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Examples of the Unification Algorithm { X = int, Y = X X } unify({ X = int, Y = X X }) S=X, T=int, C’={Y = X X} = [ X int ] ; unify({ Y = int int }) S=Y, T=int int, C’={ } = [ X int ] ; [ Y int int ] ; unify({ }) = [ X int ] ; [ Y int int ] ; [ ] = [ X int, Y int int ] { int int = X Y } unify({ int int = X Y }) S=int int, T=X Y, C’={ } = unify({ int = X, int = Y }) S=int, T=X, C’={ int = Y } = [ X int ] ; unify({ int = Y }) S=int, T=Y, C’={ } = [ X int ] ; [ Y int ] ; unify({ }) = [ X int, Y int ]
![Examples of the Unification Algorithm { X = int, Y = X X } unify({ X = int, Y = X X }) S=X, T=int, C’={Y = X X} = [ X int ] ; unify({ Y = int int }) S=Y, T=int int, C’={ } = [ X int ] ; [ Y int int ] ; unify({ }) = [ X int ] ; [ Y int int ] ; [ ] = [ X int, Y int int ] { int int = X Y } unify({ int int = X Y }) S=int int, T=X Y, C’={ } = unify({ int = X, int = Y }) S=int, T=X, C’={ int = Y } = [ X int ] ; unify({ int = Y }) S=int, T=Y, C’={ } = [ X int ] ; [ Y int ] ; unify({ }) = [ X int, Y int ]](http://images.slideplayer.com/26/8615043/slides/slide_1.jpg "Examples of the Unification Algorithm { X = int, Y = X X } unify({ X = int, Y = X X }) S=X, T=int, C’={Y = X X} = [ X int ] ; unify({ Y = int int }) S=Y, T=int int, C’={ } = [ X int ] ; [ Y int int ] ; unify({ }) = [ X int ] ; [ Y int int ] ; [ ] = [ X int, Y int int ] { int int = X Y } unify({ int int = X Y }) S=int int, T=X Y, C’={ } = unify({ int = X, int = Y }) S=int, T=X, C’={ int = Y } = [ X int ] ; unify({ int = Y }) S=int, T=Y, C’={ } = [ X int ] ; [ Y int ] ; unify({ }) = [ X int, Y int ]")
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Examples of the Unification Algorithm { X Y = Y Z, Z = U W } unify({ X Y = Y Z, Z = U W }) S=X Y, T= Y Z, C’={Z = U W} = unify({ Z = U W, X = Y, Y = Z }) S=Z, T=U W, C’={ X = Y, Y = Z } = [ Z U W ] ; unify({ X = Y, Y = U W }) = [ Z U W ] ; [ X Y ] ; unify({ Y = U W }) = [ Z U W ] ; [ X Y ] ; [ Y U W ] = [ Z U W, X Y ] ; [ Y U W ] = [ Z U W, X U W, Y U W ]
![Examples of the Unification Algorithm { X Y = Y Z, Z = U W } unify({ X Y = Y Z, Z = U W }) S=X Y, T= Y Z, C’={Z = U W} = unify({ Z = U W, X = Y, Y = Z }) S=Z, T=U W, C’={ X = Y, Y = Z } = [ Z U W ] ; unify({ X = Y, Y = U W }) = [ Z U W ] ; [ X Y ] ; unify({ Y = U W }) = [ Z U W ] ; [ X Y ] ; [ Y U W ] = [ Z U W, X Y ] ; [ Y U W ] = [ Z U W, X U W, Y U W ]](http://images.slideplayer.com/26/8615043/slides/slide_2.jpg "Examples of the Unification Algorithm { X Y = Y Z, Z = U W } unify({ X Y = Y Z, Z = U W }) S=X Y, T= Y Z, C’={Z = U W} = unify({ Z = U W, X = Y, Y = Z }) S=Z, T=U W, C’={ X = Y, Y = Z } = [ Z U W ] ; unify({ X = Y, Y = U W }) = [ Z U W ] ; [ X Y ] ; unify({ Y = U W }) = [ Z U W ] ; [ X Y ] ; [ Y U W ] = [ Z U W, X Y ] ; [ Y U W ] = [ Z U W, X U W, Y U W ]")
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Examples of the Unification Algorithm { int = int Y } unify({ int = int Y }) S=int, T= int Y, C’={ } fails { Y = int Y } unify({ Y = int Y }) S=Y, T= int Y, C’={ } fails { } unify({ }) = [ ]
![Examples of the Unification Algorithm { int = int Y } unify({ int = int Y }) S=int, T= int Y, C’={ } fails { Y = int Y } unify({ Y = int Y }) S=Y, T= int Y, C’={ } fails { } unify({ }) = [ ]](http://images.slideplayer.com/26/8615043/slides/slide_3.jpg "Examples of the Unification Algorithm { int = int Y } unify({ int = int Y }) S=int, T= int Y, C’={ } fails { Y = int Y } unify({ Y = int Y }) S=Y, T= int Y, C’={ } fails { } unify({ }) = [ ]")
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Reference http://www.dcs.gla.ac.uk/~simon/teaching/tpl/
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