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Formalisation of Appendix A 'relcons'

dandl@david-bennett-2
#1 · May 29, 2020, 8:34 am

Here is my attempt at a formal definition of a 'relcon' per App-A. It would serve as the definition for a 'function relation' and perhaps even an HHT 'algorithmic relation'.

Monadic

Given a function f with the type signature Tx->Ty, the relcon S is defined as follows.

Hs = <X,Tx>, <Y,Ty>
Bs = { ts | f(X) = Y }

Dyadic

Given a function f with the type signature Tx->Ty->Tz, the relcon S is defined as follows.

Hs = <X,Tx>, <Y,Ty>, <Z,Tz>
Bs = { ts | f(X,Y) = Z }

For the relcon PLUS in App-A, types Tx, Ty and Tz are all INTEGER, and the dyadic function f is the scalar operator "+".

Andl - A New Database Language - andl.org