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On a modal lambda calculus for S4

1995 Theoretical Computer Science  
We first describe a new type system inspired in part by linear logic and verify that reductions preserve typings.  ...  of these models.  ...  Frank Pfenning and Hao-Chi Wong On a modal lambda calculus for S4 http://www.elsevier.nl/locate/entcs/voluel/pfenning We present A'O, a concise formulation of a proof term caIculus for the intuitionistic  ... 
doi:10.1016/0304-3975(96)80140-x fatcat:34yi3zt6lndvnb7vsbrnk2wuoa

Syntactic control of interference revisited

1995 Theoretical Computer Science  
We first describe a new type system inspired in part by linear logic and verify that reductions preserve typings.  ...  of these models.  ...  Frank Pfenning and Hao-Chi Wong On a modal lambda calculus for S4 http://www.elsevier.nl/locate/entcs/voluel/pfenning We present A'O, a concise formulation of a proof term caIculus for the intuitionistic  ... 
doi:10.1016/0304-3975(96)80138-1 fatcat:k3rggrbb5zfflbka3rpi243s3a

Quantum Computation, Categorical Semantics and Linear Logic [article]

André van Tonder, Miquel Dorca
2011 arXiv   pre-print
Antal Jevicki and the Brown University Physics department for their support.  ...  The calculus turned out to be closely related to the linear lambda calculi used in the study of linear logic [5, 6, 7, 8] .  ...  Bundle categories Hilbert bundles form a category with particularly nice properties, making it very suitable for providing a semantics of our linear quantum lambda calculus [9, 10] . Theorem 6.1.  ... 
arXiv:quant-ph/0312174v5 fatcat:tfp5hbsrkfcipmcbakoe5p2z4m

On the discriminating power of tests in resource lambda-calculus [article]

Flavien Breuvart
2012 arXiv   pre-print
Proof nets can be used naturally to extend the into the lambda calculus with resources, a calculus that contains notions of linearity and differentiations.  ...  In denotational semantics, categorical models of DLL are now commune, and the simplest one is Rel, the category of sets and relations.  ...  A The model M ∞ A.1 Categorical model The category Rel of sets and relations is known to be a model of linear logic as it is a Seely category (we are giving the interpretation, but we will let the comutative  ... 
arXiv:1205.4691v2 fatcat:55cemwrkdfdv3ls6vzlarhcg4u

Some aspects of categories in computer science [chapter]

P.J. Scott
2000 Handbook of Algebra  
A dA Domain-Theoretic Models. The category LIN = coherent spaces and linear maps gave the rst non-trivial model of LL proofs.  ...  Remark 4.16 The categorical comonad approach to models of linear logic has been put to use by Asperti in clarifying optimal graph reduction techniques in the untyped lambda calculus Asp] (see also Mix`  ...  The following facts about partially additive categories follow from Manes and Arbib MA86]:  ... 
doi:10.1016/s1570-7954(00)80027-3 fatcat:oeaqbcqgzjhuzl2ddangzergr4

Higher-order theories [article]

Andre' Hirschowitz, Marco Maggesi
2008 arXiv   pre-print
We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature.  ...  Then we obtain a modularity result as requested by Ghani and Uustalu (2003): in our setting, merging two extensions of syntax corresponds to building an amalgamated sum.  ...  In our previous work [HM07] we treated the examples of the untyped lambda-calculus modulo α-equivalence and αβη-equivalence. In section 6 we revisit these two examples.  ... 
arXiv:0704.2900v2 fatcat:lupcekpfhbd35eqt5ynbil2pxu

Objects, interference and the Yoneda embedding

1995 Theoretical Computer Science  
We first describe a new type system inspired in part by linear logic and verify that reductions preserve typings.  ...  of these models.  ...  Frank Pfenning and Hao-Chi Wong On a modal lambda calculus for S4 http://www.elsevier.nl/locate/entcs/voluel/pfenning We present A'O, a concise formulation of a proof term caIculus for the intuitionistic  ... 
doi:10.1016/0304-3975(96)80139-3 fatcat:bqcssjjpjzhnvgj27ohd26ukku

What is a categorical model of the differential and the resource lambda-calculi? [article]

