1995
DOI: 10.1007/3-540-60164-3_27
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Categorical reconstruction of a reduction free normalization proof

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Cited by 73 publications
(92 citation statements)
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“…the setoid interpretation and the presheaf interpretation. The setoid interpretation is essential for a formal justification of QITs and the presheaf interpretation is an essential ingredient to extend normalisation by evaluation [4] to dependent types. These constructions for dependent types require an attention to detail which can only convincingly demonstrated by a formal development.…”
Section: Discussion and Further Workmentioning
confidence: 99%
“…the setoid interpretation and the presheaf interpretation. The setoid interpretation is essential for a formal justification of QITs and the presheaf interpretation is an essential ingredient to extend normalisation by evaluation [4] to dependent types. These constructions for dependent types require an attention to detail which can only convincingly demonstrated by a formal development.…”
Section: Discussion and Further Workmentioning
confidence: 99%
“…The reader may be accustomed to the more restrictive notion of renamings as described variously as Order Preserving Embeddings (Chapman 2009), thinnings (which we use) or context inclusions, or just weakenings (Altenkirch et al 1995). Writing non-injective or non-order preserving renamings would take perverse effort given that we only implement generic interpretations.…”
Section: A Generic Notion Of Environmentmentioning
confidence: 99%
“…Normalization by evaluation has been developed in intuitionistic type theory [16,54], proof theory [11,12], category theory [4], λ-definability [40], and partial evaluation [18,19], where it has emerged as a new field of application for delimited continuations [9,19,29,38,41,44,69].…”
Section: Normalization By Evaluationmentioning
confidence: 99%