Probabilistic Programming

Types in programming languages are commonly thought of as a way of preventing certain bad things from happening, such as multiplying a number by a string. But this is only half of the benefit of types: it is what types are against. Types in programming languages are also what enable some good things to happen, such as selecting the right implementation of a heterogeneous operation like comparison or printing based on type information; this is what are types for. This ability is surprisingly powerful, and gives rise to a variety of highly expressive generic programming techniques. Jeremy illustrates with some examples based on the rank-polymorphic array operations introduced in Iverson’s APL: not only does the type information prevent array shape errors, it is what directs the lifting of operations across array dimensions.

In this presentation, Uday brings together two strands of Christopher Strachey’s thought: parametric polymorphism and abstract models of storage. The term parametric polymorphism was introduced in by Strachey who distinguished it from “ad hoc” polymorphism. In the words of John Reynolds, “a parametric polymorphic function is one that behaves the same way for all types,” whereas an ad hoc polymorphic function may have unrelated meanings at different types. A very similar intuition arose in mathematics, some twenty years earlier, for which Eilenberg and MacLane proposed a “General Theory of Natural Equivalences”, what we now call category theory. Relating the two notions allows us to develop a broad view of “parametricity” (the idea of acting the same way for all types), which is applicable not only to programming languages but also to mathematics and perhaps other disciplines. A particularly important application of this broad view is for Strachey’s “mathematical semantics” of programming languages. For modelling imperative programming languages that operate by manipulating a store, Strachey presented a basic model of storage based on “locations”, while promising a further paper on an “abstract model of storage” to appear in future. Unfortunately the latter never appeared. In succeeding work, Reynolds proposed an abstract model of store as well as an “intuitionistic” functor category approach to model the stack discipline of the store. O'Hearn and Tennent made the crucial observation that the model needs to be embellished with parametricity to capture the data abstraction aspects of the store. In this talk, Uday reviews these developments as well as his own recent work on integrating the Reynolds model with parametricity to capture the fact that state changes of the store are irreversible. One way to understand these developments is to view them as a “parametric mathematical semantics” of programming languages.

Hongseok begins by talking about a program of Strachey’s that wrote “love letters” using the Manchester University computer. He then uses this as a lead in for discussing probabilistic methods of generating algorithms and programs.

Philip reviews Christopher Strachey’s influence on modern-day functional programming languages.

In this talk, Jane presents about her work on modelling dynamic behaviour of systems using quantative modelling techniques. Particular kinds of modelling diagrams are used and a mathematical approach to looking at their meaning is presented.

The logician Dana Scott played a crucial part in the story of denotational semantics, working for a term with Christopher Strachey in Autumn 1969, when he created a mathematical model for the foundation of the method. In this talk, Dana discusses this period as well as reminiscing about his life and career up to that point.

In this panel discussion, three people who knew Christopher Strachey in different contexts talk about their memories of him. Michael Jackson discusses being taught by Strachey as a boy at Harrow, David Hartley talks about work with Strachey on the programming language CPL, and Roger Penrose remembers working with Strachey at the National Research Development Corporation and introducing him to lambda calculus.

Christopher Strachey believed that the gap between theory and practice was impeding the development of computing science. In Robert’s talk, he considers how the work he did with Strachey on the essay that ultimately became their book tried to narrow the gap, by formalising, and reasoning about, the implementation concepts for programming languages. A particular focus will be the proof techniques for imperative programs that use storage, which were implicit, but not very easy to discern, in the book.

During Peter’s DPhil studies, supervised by Christopher Strachey, he developed a prototype of a system for executing programs based on their denotational semantics. It involved partial evaluation of lambda-notation, implemented using Wadsworth's call-by-need algorithm. He continued the development of the system as a postdoc at Oxford, and subsequently at Aarhus, Denmark. The system was called SIS: Semantics Implementation System. In this talk, Peter recalls Strachey's influence on his research and on the development of SIS, starting from Strachey’s summer school course on symbolic computation at the PRG in 1969.

Chrisopher Strachey was the most significant contributor to the design and implementation of the programming language CPL. At the time there was little understanding of the complexities of computer language design and how type systems could cope with lists and the kinds of structures needed to represent, for instance, parse trees. The CPL project cannot be regarded as being successful since it did not result in a usable CPL compiler. The reasons being that the language became too large and complicated, there were insufficient people to implement the compiler and, in the middle of the three year project, all work had to be transferred from Edsac 2 to Titan, a newly designed version of the Ferranti Atlas computer which as yet had no operating system. Even so, we can be proud of the work that went into CPL and its influence on the design of many later languages.