Manzonetto Giulio
2010 arXiv   pre-print
In this paper we provide an abstract model theory for the untyped differential lambda-calculus and the resource calculus.  ...  In particular we propose a general definition of model of these calculi, namely the notion of linear reflexive object in a Cartesian closed differential category.  ...  We are grateful to Antonio Bucciarelli, Thomas Ehrhard and Guy McCusker. Many thanks to Michele Pagani and Paolo Tranquilli for helpful comments and suggestions.  ... 
arXiv:1011.2307v1 fatcat:bjaj2rb3sjdq7bbs5lt3zadyl4

The Smyth completion: a common foundation for denotational semantics and complexity analysis

1995 Theoretical Computer Science  
Frank Pfenning and Hao-Chi Wong On a modal lambda calculus for S4 http://www.elsevier.nl/locate/entcs/voluel/pfenning We present A'O, a concise formulation of a proof term caIculus for the intuitionistic  ...  of these models.  ... 
doi:10.1016/0304-3975(96)80141-1 fatcat:2rpt7dgkkncqjic42lsk5jteqi

Page 5552 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Martin E.] (4-CAMB; Cambridge) Linear A-calculus and categorical models revisited. Computer science logic (San Miniato, 1992), 61-84, Lecture Notes in Comput. Sci., 702, Springer, Berlin, 1993.  ...  We then show that SK-domains and SI-functions constitute a Cartesian closed category which can be order enriched with Scott’s ordering, i.e., can be used to provide order extensional models for A-calculus-based  ... 

What is a categorical model of the differential and the resource λ-calculi?

GIULIO MANZONETTO
2012 Mathematical Structures in Computer Science  
We prove that the extensional model D of λ-calculus we have recently built in MRel is linear, and therefore it is also an extensional model of the untyped differential λ-calculus.  ...  Starting from the work of Blute, Cockett and Seely on differential categories we provide the notion of Cartesian closed differential category and we prove that linear reflexive objects living in such categories  ...  Many thanks to Michele Pagani, Paolo Tranquilli and the anonymous reviewers for helpful comments and suggestions.  ... 
doi:10.1017/s0960129511000594 fatcat:oahkwj3ihndovlixd4tp5yflg4

Page 2211 of Mathematical Reviews Vol. , Issue 93d [page]

1993 Mathematical Reviews  
Robinson and Giuseppe Rosolini, Dinaturality for free (107- 118); Bart Jacobs, Simply typed and untyped lambda calculus revisited (119-142); C.  ...  Barry Jay, Modelling reduction in conflu- ent categories (143-162); G. M.  ... 

Linear lambda terms as invariants of rooted trivalent maps

NOAM ZEILBERGER
2016 Journal of functional programming  
of the Four Color Theorem as a statement about typing in lambda calculus.  ...  The main aim of the paper is to give a simple and conceptual account for the correspondence (originally described by Bodini, Gardy, and Jacquot) between α-equivalence classes of closed linear lambda terms  ...  I am grateful to Alain Giorgetti for introducing me to the idea of Tutte decomposition and for emphasizing its importance as a way of representing rooted maps.  ... 
doi:10.1017/s095679681600023x fatcat:piay34hwofcabcwlinuic2qblu

Signatures and models for syntax and operational semantics in the presence of variable binding [article]

Ambroise Lafont
2019 arXiv   pre-print
Languages with variable binding, such as the pure lambda calculus, are monads on the category of sets specified through the classical algebraic signatures.  ...  Finally, we takle the specification of the operational semantics of a programming language such as lambda calculus with beta-reduction.  ...  Gabbay and Pitts [GP99] employ a different technique for modelling variable binding, based on nominal sets. This nominal approach to binding syntax has been actively studied 14 .  ... 
arXiv:1910.09162v4 fatcat:dmbqxqqn3zbzlmt5gyz7hnuzvm

A Generalisation of Pre-logical Predicates to Simply Typed Formal Systems [chapter]

Shin-ya Katsumata
2004 Lecture Notes in Computer Science  
Logical predicates (and relations) have been widely used as a tool to study properties of the simply typed lambda calculus.  ...  In section 2, we first introduce a category of presentation models M T , and typed binding signatures as a description of typed formal systems.  ...  Acknowledgments I thank Donald Sannella, Daniel Turi and John Power for useful discussions. This work was supported by an LFCS studentship.  ... 
doi:10.1007/978-3-540-27836-8_70 fatcat:frh37tkwgzdnbk7t2oc2caa5p4
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