
Probabilistic Rewriting: Relations between Normalization, Termination, and Unique Normal Forms
We investigate how techniques from Rewrite Theory can help us to study c...
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An Abstract Machine for Strong Call by Value
We present an abstract machine that implements a fullreducing (a.k.a. s...
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Revisiting Callbyvalue Bohm trees in light of their Taylor expansion
The callbyvalue lambda calculus can be endowed with permutation rules,...
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Degrees of extensionality in the theory of Böhm trees and Sallé's conjecture
The main observational equivalences of the untyped lambdacalculus have ...
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Eliminating the unit constant in the Lambek calculus with brackets
We present a translation of the Lambek calculus with brackets and the un...
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Connecting Constructive Notions of Ordinals in Homotopy Type Theory
In classical set theory, there are many equivalent ways to introduce ord...
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On reduction and normalization in the computational core
We study the reduction in a lambdacalculus derived from Moggi's computa...
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Strict Ideal Completions of the Lambda Calculus
The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. To obtain infinitary normalisation and infinitary confluence properties for these calculi, Kennaway et al. extend βreduction with infinitely many `rules', which contract meaningless terms directly to . Three of the resulting Böhm reduction calculi have unique infinitary normal forms corresponding to Böhmlike trees. In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion. We show that each of our calculi conservatively extends the corresponding metricbased calculus. Three of our calculi are infinitarily normalising and confluent; their unique infinitary normal forms are exactly the Böhmlike trees of the corresponding metricbased calculi. Our calculi dispense with the infinitely many rules of the metricbased calculi. The fully nonstrict calculus (called 111) consists of only βreduction, while the other two calculi (called 001 and 101) require two additional rules that precisely state their strictness properties: λ x.→ (for 001) and M → (for 001 and 101).
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