Examples of the Unification Algorithm

{ X = int, Y = XX }

unify({ X = int, Y = XX }) S=X, T=int, C’={Y = XX}= [ X int ] ; unify({ Y = intint }) S=Y, T=intint, C’={ }= [ X int ] ; [ Y intint ] ; unify({ })= [ X int ] ; [ Y intint ] ; [ ]= [ X int, Y intint ]

{ intint = XY }

unify({ intint = XY }) S=intint, T=XY, 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

{ XY = YZ, Z = UW }

unify({ XY = YZ, Z = UW }) S=XY, T= YZ, C’={Z = UW}= unify({ Z = UW, X = Y, Y = Z }) S=Z, T=UW, C’={ X = Y, Y = Z }= [ Z UW ] ; unify({ X = Y, Y = UW })= [ Z UW ] ; [ X Y ] ; unify({ Y = UW })= [ Z UW ] ; [ X Y ] ; [ Y UW ]= [ Z UW, X Y ] ; [ Y UW ]= [ Z UW, X UW, Y UW ]

Examples of the Unification Algorithm

{ int = intY }

unify({ int = intY }) S=int, T= intY, C’={ } fails

{ Y = intY }

unify({ Y = intY }) S=Y, T= intY, C’={ } fails

{ }

unify({ }) = [ ]

Reference

http://www.dcs.gla.ac.uk/~simon/teaching/tpl/