By Harold Boley
As in different fields, in machine technological know-how sure items of research could be synthesized from diversified simple components, in numerous methods, and with varied ensuing stabilities. In subfields comparable to man made intelligence, computational good judgment, and programming languages quite a few relational and sensible components and strategies were attempted for the synthesis of declarative programs.
This textual content considers the notions of relatives, as present in good judgment programming or in relational databases, and of capabilities, as present in practical programming or in equational languages. We research a declarative integration that is tight, since it occurs correct on the point of those notions, and that is nonetheless functional, since it preserves the benefits of the commonly used relational and practical languages PROLOG and LISP. The ensuing relational and sensible language, RELFUN, is used right here for exemplifying all integration principles.
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Extra info for A Tight, Practical Integration of Relations and Functions
Pairlists(,) :& . = arrange(L2) tree [TI, X,T2]. arrange() :& void. partition([XIL] ,X,LI,L2) :- partition(L,X,LI,L2). part it ion ( [X iL], Y, [X iL i], L2) -9 before(X,Y), partition(L,Y,Li,L2). part it ion ( [X lL], Y, LI, [X lL2] ) -9 bef ore (Y, X), part it ion (L, Y, LI, L2). partition( ,Y, , ). before(pair[Xl,Y1] ,pair[X2,Y2]) :- string<(Xl,X2). = numbered(TI,NO))). numbered(void,N) :& N. Note t h a t the b o d y of the first a r r a n g e clause can be simplified to ~'While the need for non-ground terms is self-evident in relational programming (ground relational programming isn't very useful), they require some justification in functional programming.
Also notice that numbered 'updates' the p a i r structures at the roots of the t r e e structures by ". ="-binding the unavoidable logical variable N1 to the recursion result obtained from traversing the left subtree T1, a value which is incremented by 1+ for use in traversing the right subtree T2. This works since RELFUN's ". ="-builtin both binds and returns the value of its rhs. Moreover, we can extract a reusable, parameterized sorting specification from the s e r i a l i s e program, thus simplifying the remaining specification.
Note that this functional s o r t version specifies a computationally preferable (nesting) sequence by calling perm before sorted. In the relational s o r t specification commutativity of conjunction appears to permit calling s o r t e d before perm, which, however, would not run in normal PROLOGs, as discussed in [L1o87]. A related benefit of the functional formulation is that the computationally less meaningful s o r t use for 'unsorting' a given sorted list is syntactically marked by a ". ="-call over a free s o r t call, whereas the relational version employs symmetrically-looking non-ground s o r t calls for both use modes, that would suggest "equality of rights".
A Tight, Practical Integration of Relations and Functions by Harold Boley