Pdf Third Order Matching In The Polymorphic Lambda Calculus

Pdf Third Order Matching In The Polymorphic Lambda Calculus Third order matching in the polymorphic lambda calculus jan springintveld department of philosophy utrecht university p.o. box 80126, 3508 tc utrecht, the netherlands abstract we show that it is decidable whether a third order matching problem in the polymorphic lambda calculus has a solution. 1 introduction pe theory. the starting point is the fact that third order matching is decidable in the simply typed lambda calculus with constant types.

Pdf Matching For The Lambda Calculus Of Objects Inthis paper, westudy higher order matching in the polymorphic lambda calculus (a2) [gir72, rey74]. from[dow93b], it follows that higher order matching is undecidable in this calculus. The model theory of simply typed and polymorphic (second order) lambda calculus changes when types are allowed to be empty. for example, the “polymorphic boolean” type really has exactly two elements in a polymorphic model only if the “absurd” type ∀ t.t. Use your ru or radboudumc credentials to log in with surfconext to upload a file for processing by the repository team. We show that it is decidable whether a third order matching problem in the polymorphic lambda calculus has a solution.

Figure 2 From Polymorphic Lambda Calculus With Context Free Session Use your ru or radboudumc credentials to log in with surfconext to upload a file for processing by the repository team. We show that it is decidable whether a third order matching problem in the polymorphic lambda calculus has a solution. We show that it is decidable whether a third order matching problem in the polymorphic lambda calculus has a solution. the proof is constructive in the sense that an algorithm can be extracted from it that, given such a problem, returns a substitution if it has a solution and fail otherwise. Type variable match problem polymorphic variable finite order object variable references cited this publication has 6 references indexed in scilit: third order matching in the presence of type constructors published by springer nature ,1995 on equivalence classes of interpolation equations published by springer nature ,1995 third order matching. Since restricting the order of variables to finite order prohibits the use of polymorphism, this problem seems related to the problem of pattern matching in simply typed λ calculus. We extend the simply typed lambda calculus with abstraction over types, giving the polymorphic lambda calculus. a type abstraction is a new expression, written x : e, where is the upper case form of the greek letter lambda, and x is a type variable.