Computer Laboratory

Course pages 2016–17

Semantics of Programming Languages

Principal lecturer: Prof Peter Sewell
Taken by: Part IB
Past exam questions

No. of lectures: 12
Suggested hours of supervisions: 3
This course is a prerequisite for the Part II courses Topics in Concurrency, and Types.


The aim of this course is to introduce the structural, operational approach to programming language semantics. It will show how to specify the meaning of typical programming language constructs, in the context of language design, and how to reason formally about semantic properties of programs.


  • Introduction. Transition systems. The idea of structural operational semantics. Transition semantics of a simple imperative language. Language design options. [2 lectures]

  • Types. Introduction to formal type systems. Typing for the simple imperative language. Statements of desirable properties. [2 lectures]

  • Induction. Review of mathematical induction. Abstract syntax trees and structural induction. Rule-based inductive definitions and proofs. Proofs of type safety properties. [2 lectures]

  • Functions. Call-by-name and call-by-value function application, semantics and typing. Local recursive definitions. [2 lectures]

  • Data. Semantics and typing for products, sums, records, references. [1 lecture]

  • Subtyping. Record subtyping and simple object encoding. [1 lecture]

  • Semantic equivalence. Semantic equivalence of phrases in a simple imperative language, including the congruence property. Examples of equivalence and non-equivalence. [1 lecture]

  • Concurrency. Shared variable interleaving. Semantics for simple mutexes; a serializability property. [1 lecture]


At the end of the course students should

  • be familiar with rule-based presentations of the operational semantics and type systems for some simple imperative, functional and interactive program constructs;

  • be able to prove properties of an operational semantics using various forms of induction (mathematical, structural, and rule-based);

  • be familiar with some operationally-based notions of semantic equivalence of program phrases and their basic properties.

Recommended reading

* Pierce, B.C. (2002). Types and programming languages. MIT Press.
Hennessy, M. (1990). The semantics of programming languages. Wiley. Out of print, but available on the web at
Winskel, G. (1993). The formal semantics of programming languages. MIT Press.