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General approach to domain design

Learn how to use simple lattices, boolean logic, and combinator techniques to construct complex lattice structures. Explore the concepts of May vs. Must analysis, common sub-expression elimination, and flow functions optimization in program domains.

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General approach to domain design

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  1. General approach to domain design • Simple lattices: • boolean logic lattice • powerset lattice • incomparable set: set of incomparable values, plus top and bottom (eg const prop lattice) • two point lattice: just top and bottom • Use combinators to create more complicated lattices • tuple lattice constructor • map lattice constructor

  2. May vs Must • Has to do with definition of computed info • Set of x ! y must-point-to pairs • if we compute x ! y, then, then during program execution, x must point to y • Set of x! y may-point-to pairs • if during program execution, it is possible for x to point to y, then we must compute x ! y

  3. May vs must

  4. May vs must

  5. Common Sub-expression Elim • Want to compute when an expression is available in a var • Domain:

  6. Common Sub-expression Elim • Want to compute when an expression is available in a var • Domain:

  7. Flow functions in FX := Y op Z(in) = X := Y op Z out in FX := Y(in) = X := Y out

  8. Flow functions in FX := Y op Z(in) = in – { X ! * } – { * ! ... X ... } [ { X ! Y op Z | X  Y Æ X  Z} X := Y op Z out in FX := Y(in) = in – { X ! * } – { * ! ... X ... } [ { X ! E | Y ! E 2 in } X := Y out

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