Quantitative Semantics.

Classical approaches to semantics essentially represent the meaning of programs by terms, trees, or graphs. In denotational semantics programs are modelled by terms in the typed $\lambda$-calculus; in operational semantics, program meaning is represented by a derivation tree (or a sequence of derivation trees for SOS). Our work on quantitative semantics is based on a rather different approach based on linear algebra: the semantics of a program is represented as a linear operator (or matrix). The execution of a program is represented by the iterated multiplication of the operator and some start state (vector); this is analogous to the derivation steps in an SOS semantics.