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Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisations (1994)  (Make Corrections)  (8 citations)
Ralph Loader



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Abstract: Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisations Ralph Loader, of St. Hugh's College, Oxford. Thesis submitted for the Degree of D.Phil. Michaelmas term, 1994. T his thesis is an investigation into models of typed -calculi and of linear logic. The models we investigate are denotational in nature; we construct various categories, in which types (or formulae) are interpreted by objects, and terms (proofs) by morphisms. The results we... (Update)

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.... full completeness results for a variety of models with respect to various versions of Multiplicative Linear Logic (MLL) [HO92, BS96, Loa94a, Loa94b]. However, there have been no results for logics beyond the (very weak) multiplicative fragment of Linear Logic. In this paper,...

...and totality spaces. The categories LLP of linear logical predicates and Tot of totality spaces were rst considered by Loader (see [43, 44]) Loader gave full completeness results for his categories and these were reconsidered by Tan [51] The objects of LLP are sets A...

Cited by:   More
Concurrent Games and Full Completeness - Samson Abramsky Lfcs (1998)   (Correct)
Sequentiality vs. Concurrency in Games and Logic - Abramsky (2001)   (Correct)
Glueing and Orthogonality for Models of Linear Logic - Hyland (2001)   (Correct)

Active bibliography (related documents):   More   All
1.7:   Equational Theories for Inductive Types - Loader (1997)   (Correct)
1.6:   Linear Logic, Totality and Full Completeness - Loader (1994)   (Correct)
0.7:   The Undecidability of lambda-Definability - Loader   (Correct)

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7:   Concurrent games and full completeness - Abramsky, Mellies - 1998
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BibTeX entry:   (Update)

R. Loader, Models of lambda calculi and linear logic: structural, equational and proof-theoretic characterisations, PhD Thesis, Oxford, 1994. http://citeseer.ist.psu.edu/loader94models.html   More

@misc{ loader94models,
  author = "R. Loader",
  title = "Models of lambda calculi and linear logic: structural",
  text = "R. Loader, Models of lambda calculi and linear logic: structural, equational
    and proof-theoretic characterisations, PhD Thesis, Oxford, 1994.",
  year = "1994",
  url = "citeseer.ist.psu.edu/loader94models.html" }
Citations (may not include all citations):
982   Theoretical Computer Science (context) - Girard, System et al. - 1986
982   Theoretical Computer Science (context) - Girard - 1986
562   Categories for the Working Mathematician (context) - Lane - 1970
359   Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
175   Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1994
104   Metamathematical Investigation of Intuitionistic Arithmetic .. (context) - Troelstra - 1973
72   Archive for Mathematical Logic (context) - Danos, Regnier et al. - 1989
58   Algebraically Complete Categories (context) - Freyd - 1990
51   autonomous categories and cofree coalgebras (context) - Seely - 1989
39   Total Sets and Objects in Domain Theory (context) - Berger - 1993
37   Formal Parametric Polymorphism - Plotkin, Cardelli et al. - 1992
22   Lecture Notes in Mathematics (context) - Barr, Categories - 1979
21   Reasoning about sequential functions via logical relations (context) - Sieber - 1992
17   Correspondence between Operational and Denotational Semantic.. - Ong
15   Totality and Full Completeness (context) - Loader - 1994
13   Journal of Symbolic Logic (context) - Statman, invariance - 1982
12   School of Artificial Intelligence (context) - Plotkin, logical et al. - 1973
9   Unsolvable Problems (context) - Davis - 1977
7   A New Characterisation of Lambda Definability (context) - Jung, Tiuryn
5   Typed Lambda Calculi and Applications (context) - Bezem, Groote - 1993
4   Interpreting higher computations as types with totality (context) - Kristiansen, Normann - 1992
3   Totality in Qualitative Domains (context) - Kristiansen - 1993
3   definability in the full type hierarchy (context) - Plotkin - 1980
2   Full Completeness for Multiplicative Linear Logic without th.. (context) - Hyland, Ong - 1993
2   Iterated Inductive Definitions (context) - Lof - 1971
2   Models of Linear Logic and Inductive Datatypes (context) - Loader - 1993
2   Association of Symbolic Logic (context) - Gandy, Recursive et al. - 1962
1   Mathematics Made Difficult (context) - Linderhold - 1972
1   Unpublished manuscript on constant result matching (context) - Padovani - 1994
1   Fourth Order Matching is Decidable (context) - Padovani - 1994
1   Effective Operators in a Topological Setting (context) - Spreen, Young - 1984



The graph only includes citing articles where the year of publication is known.


Documents on the same site (http://www.dcs.ed.ac.uk/home/loader/index.html):   More
Normalisation by Calculation - Loader (1995)   (Correct)
Equational Theories for Inductive Types - Loader (1997)   (Correct)
Elementary Proofs of Adequacy - Loader (1997)   (Correct)

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