Interaction trees (ITrees) are a general-purpose data structure for representing the behaviors
of recursive programs that interact with their environments. A coinductive variant of “free …

Part I of this book is a practical introduction to working with the Isabelle proof assistant. It
teaches you how to write functional programs and inductive definitions and how to prove …

We define logical relations between the denotational semantics of a simply typed functional
language with recursion and the operational behaviour of low-level programs in a variant …

There are two approaches to formalizing the syntax of typed object languages in a proof
assistant or programming language. The extrinsic approach is to first define a type that …

Capretta's delay monad can be used to model partial computations, but it has the “wrong”
notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by …

Even well-typed programs can go wrong in modern functional languages, by encountering a
pattern-match failure, or simply returning the wrong answer. An increasingly-popular …

The operational semantics of a partial, functional language is often given as a relation rather
than as a function. The latter approach is arguably more natural: if the language is …

The delay datatype was introduced by Capretta (Logical Methods in Computer Science, 1
(2), article 1, 2005) as a means to deal with partial functions (as in computability theory) in …

Guarded recursion is a form of recursion where recursive calls are guarded by delay
modalities. Previous work has shown how guarded recursion is useful for reasoning …

We develop domain theory in constructive univalent foundations without Voevodsky's
resizing axioms. In previous work in this direction, we constructed the Scott model of PCF …