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(moved from stackoverflow to here)

I'm trying to understand dataflow stuff for program analysis. Transfer functions move lattice elements up (towards top ⊤) and down (towards bottom ⊥). Sometimes the direction confuses me a bit (I'd do it in the other direction), so

  • do the top and bottom elements of a lattice have any intrinsic mathematical meaning other than "I'm greater/smaller than everything else", respectively? (I suspect not)

  • do the top and bottom elements have any meaning by common human convention? By this I mean moving up towards top means 'more information has been found' or 'we know more about this thing', and moving down towards bottom means 'less is known' or 'useful information has been lost'

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No, there is no intrinsic meaning. Their meaning depends on the specific data analysis and how it uses the particular lattice or what interpretation we put on them.

Often, bottom is used for uninitialized values (it is the most restrictive element) and top to represent values where nothing is known (it is the least restrictive element, i.e., if conveys the least information about the corresponding value), but this is not mandatory.

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