Year: 2011
Type: article
Abstract: We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The resulting denotations are smaller and better-behaved, in ways we make precise, than functional valuation-based models. Using these new models, we then develop a generalisation of \lambda-term syntax enriching them with existential meta-variables, thus yielding a theory of incomplete functions. This incompleteness is orthogonal to the usual notion of incompleteness given by function abstraction and application, and corresponds to holes and incomplete objects.
DOI: 10.4204/eptcs.71.5
Authors: Murdoch J. Gabbay, Dominic P. Mulligan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: G5676906063, CERTIFIED COMPLEXITY
OpenAlex ID: W2155205018