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On a modal lambda calculus for S4
1995
Theoretical Computer Science
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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
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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]
2011
arXiv
pre-print
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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]
2012
arXiv
pre-print
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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]
2000
Handbook of Algebra
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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]
2008
arXiv
pre-print
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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
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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]
2010
arXiv
pre-print
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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
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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
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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?
2012
Mathematical Structures in Computer Science
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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
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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
2016
Journal of functional programming
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2016 pre-print arXiv:1512.06751v2 fatcat:rzfl2s2dnnhvdjrmgkd7gxxhd4Other Versions
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]
2019
arXiv
pre-print
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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]
2004
Lecture Notes in Computer Science
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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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