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.

Abstract. Higher-order programming languages (i.e., languages in which procedures or labels can occur as values) are usually defined by interpreters that are themselves written in a programming language based on the lambda calculus (i.e., an applicative language such as pure LISP). Examples include McCarthy’s definition of LISP, Landin’s SECD machine, the Vienna definition of PL/I, Reynolds ’ definitions of GEDANKEN, and recent unpublished work by L. Morris and C. Wadsworth. Such definitions can be classified according to whether the interpreter contains higher-order functions, and whether the order of application (i.e., call by value versus call by name) in the defined language depends upon the order of application in the defining language. As an example, we consider the definition of a simple applicative programming language by means of an interpreter written in a similar language. Definitions in each of the above classifications are derived from one another by informal but constructive methods. The treatment of imperative features such as jumps and assignment is also discussed.

The syntactic theories of control and state are conservative extensions of the v -calculus for equational reasoning about imperative programming facilities in higher-order languages. Unlike the simple v -calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higher-order programming languages. The new theories subsume the original calculi of control and state and satisfy the usual Church-Rosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs. 1 The syntactic theories of control and state Most -calculus-based programming languages provide imperative programming facilities such as assignment statements, exceptions, and continuations. Typical examples are ML [16], Schem...

The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with first-class labels and jumps. We show that the well-known formulae-astypes correspondence, which relates a constructive proof of a formula ff to a program of type ff, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting "classical programs" --- programs of type ff, where ff holds classically, but not constructively --- is illustrated by the definition of conjunctive, disjunctive, and existential types using standard classical definitions. We also prove that all evaluations of typed terms in Idealized Scheme are finite.

Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type and module system, Standard ML manages to combine safety, security, and robustness with much of the flexibility of dynamically typed languages like Lisp. It is also has the most well-developed scientific foundation of any major language. Here I review the strengths and weaknesses of Standard ML and describe some of what we have learned through the design, implementation, and use of the language.

Lambda lifting is a technique for transforming a functional program with local function definitions, possibly with free variables in the function definitions, into a program consisting only of global function (combinator) definitions which will be used as rewrite rules. Different ways of doing lambda lifting are presented, as well as reasons for rejecting or selecting the method used in our Lazy ML compiler. An attribute grammar and a functional program implementing the chosen algorithm is given. Originally publised in Proceedings 1985 Conference on Functional Programming Languages and Computer Architecture, Lecture Notes in Computer Science 201, Nancy, France, 1985. Springer Verlag. y As part B of author's thesis. Main addition: the attribute grammar formulation. 1 Introduction When compiling a lazy functional language using the technique described in [Joh84] it is presumed that the input program is in the form of a set of function definitions, possibly mutually recursive, tog...

This paper describes the principles underlying an efficient implementation of a lazy functional language, compiling to code for ordinary computers. It is based on combinator-like graph reduction: the user defined functions are used as rewrite rules in the graph. Each function is compiled into an instruction sequence for an abstract graph reduction machine, called the G-machine, the code reduces a function application graph to its value. The G-machine instructions are then translated into target code. Speed improvements by almost two orders of magnitude over previous lazy evaluators have been measured; we provide some performance figures.

The literature on programming languages contains an abundance of informal claims on the relative expressive power of programming languages, but there is no framework for formalizing such statements nor for deriving interesting consequences. As a first step in this direction, we develop a formal notion of expressiveness and investigate its properties. To validate the theory, we analyze some widely held beliefs about the expressive power of several extensions of functional languages. Based on these results, we believe that our system correctly captures many of the informal ideas on expressiveness, and that it constitutes a foundation for further research in this direction. 1 Comparing Programming Languages The literature on programming languages contains an abundance of informal claims on the expressive power of programming languages. Arguments in these contexts typically assert the expressibility or non-expressibility of programming constructs relative to a language. Unfortunately, pro...

This is a description of the programming language Forsythe, which is a descendant of Algol 60 intended to be as uniform and general as possible, while retaining the basic character of its progenitor. This document supercedes Report CMU--CS--88--159, "Preliminary Design of the Programming Language Forsythe" [1]. c fl1996 John C. Reynolds Research suuported by National Science Foundation Grant CCR-9409997. Keywords: Forsythe, Algol-like languages, Algol 60, intersection types 1. Introduction In retrospect, it is clear that Algol 60 [2, 3] was an heroic and surprisingly successful attempt to design a programming language from first principles. Its creation gave a formidable impetus to the development and use of theory in language design and implementation, which has borne rich fruit in the intervening thirty-six years. Most of this work has led to languages that are quite different than Algol 60, but there has been a continuing thread of concern with languages that retain the essentia...

Domain-specific embedded languages (DSELs) expressed in higher-order, typed (HOT) languages provide a composable framework for domain-specific abstractions. Such a framework is of greater utility than a collection of stand-alone domain-specific languages. Usually, embedded domain specific languages are build on top of a set of domain specific primitive functions that are ultimately implemented using some form of foreign function call. We sketch a general design pattern for embedding client-server style services into Haskell using a domain specific embedded compiler for the server's source language. In particular we apply this idea to implement Haskell/DB, a domain specific embdedded compiler that dynamically generates of SQL queries from monad comprehensions, which are then executed on an arbitrary ODBC database server.