The MetaLanguage of the Edinburgh LCF theorem proving system has become a programming language in its own right, popular among a reasonably wide segment of the research community. ML has also become a lingua franca among applied type theorists, as they investigate type systems for the 90's as extensions of the remarkably influential Hindley-Milner type system.

A common technique for improving the speed of program specialization is to specialize the program specializer itself on the program to be specialized, creating a custom program generator. Much research has been devoted to the problem of generating efficient program generators, which do not perform reductions at program generation time which could instead have been performed when the program generator was constructed. The conventional wisdom holds that only program specializers using binding-time approximations can be specialized into such efficient program generators. This paper argues that this is not the case, and demonstrates that the specialization of a nontrivial online program specializer similar to the original ‘naive MIX’ can indeed yield an efficient program generator. The key to our argument is that, while the use of binding-time information at program generator generation time is necessary for the construction of an efficient custom specializer, the use of explicit binding-time approximation techniques is not. This allows us to distinguish the problem at hand (i.e. the use of binding-time information during program generator generation) from particular solutions to that problem (i.e. offline specialization). We show that, given a careful choice of specializer data structures, and sufficiently powerful specialization techniques, binding-time information can be inferred and utilized without explicit approximations. This allows the construction of efficient, optimizing program generators from online program specializers.

We extend the definition of natural semantics to include simply typed λ-terms, instead of first-order terms, for representing programs, and to include inference rules for the introduction and discharge of hypotheses and eigenvariables. This extension, which we call extended natural semantics, affords a higher-level notion of abstract syntax for representing programs and suitable mechanisms for manipulating this syntax. We present several examples of semantic specifications for a simple functional programming language and demonstrate how we achieve simple and elegant manipulations of bound variables in functional programs. All the examples have been implemented and tested in λProlog, a higher-order logic programming language that supports all of the features of extended natural semantics.

A new program transformation method is presented. It is a further refinement of supercompilation where the supercompiler is not applied directly to the function to be transformed, but to a metafunction, namely an interpreter which computes this function using its definition and an abstract (i.e. including variables) input. It is shown that with this method such tranformations become possible which the direct application of the supercompiler cannot perform. Examples include the merging of iterative loops, function inversion, and transformation of deterministic into non-deterministic algorithms, and vice-versa.

We show how improving values (Burton, 1991) can be extended to handle both upper and lower bounds. The result is a new data type, called improving intervals. We give a simple implementation of improving intervals that uses a list of successively tighter bounds to represent a value. A program using improving intervals can be evaluated as a parallel program using speculative evaluation. The utility of improving intervals is demonstrated through two programs: parallel alpha-beta and parallel branch-and-bound

Pattern matching in modern functional programming languages is tied to the representation of data. Unfortunately, this is incompatible with the philosophy of abstract data types.

Two proposals have been made to generalize pattern matching to a broader class of types. The laws mechanism of Miranda allows pattern matching with non-free algebraic data types. More recently, Wadler proposed the concept of views as a more general solution, making it possible to define arbitrary mappings between a physical implementation and a view supporting pattern matching. Originally, it was intended to include views in the new standard lazy functional programming language Haskell.

Laws and views each offer important advantages, particularly with respect to data abstraction. However, if not used with great care, they also introduce serious problems in equational reasoning. As a result, laws have been removed from Miranda and views were not included in the final version of Haskell.

We propose a third approach which unifies the laws and views mechanisms while avoiding their problems. Philosophically, we view pattern matching as a bundling of case recognition and component selection functions instead of a method for inverting data construction. This can be achieved by removing the implied equivalence between data constructors and pattern constructors. In practice, we allow automatic mapping into a view but not out of the view. We show that equational reasoning can still be used with the resulting system. In fact, equational reasoning is easier, since there are fewer hidden traps.

Based on Henglein's efficient binding-time analysis for the lambda calculus (with constants and ‘fix’) (Henglein, 1991), we develop three efficient analyses for use in the preprocessing phase of Similix, a self-applicable partial evaluator for a higher-order subset of Scheme. The analyses developed in this paper are almost-linear in the size of the analysed program. (1) A flow analysis determines possible value flow between lambda-abstractions and function applications and between constructor applications and selector/predicate applications. The flow analysis is not particularly biased towards partial evaluation; the analysis corresponds to the closure analysis of Bondorf (1991b). (2) A (monovariant) binding-time analysis distinguishes static from dynamic values; the analysis treats both higher-order functions and partially static data structures. (3) A new is-used analysis, not present in Bondorf (1991b), finds a non-minimal binding-time annotation which is ‘safe’ in a certain way: a first-order value may only become static if its result is ‘needed’ during specialization; this ‘poor man's generalization’ (Holst, 1988) increases termination of specialization. The three analyses are performed sequentially in the above mentioned order since each depends on results from the previous analyses. The input to all three analyses are constraint sets generated from the program being analysed. The constraints are solved efficiently by a normalizing union/find-based algorithm in almost-linear time. Whenever possible, the constraint sets are partitioned into subsets which are solved in a specific order; this simplifies constraint normalization. The framework elegantly allows expressing both forwards and backwards components of analyses. In particular, the new is-used analysis is of backwards nature. The three constraint normalization algorithms are proved correct (soundness, completeness, termination, existence of a best solution). The analyses have been implemented and integrated in the Similix system. The new analyses are indeed much more efficient than those of Bondorf (1991b); the almost-linear complexity of the new analyses is confirmed by the implementation.

