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Denotational aspects of untyped normalization by evaluation

Andrzej Filinski; Henning Korsholm Rohde — 2005

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that the standard normalization-by-evaluation construction for the simply-typed $λ_{β η}$ -calculus has a natural counterpart for the untyped $λ_{β}$ -calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms,...

Denotational aspects of untyped normalization by evaluation

Andrzej Filinski; Henning Korsholm Rohde — 2010

RAIRO - Theoretical Informatics and Applications

We show that the standard normalization-by-evaluation construction for the simply-typed -calculus has a natural counterpart for the untyped -calculus, with the central type-indexed logical relation replaced by a “recursively defined” , in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms, so the normalization...

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