# Weak normalization implies strong normalization in a class of non-dependent pure type systems

@article{Barthe2001WeakNI, title={Weak normalization implies strong normalization in a class of non-dependent pure type systems}, author={Gilles Barthe and John Hatcliff and M S{\o}rensen}, journal={Theor. Comput. Sci.}, year={2001}, volume={269}, pages={317-361} }

Abstract The Barendregt–Geuvers–Klop conjecture states that every weakly normalizing pure type system is also strongly normalizing. We show that this is true for a uniform class of systems which includes, e.g., the left-hand side of Barendregt's λ -cube as well as the system λU . This seems to be the first result giving a positive answer to the conjecture not merely for some concrete systems for which strong normalization is known to hold, but for a uniform class of systems in which not all… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 24 REFERENCES

## On weak and strong normalisations

VIEW 2 EXCERPTS

## A - Translation and Looping Combinators in Pure Type Systems

VIEW 16 EXCERPTS

HIGHLY INFLUENTIAL

## The Conservation Theorem revisited

VIEW 2 EXCERPTS

## Extensions of Pure Type Systems

VIEW 2 EXCERPTS

## CPS Translations and Applications: The Cube and Beyond

VIEW 1 EXCERPT