The functional programming language Miranda has been used as a first programming language at the University of NSW since the beginning of 1989, when a new computer engineering course and a revised computer science course were introduced. This paper explains the reasons for choosing the language, and describes the subject in which Miranda is introduced. Examples of the presentation of the material, and of exercises and assignment used in the course, are given. Finally, an assessment of the experience is given.

Standard ML is an excellent language for many kinds of programming. It is safe, efficient, suitably abstract, and concise. There are many aspects of the language that work well.

However, nothing is perfect: Standard ML has a few shortcomings. In some cases there are obvious solutions, and in other cases further research is required.

A functional language, Miranda, is being used on an introductory programming course for business students. This paper describes the rationale for such a course and choice of language. An application in the area of operations management, which is used in teaching, is given as an example of the benefits of using a functional language in this area. The reaction of the students and staff to this (for them) new paradigm of programming is described. Some conclusions are drawn for computing education for non-specialists.

Values belonging to lazy data types have the advantage that sub-components can be accessed without evaluating the values as a whole: unneeded components remain unevaluated. A disadvantage is that often a large amount of space and time is required to handle lazy data types properly. Many special constructor cells are needed to ‘glue’ the individual parts of a composite object together and to store it in the heap. We present a way of representing data in functional languages which makes these special constructor cells superfluous. In some cases, no heap at all is needed to store this data. To make this possible, we introduce a new kind of data type: (partially) strict non-recursive data types. The main advantage of these types is that an efficient call-by-value mechanism can be used to pass arguments. A restrictive subclass of (partially) strict non-recursive data types, partially strict tuples, is treated more comprehensively. We also give examples of important classes of applications. In particular, we show how partially strict tuples can be used to define very efficient input and output primitives. Measurements of applications written in Concurrent Clean which exploit partially strict tuples have shown that speedups of 2 to 3 times are reasonable. Moreover, much less heap space is required when partially strict tuples are used.

Objects with dynamic types allow the integration of operations that essentially require runtime type-checking into statically-typed languages. This paper presents two extensions of the ML language with dynamics, based on our work on the CAML implementation of ML, and discusses their usefulness. The main novelty of this work is the combination of dynamics with polymorphism.

A binding-time analysis is correct if it always produces consistent binding-time information. Consistency prevents partial evaluators from ‘going wrong’. A sufficient and decidable condition for consistency, called well-annotatedness, was first presented by Gomard and Jones. In this paper we prove that a weaker condition implies consistency. Our condition is decidable, subsumes the one of Gomard and Jones, and was first studied by Schwartzbach and the present author. Our result implies the correctness of the binding-time analysis of Mogensen, and it indicates the correctness of the core of the binding-time analyses of Bondorf and Consel. We also prove that all partial evaluators will on termination have eliminated all ‘eliminable’-marked parts of an input which satisfies our condition. This generalizes a result of Gomard. Our development is for the pure λ-calculus with explicit binding-time annotations.

An extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuation-based operational semantics is defined for a small, purely functional language, and the soundness of the Damas–Milner polymorphic type assignment system with respect to this semantics is proved. The full Damas–Milner type system is shown to be unsound in the presence of first-class continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness.

In the period 1986–1991, experiments have been carried out with an introductory course in computer programming, based on functional programming. Due to thorough educational design and evaluation, a successful course has been developed. This has led to a revision of the computer programming education in the first year of the computer science curriculum at the University of Twente.

This article describes the approach, the aim of the computer programming course, the outline and subject matter of the course, and the evaluation. Educational research has been done to assess the quality of the course.

Mogensen has exhibited a very compact partial evaluator for the pure lambda calculus, using binding-time analysis followed by specialization. We give a correctness criterion for this partial evaluator and prove its correctness relative to this specification. We show that the conventional properties of partial evaluators, such as the Futamura projections, are consequences of this specification. By considering both a flow analysis and the transformation it justifies together, this proof suggests a framework for incorporating flow analyses into verified compilers.

We describe the design, implementation and use of a new kind of profiling tool that yields valuable information about the memory use of lazy functional programs. The tool has two parts: a modified functional language implementation which generates profiling information during the execution of programs, and a separate program which converts this information to graphical form. With the aid of profile graphs, one can make alterations to a functional program which dramatically reduce its space consumption. We demonstrate this in the case of a genuine example - the first to which the tool was applied - for which the results are strikingly successful.