objects. We also discuss the applicability of relational database theory to nonrelational structures such as records with variants, higher-order relations, recursive structures and other ordered spaces.

A polymorphic record calculus and its compilation

The motivation of this work is to provide a type-theoretical basis for developing a practical polymorphic programming language with labeled records and labeled variants. Our goal is to establish both a polymorphic type discipline and an efficient compilation method for a calculus with those labeled data structures. We define a second-order, polymorphic record calculus as an extension of Girard-Reynolds polymorphic lambda calculus. We then develop an ML-style type inference algorithm for a predicative subset of the second-order record calculus. The soundness of the type system and the completeness of the type inference algorithm are shown. These results extend Milners type inference algorithm, Damas and Milners account of MLs let polymorphism, and Harper and Mitchells analysis on XML. To establish an efficient compilation method for the polymorphic record calculus, we first define an implementation calculus, where records are represented as vectors whose elements are accessed by direct indexing, and variants are represented as values tagged with a natural number indicating the position in the vector of functions in a switch statement. We then develop an algorithm to translate the polymorphic record calculus into the implementation calculus using type information obtained by the type inference algorithm. The correctness of the compilation algorithm is proved ; that is, the compilation algorithm is shown to preserve both typing and the operational behavior of a program. Based on these results, Standard ML has been extended with labeled records, and its compiler has been implemented.

Type inference in a database programming language

We extend an ML-like implicit type system to include a number of structures and operations that are common in database programming including sets, labeled records, joins and projections. We then show that the type inference problem of the system is decidable by extending the notion of principal type schemes to include conditions on substitutions. Combined with Milners polymorphic let constructor, our language also supports type inheritance.

Polymorphism and type inference in database programming

In order to find a static type system that adequately supports database languages, we need to express the most general type of a program that involves database operations. This can be achieved through an extension to the type system of ML that captures the polymorphic nation of field selection, together with a techniques that generalizes relational operators to arbitrary data structures. The combination provides a statically typed language in which generalized relational databases may be cleanly represented as typed structures. As in ML types are inferred, which relieves the programmer of making the type assertions that may be required in a complex database environment. These extensions may also be used to provide static polymorphic typechecking in object-oriented languages and databases. A problem that arises with object-oriented databases is the apparent need for dynamic typechecking when dealing queries on heterogeneous collections of objects. An extension of the type system needed for generalized relational operations can also be used for manipulating collections of dynamically typed values in a statically typed language. A prototype language based on these ideas has been implemented. While it lacks a proper treatment of persistent data, it demonstrates that a wide variety of database structures can be cleanly represented in a polymorphic programming language.

A compilation method for ML-style polymorphic record calculi

Polymorphic record calculi have recently attracted much attention as a typed foundation for object-oriented programming. This is based on the fact that a function that selects a field l of a record can be given a polymorphic type that enables it to be applied to various records containing a field l. Recent studies have established techniques to develop an ML-style type inference algorithm for such a polymorphic type system. There seems to be, however, no established method to compile an ML-style polymorphic record calculus into efficient code. The purpose of this paper is to present one such method. We define a polymorphic record calculus as an extension of Damas and Milers proof system for ML. For this calculus, we define an implementation calculus where records are represented as arrays of (references to) values and field selection is performed by direct indexing. To represent polymorphic field selection, the implementation calculus contains an abstraction mechanism over indexes. We then develop an algorithm to translate the polymorphic record calculus into the implementation calculus by refining a type inference algorithm; it simultaneously computes a principal type scheme in the polymorphic record calculus and a correct implementation term in the implementation calculus. The type inference is shown to be sound and complete in the sense of Damas-Milners algorithm for ML. Moreover, the polymorphic type system is shown to be sound with respect to an operational semantics of the translated terms in the implementation calculus.

Static type inference for parametric classes

Central features of object-oriented programming are method inheritance and data abstraction attained through hierarchical organization of classes. Recent studies show that method inheritance can be nicely supported by ML style type inference when extended to labeled records. This is based on the fact that a function that selects a field ƒ of a record can be given a polymorphic type that enables it to be applied to any record which contains a field ƒ. Several type systems also provide data abstraction through abstract type declarations. However, these two features have not yet been properly integrated in a statically checked polymorphic type system. This paper proposes a static type system that achieves this integration in an ML-like polymorphic language by adding a class construct that allows the programmer to build a hierarchy of classes connected by multiple inheritance declarations. Moreover, classes can be parameterized by types allowing “generic” definitions. The type correctness of class declarations is statically checked by the type system. The type system also infers a principal scheme for any type correct program containing methods and objects defined in classes.

Lightweight fusion by fixed point promotion

This paper proposes a lightweight fusion method for general recursive function definitions. Compared with existing proposals, our method has several significant practical features: it works for general recursive functions on general algebraic data types; it does not produce extra runtime overhea (except for possible code size increase due to the success of fusion); and it is readily incorporated in standard inlining optimization. This is achieved by extending the ordinary inlining process with a new fusion law that transforms a term of the form f o (fixgλx.E) to a new fixed point term fixhλx.E′ by promoting the function f through the fixed point operator. This is a sound syntactic transformation rule that is not sensitive to the types of f and g. This property makes our method applicable to wide range of functions including those with multi-parameters in both curried and uncurried forms. Although this method does not guarantee any form of completeness, it fuses typical examples discussed in the literature and others that involve accumulating parameters, either in the tt foldl-like specific forms or in general recursive forms, without any additional machinery. In order to substantiate our claim, we have implemented our method in a compiler. Although it is preliminary, it demonstrates practical feasibility of this method.

Semantics for communication primitives in a polymorphic language

We propose a method to extend an ML-style polymorphic language with transparent communication primitives, and give their precise operational semantics. These primitives allow any polymorphic programs definable in ML to be used remotely in a manner completely transparent to the programmer. Furthermore, communicating programs may be based on different architecture and use different data representations. We define a polymorphic functional calculus with transparent communication primitives, which we call dML, as an extension of Damas and Milners proof system for ML. We then develop an algorithm to translate dML to a “core” language containing only low-level communication primitives that are readily implementable in most of distributed environments. To establish the type safety of communicating programs, we define an operational semantics of the core language and prove that the polymorphic type system of dML is sound with respect to the operational semantics of the translated terms of the core language.

Semantics of types for database objects

This paper proposes a denotational semantics of types for database objects. A simple typed language to represent database objects is defined and its denotational semantics is given. In this language, sets are first-class values and a join and a projection are available as typed operations on general data structures including sets.