## Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisations (1994)

Citations: | 11 - 0 self |

### BibTeX

@MISC{Loader94modelsof,

author = {Ralph Loader and Proof-theoretic Characterisations},

title = {Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisations},

year = {1994}

}

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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 investigate compare particular properties of the syntax and the semantics of a calculus, by trying to use syntax to characterise features of a model, or vice versa. There are four chapters in the thesis, one each on linear logic and the simply typed -calculus, and two on inductive datatypes. In chapter one, we look at some models of linear logic, and prove a full completeness result for multiplicative linear logic. We form a model, the linear logical predicates , by abstracting a little the structure ...