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General approach to domain design

Explore different lattice structures like boolean logic and powerset lattice; create complex lattices using combinator techniques; understand the distinction between May versus Must computations. Improve efficiency in sub-expression elimination and flow functions.

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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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