We propose a semantic model of PAF!, a proof assistant dedicated to program verification focused on the functional fragment of ML. In particular, we model the strong typing predicate, specific to the PAF! system. From the semantic correctness of the system, we prove the consistency of the formalism, as well as the termination property for all strongly typed programs (as defined in the system). ...

We examine the problem of how to ensure behavioral consistency of an object-oriented system after its schema has been updated. The problem is viewed from the perspective of both the strongly typed and the untyped language model. Solutions are compared in both models using C++ and CLOS as examples.

Scientists and engineers must ensure that physical equations are dimensionally consistent, but existing programming languages treat all numeric values as dimensionless. This paper extends a strongly-typed programming language with a notion of dimension type. Our approach improves on previous proposals in that dimension types may be polymorphic. Furthermore, any expression which is typable in th...

Given a graph H on vertex set {1, 2, · · · , n} and a function f : [0, 1] → R, define ‖f‖H := ∣∣∣∣∣ ∫ ∏ ij∈E(H) f(xi, xj)dμ |V (H)| ∣∣∣∣∣ 1/|E(H)| , where μ is the Lebesgue measure on [0, 1]. We say that H is norming if ‖·‖H is a semi-norm. A similar notion ‖·‖r(H) is defined by ‖f‖r(H) := ‖|f |‖H and H is said to be weakly norming if ‖·‖r(H) is a norm. Classical results show that weakly normin...

Fibonacci is an object-oriented database programming language characterized by static and strong typing and by new mechanisms for modelling databases in terms of objects with roles, classes and associations. A brief introduction to the language is provided to present those features which are particularly suited to modelling complex databases. Examples of the use of Fibonacci are given with refe...

Programs involving precise types enforce more properties via type-checking, but precise types also prevent the reuse of functions throughout a program since no single precise type is used throughout a large program. My work is a step toward eliminating the underlying dilemma regarding type precision versus function reuse. It culminates in a novel traversal operator that recovers the reuse by au...

Example Output • Type Strength – A language characteristic based on the amount of coercion (casting) permitted and performed among its data types  Less coercions = stronger typing – Coercion is generally performed during compile time to insure compatibility of operator and operand types – C integer coercions are rule based  Integer ranking  Integer promotion rules  Usual arithmetic conversi...

We consider a semantic class, weakly-chase-sticky (WChS), and a syntactic subclass, jointly-weakly-sticky (JWS), of Datalog programs. Both extend that of weakly-sticky (WS) programs, which appear in our applications to data quality. For WChS programs we propose a practical, polynomial-time query answering algorithm (QAA). We establish that the two classes are closed under magic-sets rewritings....

The F# language includes a feature called “F# 3.0 Type Providers” to support the integration of internet-scale information sources into a strongly typed functional-first programming environment. In this position paper we describe the key themes in information-rich functional programming that we have observed during this work. Our contribution is to document these themes and highlight future cha...

The most powerful control constructs in modern programming languages are continuations and exceptions. Although they can be used interchangeably in some cases, they are fundamentally different semantically. We consider two simply-typed functional languages with exceptions and continuations, respectively. We give theorems, one that holds in the language with exceptions and one that holds in the ...