Interpreting Lambda Calculus in Domain-Valued Random Variables
Robert Furber, Radu Mardare, Prakash Panangaden, and Dana Scott
TL;DR
This paper introduces a Boolean-valued domain theory framework to interpret lambda calculus using domain-valued random variables, emphasizing the reflexive domain construction and Boolean algebra-based equality.
Contribution
It develops a novel Boolean-valued domain theory for lambda calculus, focusing on interpretation via domain-valued random variables and Boolean algebra semantics.
Findings
Boolean-valued domain theory for lambda calculus
Interpretation of equations as top elements in Boolean algebra
Focus on reflexive domain construction
Abstract
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of equality has to be interpreted in the Boolean algebra and when we say that an equation is valid in the model we mean that its interpretation is the top element of the Boolean algebra.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.