Higher Dimensional Algebraic Data Types

We investigate a natural hierarchy of free Lawvere theories.
Algebraic data types turn out to live at the second level of this
hierarchy. This is the basis for the main two applications presented here :
We solve the problem of finding a general fold algorithm and we introduce 
the novel programming feature of higher dimensional algebraic data types.
These data types are presented with a general type inference method.
Further we identify the iteration schemes map and fold in the higher 
dimensional version.