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I am wondering if there exists an example attribute grammar that is non-circular but not l-ordered (l-ORD) as well.

The reason I am asking this is one can find an attribute grammar that is circular, then it will obviously not be an l-ORD. But I am wondering if there even exists a non-circular AG that is also not l-ORD.

Node.JS
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3 Answers3

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In Figure 12 of my paper on conditional attribute grammars, it gives the following strongly non-circular attribute grammar that is not doubly non-circular (and therefore not l-ORD):

S -> 0 L
    L.inh1 = 0
    L.inh2 = L.syn1
    S.result = L.syn2

S -> 1 L
    L.inh2 = 0
    L.inh1 = L.syn2
    S.result = L.syn1


L ->
    L.syn1 = L.inh1
    L.syn2 = L.syn2

It is non-circular (even strongly non-circular) since each synthesized attribute of L depends only on the corresponding inherited attribute, but depending on the context, each may need to be done before the other. Hence no fixed order of attributes can be required.

John Tang Boyland
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You could take an L-Ord Attribute Grammar, replace all inherit attributes by synthetic attributes and all synthetic attributes by inherit ones and reverse all assignments... then you have a grammar that isn't L-Ord and still non-circular. I would call that R-Ord, because you have reversed all arrows and can traverse it right-to-left instead of left-to-right.

Algoman
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The Grammar in my answer to Full circularity vs strong circularity for attribute grammars (that you had already found) is also not L-Ord, because L-Ord Attribute Grammars are strongly-non-circular. Since said grammar isn't strongly-non-circular, it's not L-Ord. (And it's also not circular).

Algoman
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