#### Date of Award

1984

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics

#### Abstract

Although the (lamda)-calculus has been studied for over fifty years, the first models for the lambda calculus were constructed by Dana Scott in 1972. Scott's models were constructed using inverse limits of continuous lattices. We investigate this inverse limit construction in the context of up-complete posets with zero. We show that the correspondence between an up-complete poset with zero P and its associated model for the (lamda)-calculus defines a monofunctor between appropriate categories. We calculate the values in the model corresponding to several combinators in the lambda calculus. Finally, we investigate certain submonoids of the monoid of combinators. We show that this monoid contains as submonoids the non-negative integers and a free monoid on infinitely many generators.

#### Recommended Citation

Sullivan, Frederick Joseph, "Ordered Models for the Lambda Calculus." (1984). *LSU Historical Dissertations and Theses*. 3995.

https://repository.lsu.edu/gradschool_disstheses/3995

#### Pages

78

#### DOI

10.31390/gradschool_disstheses.3995