1. Ideal DEductive Applicative Language. A language by Pier Bosco and Elio Giovannetti combining Miranda and Prolog. Function definitions can have a guard condition (introduced by ":-") which is a conjunction of equalities between arbitrary terms, including functions. These guards are solved by normal Prolog resolution and unification. It was originally compiled into C-Prolog but was eventually to be compiled to K-leaf.
In domain theory, a non-empty, downward closed subset which is also closed under binary least upper bounds. I.e. anything less than an element is also an element and the least upper bound of any two elements is also an element.