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- Willem Heijltjes
- Ann. Pure Appl. Logic
- 2010

Classical proof forests are a proof formalism for first-order classical logic based on Herbrandâ€™s Theorem and backtracking games in the style of Coquand. First described by Miller in a cut-freeâ€¦ (More)

- Willem Heijltjes
- 2012

An interesting problem in proof theory is to find representations of proof that do not distinguish between proofs that are â€˜morallyâ€™ the same. For many logics, the presentation of proofs in aâ€¦ (More)

- Willem Heijltjes, Robin Houston
- CSL-LICS
- 2014

MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem forâ€¦ (More)

- Willem Heijltjes, Lutz StraÃŸburger
- Mathematical Structures in Computer Science
- 2016

- Tom Gundersen, Willem Heijltjes, Michel Parigot
- 2013 28th Annual ACM/IEEE Symposium on Logic inâ€¦
- 2013

An explicit -- sharing lambda-calculus is presented, based on a Curry -- Howard-style interpretation of the deep inference proof formalism. Duplication of subterms during reduction proceedsâ€¦ (More)

- Willem Heijltjes
- 2011 IEEE 26th Annual Symposium on Logic inâ€¦
- 2011

Additive linear logic, the fragment of linear logic concerning linear implication between strictly additive formulae, coincides with sum-product logic, the internal language of categories with freeâ€¦ (More)

- Dominic J. D. Hughes, Willem Heijltjes
- LICS
- 2016

Proof nets for MLL (unit-free multiplicative linear logic) and ALL (unit-free additive linear logic) are graphical abstractions of proofs which are efficient (proofs translate in linear time) andâ€¦ (More)

- Tom Gundersen, Willem Heijltjes, Michel Parigot
- LPAR
- 2013

The atomic lambda-calculus is a typed lambda-calculus with explicit sharing, which originates in a Curry-Howard interpretation of a deep-inference system for intuitionistic logic. It has been shownâ€¦ (More)

In this paper it is proved that Girard's proof nets for multiplicative linear logic characterise free semi-â‹†-autonomous-categories.

- Willem Heijltjes, Dominic J. D. Hughes
- 2015 30th Annual ACM/IEEE Symposium on Logic inâ€¦
- 2015

We investigate efficient algorithms for the additive fragment of linear logic. This logic is an internal language for categories with finite sums and products, and describes concurrent two-playerâ€¦ (More)