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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