Parametric Compositional Data Types

Parametric Compositional Data Types

In previous work we have illustrated the benefits that compositional data types (CDTs) offer for implementing languages and in general for dealing with abstract syntax trees (ASTs). Based on Swierstra’s data types à la carte, CDTs are implemented as a Haskell library that enables the definition of recursive data types and functions on them in a modular and extendable fashion. Although CDTs prov...

Compositional Coinduction with Sized Types

Proofs by induction on some inductively defined structure, e. g., finitely-branching trees, may appeal to the induction hypothesis at any point in the proof, provided the induction hypothesis is only used for immediate substructures, e. g., the subtrees of the node we are currently considering in the proof. The basic principle of structural induction can be relaxed to course-of-value induction,...

The Inverse Compositional Algorithm for Parametric Registration

We present an implementation of the inverse compositional algorithm for parametric motion estimation. It computes a global motion between two images using a non-linear least square technique. Our implementation allows computing several types of planar transformations, such as translations, similarities, affinities or homographies. The algorithm is iterative so it typically yields solutions with...

Compositional Compiler Verification via Parametric Simulation

Compiler verification is essential for the construction of fully verified software, but most prior work (such as CompCert) has focused on verifying whole-program compilers. To support separate compilation and to enable linking of results from different verified compilers, it is important to develop a compositional notion of compiler correctness that is modular (preserved under linking), transit...

Subtyping Parametric and Dependent Types