TY - JOUR

T1 - A Model of PCF in Guarded Type Theory

AU - Paviotti, Marco

AU - Møgelberg, Rasmus Ejlers

AU - Birkedal, Lars

PY - 2015

Y1 - 2015

N2 - Guarded recursion is a form of recursion where recursive calls are guarded by delay modalities. Previous work has shown how guarded recursion is useful for constructing logics for reasoning about programming languages with advanced features, as well as for constructing and reasoning about elements of coinductive types. In this paper we investigate how type theory with guarded recursion can be used as a metalanguage for denotational semantics useful both for constructing models and for proving properties of these. We do this by constructing a fairly intensional model of PCF and proving it computationally adequate. The model construction is related to Escardo's metric model for PCF, but here everything is carried out entirely in type theory with guarded recursion, including the formulation of the operational semantics, the model construction and the proof of adequacy.

AB - Guarded recursion is a form of recursion where recursive calls are guarded by delay modalities. Previous work has shown how guarded recursion is useful for constructing logics for reasoning about programming languages with advanced features, as well as for constructing and reasoning about elements of coinductive types. In this paper we investigate how type theory with guarded recursion can be used as a metalanguage for denotational semantics useful both for constructing models and for proving properties of these. We do this by constructing a fairly intensional model of PCF and proving it computationally adequate. The model construction is related to Escardo's metric model for PCF, but here everything is carried out entirely in type theory with guarded recursion, including the formulation of the operational semantics, the model construction and the proof of adequacy.

UR - http://www.entcs.org/

U2 - 10.1016/j.entcs.2015.12.020

DO - 10.1016/j.entcs.2015.12.020

M3 - Journal article

VL - 319

SP - 333

EP - 349

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

SN - 1571-0661

ER -