Core Concepts
The proposed non-idempotent intersection type system H characterizes normalization of the hybrid evaluation strategy of PCF, providing both upper and exact bounds for the length of reduction sequences to normal form.
Abstract
The paper introduces a quantitative type system H for the hybrid calculus PCFH, which combines call-by-value (CBV) and call-by-name (CBN) evaluation strategies.
Key highlights:
System H captures the hybrid nature of PCFH by splitting the typing information into two parts: a typing context for variables bound by abstractions (CBV-like) and a family context for variables bound by fixed-point operators (CBN-like).
H is proven to be sound and complete with respect to the operational semantics of PCFH: typability implies normalization, and vice versa.
The type system provides upper bounds for the length of normalization sequences. By considering only tight derivations, it also provides exact bounds.
This is the first quantitative type interpretation that is adequate for a hybrid computational model, synthesizing characteristics of both CBN and CBV in a single system.
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