The support for derived instances of Eq and Show makes their methods = = and show generic in a qualitatively different way from parametrically polymorphic functions : these " functions " ( more accurately, type-indexed families of functions ) can be applied to values of various types, and although they behave differently for every argument type, little work is needed to add support for a new type.
12.
For this we consider structures \ langle X, ( R _ i ) _ I, \ mathcal { F } \ rangle where \ langle X, ( R _ i ) _ I \ rangle is a relational structure i . e . a set with an indexed family of relations defined on it, and \ langle X, \ mathcal { F } \ rangle is a field of sets.
13.
The supremum of a " directed family of simple valuations " ( i . e . an indexed family of simple valuations which is also directed in the sense that for each pair of indexes i and j belonging to the index set I, there exists an index k such that \ scriptstyle v _ i ( U ) \ leq v _ k ( U ) \ ! and \ scriptstyle v _ j ( U ) \ subseteq v _ k ( U ) \ ! ) is called "'quasi-simple valuation "'
