Values in Non-Strict Languages

In the literature on non-strict languages, the term "value" seems to be used in a different way. In call-by-value languages, we classify a set of normal forms that we define as the "values" of the language, and arguments to functions must evaluate to values before the functions can be applied. But because in call-by-name or call-by-need languages, you can pass arbitrary, unevaluated expressions to functions, the notion of a value is in a sense less critical. You still need to define the normal forms in order to determine when to stop evaluating the whole program (or when to stop evaluating arguments to primitives with strict positions). But interestingly, in The Implementation of Functional Programming Languages, Peyton Jones still refers to the expression that a function argument is bound to as the variable's "value" -- despite the fact that it may not be in weak head normal form. Apparently the term "value" is informally used to mean a variable's binding, whereas the final result of an evaluation is only referred to as a normal form.