3 research outputs found
Relational Programming in miniKanren: Techniques, Applications, and Implementations
Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009The 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