The promise of logic programming is that programs can be written relationally, without distinguishing between input and output arguments. Relational programs are remarkably flexible—for example, a relational type-inferencer also performs type checking and type inhabitation, while a relational theorem prover generates theorems as well as proofs and can even be used as a simple proof assistant.
Unfortunately, writing relational programs is difficult, and requires many interesting and unusual tools and techniques. For example, a relational interpreter for a subset of Scheme might use nominal unification to support variable binding and scope, Constraint Logic Programming over Finite Domains (CLP(FD)) to implement relational arithmetic, and tabling to improve termination behavior.
In this dissertation I present miniKanren, a family of languages specifically designed for relational programming, and which supports a variety of relational idioms and techniques. I show how miniKanren can be used to write interesting relational programs, including an extremely flexible lean tableau theorem prover and a novel constraint-free binary arithmetic system with strong termination guarantees. I also present interesting and practical techniques used to implement miniKanren, including a nominal unifier that uses triangular rather than idempotent substitutions and a novel “walk”-based algorithm for variable lookup in triangular substitutions.
The result of this research is a family of languages that supports a variety of relational idioms and techniques, making it feasible and useful to write interesting programs as relations.
|Advisor:||Friedman, Daniel P.|
|Commitee:||Haynes, Christopher T., Moss, Lawrence S., Sabry, Amr|
|School Location:||United States -- Indiana|
|Source:||DAI-B 70/12, Dissertation Abstracts International|
|Keywords:||Logic programming, Relational programming, Schemes, miniKanren|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be