Encode Method

One we have created a DomainProduct object O, we can use it to turn a specification into a set of integers encoding the tuples corresponding to this specification. We want to allow the user to write specifications with the following abstract syntax:

\phi\quad{:}{:}{=}\quad v^\ell_i\mid

A tuple satisfies specification v^\ell_i if it contains value v^\ell_i. It satisfies \phi\wedge\phi' if it satisfies both \phi and \phi'. It satisfies \phi\vee\phi' if it satisfies either \phi or \phi'.

Instead of explicit connectives, we will simply allow a specification to consist of arbitrarily nested lists, eventually bottoming out with domain values. The outer level is interpreted disjunctively, and each nesting switches the interpretation of the connective: thus the 2nd level is interpreted conjunctively, the 3rd disjunctively, etc. For example, let us consider agreement information limited to just gender and person. The specification:

[[masc [1 3]] [fem 2]]

denotes the 3 tuples [masc 1], [masc 3], [fem 2]. However:

[[masc 1 3] [fem 2]]

just denotes [fem 2] since a tuple cannot contain both 1 and 2. The spec:

[[masc 1] fem]

denotes the 4 tuples [masc 1], [fem 1], [fem 2] and [fem 3].

<DomainProduct encode method>=
meth encode(Desc $)
   {self Disj(Desc $)}
meth Disj(Desc $)
   case Desc
   of _|then {FoldL Desc
                fun {$ Accu Desc}
                   {FS.union Accu
                    {self Conj(Desc $)}}
                end self.empty}
   [] nil then self.empty
   else @value2set.Desc end 
meth Conj(Desc $)
   case Desc
   of _|then {FoldL Desc
                fun {$ Accu Desc}
                   {FS.intersect Accu
                    {self Disj(Desc $)}}
                end self.full}
   [] nil then self.full
   else @value2set.Desc end 

Denys Duchier
Version 1.2.0 (20010221)