Substitution tree

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Substitution tree is a method of indexing terms, which consists in holding at each term the substitution that must be performed at the parent node to obtain the given term.

The substitution tree treats external variables (that is, just some symbols) and internal variables (used to describe only common trees).

Example for g ( b ) {\displaystyle g(b)} , f ( a , g ( b ) ) {\displaystyle f(a,g(b))} i f ( b , g ( b ) ) {\displaystyle f(b,g(b))} :

x {\displaystyle x} i Y {\displaystyle y} These are internal variables.

In the substitution tree there is much more sharing than in the discriminating tree, so it is much more efficient to use memory. Still, however g ( b ) {\displaystyle g(b)} It is shared only between certain instances.

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