Updating Complex Value Databeses

Query languages and their optimizations have been a very important issue in the database community. Languages for updating databases, however, have not been studied to the same extent, although they are clearly important since databases must change over time. The structure and expressiveness of updates is largely dependent on the data model. In relational databases, for example, the update language typically allows the user to specify changes to individual fields of a subset of a relation that meets some selection criterion. The syntax is terse, specifying only the pieces of the database that are to be altered. Because of its simplicity, most of the optimizations take place in the internal processing of the update rather than at the language level. In complex value databases, the need for a terse and optimizable update language is much greater, due to the deeply nested structures involved. Starting with a query language for complex value databases called the Collection Programming Language (CPL), we describe an extension called CPL+ which provides a convenient and intuitive specification of updates on complex values. CPL is a functional language, with powerful optimizations achieved through rewrite rules. Additional rewrite rules are derived for CPL+ and a notion of deltafication is introduced to transform complete updates, expressed as conventional CPL expressions, into equivalent update expressions in CPL+. As a result of applying these transformations, the performance of complex updates can increase substantially

A complete transformational toolkit for compilers

In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a 'transformational toolkit' to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIMt, under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starting from a straightforward 'interpreter' for closed PIM terms

Towards a complete transformational toolkit for compilers

PIM is an equational logic designed to function as a ``transformational toolkit'' for compilers and other programming tools that analyze and manipulate imperative languages.It has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis.PIM consists of the untyped lambda calculus extended with an algebraic data type that characterizes the behavior of lazy stores and generalized conditionals.A graph form of PIM terms is by design closely related to several intermediate representations commonly used in optimizing compilers. In this paper, we show that PIM's core algebraic component, PIM$_t$, possesses a complete equational axiomatization (under the assumption of certain reasonable restrictions on term formation). This has the practical consequence of guaranteeing that every semantics-preserving transformation on a program representable in PIM$_t$ can be derived by application of PIM$_t$ rules. We systematically derive the complete PIM$_t$ logic as the culmination of a sequence of increasingly powerful equational systems starting from a straightforward ``interpreter'' for closed PIM$_t$ terms. This work is an intermediate step in a larger program to develop a set of well-founded tools for manipulation of imperative programs by compilers and other systems that perform program analysis

Modular Interpreters in Haskell

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Names and higher-order functions.

Many functional programming languages rely on the elimination of 'impure' features: assignment to variables, exceptions and even input/output. But some of these are genuinely useful, and it is of real interest to establish how they can be reintroducted in a controlled way. This dissertation looks in detail at one example of this: the addition to a functional language of dynamically generated names. Names are created fresh, they can be compared with each other and passed around, but that is all. As a very basic example of state, they capture the graduation between private and public, local and global, by their interaction with higher-order functions. The vehicle for this study is the nu-calculus, an extension of the simply-typed lambdacalculus. The nu-calculus is equivalent to a certain fragment of Standard ML, omitting side-effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higher-order functions can be complex and subtle. Various operational and denotational methods for reasoning about the nu-calculus are developed. These include a computational metalanguage in the style of Moggi, which distinguishes in the type system between values and computations. This leads to categorical models that use a strong monad, and examples are devised based on functor categories. The idea of logical relations is used to derive powerful reasoning methods that capture some of the distinction between private and public names. These techniques are shown to be complete for establishing contextual equivalence between first-order expressions; they are also used to construct a correspondingly abstract categorical model. All the work with the nu-calculus extends cleanly to Reduced ML, a larger language that introduces integer references: mutable storage cells that are dynamically allocated. It turns out that the step up is quite simple, and both the computational metalanguage and the sample categorical models can be reused