UCSC-SOE-15-09: Game Semantics for Type Soundness

Tim Disney, Cormac Flanagan
05/14/2015 06:26 PM
Computer Science
The key idea of game
semantics is that a term can interact with its enclosing
context via various events, such as
function calls and returns. A trace is a
sequence of such interaction events. The meaning of the term is then
naturally represented by the set of all event traces that the term can
Game semantics allows us to define the meaning of both expressions
and types in the same domain which enables an interesting
alternative to subject reduction for proving type soundness.

This paper uses game semantics to define the meaning of and verify
type soundness for a sequence of programming languages, starting with
a functional sequential language (the call-by-value simply-typed lambda calculus),
and then extending that proof with subtyping, side effects, control
effects, and concurrency. These proofs are reasonably short and fairly
semantic in structure, focusing on the relationship between the
meanings of each term and its corresponding type. In particular, we
show that the typing and subtyping relations are both conservative
approximations of alternating trace containment.