The Spineless Tagless G-machine is an abstract machine designed to support non-strict higher-order functional languages. This presentation of the machine falls into three parts. Firstly, we give a general discussion of the design issues involved in implementing non-strict functional languages. Next, we present the STG language, an austere but recognizably-functional language, which as well as a denotational meaning has a well-defined operational semantics. The STG language is the ‘abstract machine code’ for the Spineless Tagless G-machine. Lastly, we discuss the mapping of the STG language onto stock hardware. The success of an abstract machine model depends largely on how efficient this mapping can be made, though this topic is often relegated to a short section. Instead, we give a detailed discussion of the design issues and the choices we have made. Our principal target is the C language, treating the C compiler as a portable assembler.

In a functional program, a simple random number generator may generate a lazy list of random numbers. This is fine when the random numbers are consumed sequentially at a single point in the program. However, things are more complicated in a program where random numbers are used at many locations, such as in a large simulation. The programmer should not need to worry about providing separate generators with a unique seed at each point where random numbers are used. At the same time, the programmer should not need to coordinate the use of a single stream of random numbers in many parts of the program, which can be particularly difficult with lazy evaluation or parallel processing.

We discuss several techniques for distributing random numbers to various parts of a program, and some methods of allowing different program components to evaluate random numbers locally. We then propose a new approach in which a random number sequence can be split at a random point to produce a pair of random number sequences that can be used independently at different points in the computation.

The approach can also be used in distributed procedural programs, where it is desirable to avoid dealing with a single source of random numbers. The approach has the added advantage of producing repeatable results, as might be needed in debugging, for example.

We present a simple and easy-to-understand explanation of ML type inference and parametric polymorphism within the framework of type monomorphism, as in the first order typed lambda calculus. We prove the equivalence of this system with the standard interpretation using type polymorphism, and extend the equivalence to include polymorphic fixpoints. The monomorphic interpretation gives a purely combinatorial understanding of the type inference problem, and is a classic instance of quantifier elimination, as well as an example of Gentzen-style cut elimination in the framework of the Curry-Howard propositions-as-types analogy.

A closed λ-term E is called an enumerator if

Here ⋀0 is the set of closed λ-terms,. is the set of natural numbers and the ⌜n⌝ are the Church's numerals λfx.fnx. Such an E is called reducing if, moreover

An ingenious recursion theoretic proof by Statman will be presented, showing that every enumerator is reducing. I do not know any direct proof.

At the recent TC2 working conference on constructing programs from specifications (Moeller, 1991), I presented the derivation of a functional program for solving a problem posed by Knuth (1990). Slightly simplified, the problem was to construct a shortest decimal fraction representing a given integer multiple of 1/216. Later in the conference – and in a different context – Robert Dewar described a second problem that he had recently set as an examination question. In brief, the problem was to replace sequences of blanks in a file by tab characters wherever possible. Although Knuth's and Dewar's problems appear to have little in common, I suspected that both had the same ‘deep structure’ and were instances of a single general result about greedy algorithms. The purpose of this note is to bring the genral result to light and to unify the treatment of the two problems. We begin by describing the problems more precisely.