The nabla-calculus. Functional programming with higher-order encodings.

By Carsten Schurmann, Adam Poswolsky and Jeffrey Sarnat, from TLCA 2005, available from the Elphin website:

Higher-order encodings use functions provided by one language to represent variable binders of another. They lead to concise and elegant representations, which historically have been difficult to analyze and manipulate.
In this paper we present the nabla-calculus, a calculus for defining general recursive functions over higher-order encodings. To avoid problems commonly associated with using the same function space for representations and computations, we separate one from the other. The simply-typed λ-calculus plays the role of the representation level. The computation level contains not only the usual computational primitives but also an embedding of the representation-level. It distinguishes itself from similar systems by allowing recursion under representation-level λ-binders while permitting a natural style of programming which we believe scales to other logical frameworks. Sample programs include bracket abstraction, parallel reduction, and an evaluator for a simple language with first-class continuations.

0 Responses to “The nabla-calculus. Functional programming with higher-order encodings.”



  1. Leave a Comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s





%d bloggers like this: