The aim of this work is largely a practical one. A widely employed style of programming, particularly in structure-processing languages which impose no discipline of types, entails defining procedures which work well on objects of a wide variety. We present a formal type discipline for such polymorphic procedures in the context of a simple pro-gramming language, and a compile time type-checking algorithm w which enforces the discipline. A Semantic Soundness Theorem (based on a formal semantics for the language) states that well-type programs cannot “go wrong ” and a Syntactic Soundness Theorem states that if fl accepts a program then it is well typed. We also discuss extending these results to richer languages; a type-checking algorithm based on w is in fact already implemented and working, for the metalanguage ML in the Edinburgh LCF system, 1.

The runtime data structures of the Standard ML of New Jersey compiler are simple yet general. As a result, code generators are easy to implement, programs execute quickly, garbage collectors are easy to implement and work efficiently, and a variety of runtime facilities can be provided with ease.

Program transformation is a means to formally develop efficient programs from lucid specifications. A representative sample of the diverse range of program transformation research is classified into several different approaches based upon the motivations for and styles of constructing such formal developments. Individual techniques for supporting construction of developments are also surveyed, and are related to the various approaches.

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In the last ten years declaration-free programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically typed languages (Algol68, Pascal). These polymorphic languages can be type checked at compile time, yet allow functions whose arguments range over a variety of types. We investigate several polymorphic type systems, the most powerful of which, termed Milner-Mycroft Calculus, extends the so-called let-polymorphism found in, e.g., ML with a polymorphic typing rule for recursive definitions. We show that semi-unification, the problem of solving inequalities over firstorder terms, characterizes type checking in the Milner-Mycroft Calculus to polynomial time, even in the restricted case where nested definitions are disallowed. This permits us to extend some infeasibility results for related combinato...

: HOL is a public domain system for generating proofs in higher order predicate calculus. It has been in experimental and commercial use in several countries for a number of years. ELLA 2 is a hardware design language developed at the Royal Signals and Radar Establishment (RSRE) and marketed by Computer General Electronic Design. It supports simulation models at a variety of different abstraction levels. A preliminary methodology for reasoning about ELLA designs using HOL is described. Our approach is to semantically embed a subset of the ELLA language in higher order logic, and then to make this embedding convenient to use with parsers and pretty-printers. There are a number of semantic issues that may affect the ease of verification. We discuss some of these briefly. We also give a simple example to illustrate the methodology. 1 Presented at the International Workshop on Formal Methods in VLSI Design, Miami, January 1991. 2 ELLA is a registered trademark of the Secretary of St...

Research into providing support for long term data in lazy functional programming systems is presented in this thesis. The motivation for this work has been to reap the benefits of integrating lazy functional programming languages and persistence. The benefits are . the programmer need not write code to support long term data since this is provided as part of the programming system . persistent data can be used in a type safe way since the programming language type system applies to data with the whole range of persistence . the benefits of lazy evaluation are extended to the full lifetime of a data value. Whilst data is reachable, any evaluation performed on the data persists. A data value changes monotonically from an unevaluated state towards a completely evaluated state over time. . interactive data intensive applications such as functional databases can be developed. These benefits are realised by the development of models for persistence in lazy functional programming systems. Tw...

The purpose of a type checker is to prevent an incorrect operation from being performed. A static type checker does this by stopping the compiler from generating a program with type errors, a dynamic type checker halts the program as it is about to make a type error. It is clearly useless to have a dynamic type checking system for a program which is to be produced, distributed and used by anyone other than the original authors since any type errors that occur would be meaningless to the user of the program. On the other hand, where a user is guiding a program through some data, a dynamic type-checking system is reasonable. Examples are browsing through a database or structure-editing. Here type-errors have meaning to the user. The ideal language would be basically statically type-checked but would allow dynamic type-checking when necessary. While this is possible with certain type systems there are others for which it is difficult. The implementation of dynamic type checking in various...

It has long been known that some of the most common uses of for and while-loops in imperative programs can easily be expressed using the standard higher-order functions fold and map. With this correspondence as a starting point, we derive parallel implementations of various iterative constructs, each having a better complexity than their sequential counterparts, and explore the use of monads to guarantee the soundness of the parallel implementation. As an aid to the presentation of the material, we use the proposed syntax for parallel Haskell [27] (figure 1) as a vehicle in which imperative functional programs will be expressed. Surprisingly, incorporating imperative features into a purely functional language has become an active area of research within the functional programming community [30, 24, 36, 20]. One of the techniques gaining widespread acceptance as a model for imperative functional programming is monads [38, 37, 26]. Typically monads are used to guarantee single threadedn...

Today’s increasingly computer-based society is dependent on the correctness and reliability of crucial infrastructure, such as programming languages, compilers, networks, and microprocessors. One important way to achieve the required level of assurance is to use formal specification and proof, and tool support for this approach has steadily grown to the point where the specification and verification of important system infrastructure is now feasible. To survey the state of the art and discuss future possibilities and challenges, a two day research meeting entitled Tools and Techniques for Verification of System