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...

The extension of Haskell with a built-in state monad combines mathematical elegance with operational efficiency: ffl Semantically, at the source language level, constructs that act on the state are viewed as functions that pass an explicit store data structure around. ffl Operationally, at the implementation level, constructs that act on the state are viewed as statements whose evaluation has the side-effect of updating the implicit global store in place. There are several unproven conjectures that the two views are consistent. Recently, we have noted that the consistency of the two views is far from obvious: all it takes for the implementation to become unsound is one judiciously-placed beta-step in the optimization phase of the compiler. This discovery motivates the current paper in which we formalize and show the correctness of the implementation of monadic state. For the proof, we first design a typed call-by-need language that models the intermediate language of the compiler, to...

According to folklore, Algol is an "orthogonal" extension of a simple imperative programming language with a call-by-name functional language. The former contains assignments, branching constructs, and compound statements; the latter is based on the typed -calculus. In an attempt to formalize the claim of "orthogonality", we define a simple version of Algol and an extended -calculus. The calculus includes the full fi-rule and rules for the reduction of assignment statements and commands. It has the usual properties, e.g., it satisfies a Church-Rosser and Strong Normalization Theorem. In support of the claim that the imperative and functional components are orthogonal to each other, we show that the proofs of these theorems are combinations of separate Church-Rosser and Strong Normalization theorems for each sublanguage. An acclaimed consequence of Algol's orthogonal design is the idea that the evaluation of a program has two distinct phases. The first phase corresponds to an unrolling ...