In this thesis we present and analyse a set of automatic source-to-source program transformations that are suitable for incorporation in optimising compilers for lazy functional languages. These transformations improve the quality of code in many different respects, such as execution time and memory usage. The transformations presented are divided in two sets: global transformations, which are performed once (or sometimes twice) during the compilation process; and a set of local transformations, which are performed before and after each of the global transformations, so that they can simplify the code before applying the global transformations and also take advantage of them afterwards. Many of the local transformations are simple, well known, and do not have major effects on their own. They become important as they interact with each other and with global transformations, sometimes in non-obvious ways. We present how and why they improve the code, and perform extensive experiments wit...

This paper shows how the Improvement Theorem---a semantic condition

We give a new semantics for Nuprl's constructive type theory that justifies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the last decade. The new semantics is dramatically simpler than the old, and gives a novel and general way of adding set-theoretic equivalence classes to untyped functional programming languages.

Co-induction is an important tool for reasoning about unbounded structures. This tutorial explains the foundations of co-induction, and shows how it justifies intuitive arguments about lazy streams, of central importance to lazy functional programmers. We explain from first principles a theory based on a new formulation of bisimilarity for functional programs, which coincides exactly with Morris-style contextual equivalence. We show how to prove properties of lazy streams by co-induction and derive Bird and Wadler's Take Lemma, a well-known proof technique for lazy streams.

The significance of type theory to the theory of programming languages has long been recognized. Advances in programming languages have often derived from understanding that stems from type theory. However, these applications of type theory to practical programming languages have been indirect; the differences between practical languages and type theory have prevented direct connections between the two. This dissertation presents systematic techniques directly relating practical programming languages to type theory. These techniques allow programming languages to be interpreted in the rich mathematical domain of type theory. Such interpretations lead to semantics that are at once denotational and operational, combining the advantages of each, and they also lay the foundation for formal verification of computer programs in type theory. Previous type theories either have not provided adequate expressiveness to interpret practical languages, or have provided such expressiveness at the expense of essential features of the type theory. In particular, no previous type theory has supported a notion of partial functions (needed to interpret recursion in practical languages), and a notion of total functions and objects (needed to reason about data values), and an intrinsic notion of equality (needed for most interesting results). This dissertation presents the first type theory incorporating all three, and discusses issues arising in the design of that type theory. This type theory is used as the target of a type­theoretic semantics for a expressive programming calculus. This calculus may serve as an internal language for a variety of functional programming languages. The semantics is stated as a syntax­directed embedding of the programming calculus into type theory. A critical point arising in both the type theory and the type­theoretic semantics is the issue of admissibility. Admissibility governs what types it is legal to form recursive functions over. To build a useful type theory for partial functions it is necessary to have a wide class of admissible types. In particular, it is necessary for all the types arising in the type­theoretic semantics to be admissible. In this dissertation I present a class of admissible types that is considerably wider than any previously known class.

Abstract not found

The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfold-fold method. Unfortunately the unfold-fold method itself guarantees neither improvement in efficiency nor total-correctness. The correctness problem for unfold-fold is an instance of a strictly more general problem: transformation by locally equivalence-preserving steps does not necessarily preserve (global) equivalence. This paper presents a condition for the total correctness of transformations on recursive programs, which, for the first time, deals with higher-order functional languages (both strict and non-strict) including lazy data structures. The main technical result is an improvement theorem which says that if the local transformation steps are guided by certain optimisation concerns (a fairly natural condition for a transformation), then correctness of the transformation follows. The improvement theorem make...

This paper presents a typed higher-order concurrent functional programming language, based on Moggi's monadic metalanguage and Reppy's Concurrent ML. We present an operational semantics for the language, and show that a higherorder variant of the traces model is fully abstract for maytesting. This proof uses a program logic based on Hennessy-- Milner logic and Abramsky's domain theory in logical form. 1 Introduction This paper presents an operational semantics for a concurrent functional programming language, based on Reppy's [26, 27] Concurrent ML, and Moggi's [22] monadic metalanguage. CML is a concurrent extension of New Jersey ML, which adds communication primitives based on CCS [19] and CSP [11]. Reppy introduces a new type constructor of events, which can spawn concurrent processes, and communicate with them along channels. Three of the constructors for the event type are: always : a#aevent wrap : (aeventa#b)# (bevent) sync : aevent#a These are: . alwayse is an event whic...

) David Sands y Department of Computing, Imperial College 180 Queens Gate, London SW7 2BZ email: ds@uk.ac.ic.doc Abstract In this paper we address the technical foundations essential to the aim of providing a semantic basis for the formal treatment of relative efficiency in functional languages. For a general class of "functional" computation systems, we define a family of improvement preorderings which express, in a variety of ways, when one expression is more efficient than another. The main results of this paper build on Howe's study of equality in lazy computation systems, and are concerned with the question of when a given improvement relation is subject to the usual forms of (in)equational reasoning (so that, for example, we can improve an expression by improving any sub-expression). For a general class of computation systems we establish conditions on the operators of the language which guarantee that an improvement relation is a precongruence. In addition, for...

Abstract not found