Fixed-point combinator

Abstract: A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the introduction to combinators and lambda calculus is one book that we really recommend you to read, to get more solutions in solving this problem.

Abstract: A typed lambda calculus with categorical type constructors is introduced. It has a uniform category theoretic mechanism to declare new types. Its type structure includes categorical objects like products and coproducts as well as recursive types like natural numbers and lists. It also allows duals of recursive types, i.e. lazy types, like infinite lists. It has generalized iterators for recursive types and duals of iterators for lazy types. We will give reduction rules for this simply typed lambda calculus and show that they are strongly normalizing even though it has infinite things like infinite lists.

Abstract: The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that if two term rewriting systems both have the Chruch-Rosser property, then the direct sum of these systems also has this property.