Fixed points of functions and operators are of fundamental importance in programming language semantics in giving meaning to recursive definitions and to constructs which involve self-reference. It follows therefore that fixed-point theorems are also of fundamental importance in theoretical computer science. Often, order-theoretic arguments are available in which case the well-known Knaster-Tarski theorem can be used to obtain fixed-points. Sometimes, however, analytical arguments are needed involving the Banach contraction mapping theorem as is the case for example in studying concurrency and communicating systems. Situations arise also in computational logic in the presence of negation which force non-monotonicity of the operators involved. A successful attempt was made in  to employ metrics and the contraction mapping theorem in studying some problematic logic programs. These ideas were taken further in  in examining quasi-metrics and in [17,18] in considering elementary ideas from topological dynamics in this same context of computational logic.
Seda, A. K.,
& Hitzler, P.
(1998). Generalized Ultrametrics, Domains and an Application to Computational Logic. Irish Mathematical Society Bulletin, 41, 31-43.