Inductive datatypes provide mechanisms to define finite data such as finite lists and trees via
constructors and allow programmers to analyze and manipulate finite data via pattern …

Infinitary and regular proofs are commonly used in fixed point logics. Being natural
intermediate devices between semantics and traditional finitary proof systems, they are …

Gradually typed languages are designed to support both dynamically typed and statically
typed programming styles while preserving the benefits of each. While existing gradual type …

We propose the first framework for defining relational program logics for arbitrary monadic
effects. The framework is embedded within a relational dependent type theory and is highly …

The subject of this thesis is the proof theory of logics with fixed points, such as the μ-
calculus, linear-logic with fixed points, etc. These logics are usually equipped with finitary …

We present a model of computation that heavily emphasizes the concept of duality and the
interaction between opposites–production interacts with consumption. The symmetry of this …

We present a principle for introducing new types in type theory which generalises strictly
positive indexed inductive data types. In this new principle a set A is defined inductively …

Focusing, introduced by Jean-Marc Andreoli in the context of classical linear logic [Andreoli
1992], defines a normal form for sequent calculus derivations that cuts down on the number …

The sequent calculus is a proof system which was designed as a more symmetric alternative
to natural deduction. The 𝜆𝜇𝜇-calculus is a term assignment system for the sequent …

Polarization of types in call-by-push-value naturally leads to the separation of inductively
defined observable values (classified by positive types), and coinductively defined …