Computability Theory is the foundation for computer software development. Our programming languages embody the techniques and models described by various theories of computation [1]. The Turing Machine is the canonical example of the Imperative Model [2]. Lambda Calculus is the canonical example of the Functional Model [3]. Kleene’s Churchâ€“Turing Thesis asserts the equivalence of these […]

## On Separating Values and Effects

## Implementing Actors in Kernel

Now is the time we come full-circle in our exploration of Kernel/Scheme/LISP and show how Actors can be implemented on this foundation. This should dispel the notion that Actors are just functions/procedures. Sure, when an Actor receives a message you could say that the message is “applied” to the Actor’s current behavior. In that sense, […]

## Semantic Extensibility with `Vau`

John Shutt has reformulated the foundations of LISP/Scheme [1]. Observing that Lambda is a primitive applicative constructor, he proposes Vau as a primitve operative constructor instead. This changes our focus from implicit evaluation to explicit evaluation. Applicatives evaluate their operands before evaluating the combination. Operatives act directly on their (unevaluated) operands, possibly evaluating them selectively. […]

## Fexpr the Ultimate Lambda

This article is dedicated to the memory of John McCarthy (1927–2011) We are constantly on a quest for the elegant combination of simplicity and expressiveness in computer languages—what Alan Kay calls the “Maxwell’s Equations of Software“. An important early milestone was John McCarthy’s LISP [1] (The evolution of these ideas and the thinking behind them […]

## Evaluating Expressions, part 3 – Pairs and Parallelism

In part 3 of our series implementing programming language constructs with actors, we explore parallel evaluation of sub-expressions and introduce pairs. Pairs allow the construction of tuples, generalizing structured multi-part patterns and values. In order to support pair expressions and patterns, we’ve refactored the grammar from part 2 to separate out literal constants expressions and […]

## Evaluating Expressions, part 2 – Conditional Special Form

We continue exploring actor implementation of programming language constructs by adding a special form for conditional expressions. This will not increase the expressive power of the language. In part 1 we implemented a Turing-complete pure untyped lambda calculus. Now we add direct efficient support for conditional expressions and introduce basic pattern matching. Changes from the […]

## Evaluating Expressions, part 1 – Core Lambda Calculus

One of the best ways to understand programming language constructs is to implement them. We will begin by implementing a simple, yet Turing-complete, functional expression language. In subsequent articles, we will extend this language with additional features. For now we will focus on just the “untyped” lambda calculus, augmented with constants. The grammar for our […]