On the adequacy of per models
Abstract
In this note we consider a fixed point extension of the second order lambda calculus equipped with a call by value evaluation mechanism. We interpret the language in a partial cartesian closed category of "directed complete" partial equivalence relations (pers) over a domain theoretic model of a type-free, call-by-value, lambda calculus. Our main result is that the notions of "syntactic" and "semantic" convergence coincide.