Functional Characters of Solvable Terms

Characterizing Convergent Terms in Object Calculi via Intersection Types

“…It is a type assignment system, which is an extension of system CDV ! (see 12,5,14]), also called D in 22]. To arrow a n d i n tersection type constructors we add a constructor for record types, which is from 1].…”

“…On the other hand the set of types that can be given to a term describes its functional behaviour, that is its meaning (see e.g. 12,6,22,14]). That convergency is characterized by t ypability within the system by t ypes of some speci c shape is basic with respect to the construction of denotational models using types (see 6,3,4]).…”

Principal Type Schemes for the Strict Type Assignment System

“…There exists two of those systems for which this property is proved. In [8] principal type schemes are defined for a type assignment system that is a restriction of the system as presented in [9]. This system has as a disadvantage that it is not an extension of Curry's system: if B M:τ, and the term-variable x does not occur in B, then for λx.M only the type ω→τ can be derived.…”

Essential intersection type assignment

“…In Curry's system it is, for example, not possible to assign a type to the term (λx.xx); moreover, although the lambda terms (λcd.d) and ((λxyz.xz(yz))(λab.a)) are β-equal, the principal type schemes for these terms are different. The Intersection Type Discipline as presented in [5] (a more enhanced system was presented in [4]) is an extension of Curry's system that does not have these drawbacks. The extension being made consists mainly of allowing for term variables (and terms) to have more than one type.…”

“…The type assignment system presented in [4] (the BCD-system) is based on the system as presented in [5]; it defines the set of intersection types T in a more general way, and is strengthened further by introducing a partial order relation '≤' on types as well as adding the type assignment rule (≤) and a more general form of the rules concerning intersection. The rule (≤), as well as the more general treatment of intersection types were introduced mainly to prove completeness of type assignment.…”