Combining predicate transformer semantics for effects: a case study in parsing regular languages

A Predicate Transformer Semantics for a Concurrent Language of Refinement

Circus is a combination of Z and CSP; its chief distinguishing feature is the inclusion of the ideas of the refinement calculus. Our main objective is the definition of refinement methods for concurrent programs. The original semantic model for Circus is Hoare and He’s unifying theories of programming. In this paper, we present an equivalent semantics based on predicate transformers. With this ...

A Predicate/State Transformer Semantics for Bayesian Learning

This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These def...

Predicate Transformer Semantics of a Higher Order Imperative Language With . . .

On the equivalence of state transformer semantics and predicate transformer semantics

G. Plotkin and the author [13] have worked out the equivalence between state transformer semantics and predicate transformer semantics in a domain theoretical setting for programs combining nondeterminism and probability. Works of C. Morgan and co-authors [20], Keimel, Rosenbusch and Streicher [14, 15], already go in the same direction using only discrete state spaces. In fact, Keimel and Plotk...

Certified Parsing of Regular Languages

We report on a certified parser generator for regular languages using the Agda programming language. Specifically, we programmed a transformation of regular expressions into a Boolean-matrix based representation of nondeterministic finite automata (NFAs). And we proved (in Agda) that a string matches a regular expression if and only if the NFA accepts it. The proof of the if-part is effectively...