Since record polymorphism is one of essential factors for object-oriented languages, various approaches to incorporate record polymorphism into type systems have been proposed to lay the foundation for object-oriented languages. Recursive types, which are essentially types of lists or trees, are major programming tools. In object-oriented languages, a pseudo variable \self" has a recursive type...

We prove general limit theorems for sums of functions of subtrees of (random) binary search trees and random recursive trees. The proofs use a new version of a representation by Devroye, and Stein’s method for both normal and Poisson approximation together with certain couplings. As a consequence, we give simple new proofs of the fact that the number of fringe trees of size k = kn in the binary...

In this paper we study decision problems and invertibility for two notions of equivalence of recursive types. In particular, for recursive types presented by means of a recursion operator μ, we describe an algorithm showing that the natural equivalence generated by finitely many steps of folding and unfolding of μ-types is decidable. For recursive types presented by finite systems of recursive ...

The notion of binomial coefficients (T S ) of finite planar, reduced rooted trees T, S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) = ∑

syntax trees almost copying the abstract grammar: type term = Var of string | Fn of string * term list;; and express in a direct recursive way the function returning the set of variables in a term: let rec vars tm =

The levels of trees are nodes with the same distance to the root. We derive asymptotic approximations to the correlation coefficients of two level sizes in random recursive trees and binary search trees, which undergo sharp sign-changes when one level is fixed and the other one is varying. We also propose a new means for deriving an asymptotic estimate for the expected width, which is the numbe...

Abstract Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies a higher scale level is used. Versions of proposed take seriously avoid assignment artificial scores. The construction principle based on an investigation binary models implicitly used in parametric regression. These building blocks can be fitted by combined similar...