In the following section a summation is considered in which different traversed elements are required in the summand function in order to evaluate quantities. A quantity has to be evaluated in a traversed vertex whereas a quantity is evaluated in the base element of the traversal. The non-functional description of the summation can be written as follows:
A simple method with which the argument value of the outside argument can be preserved when changing the argument list is based on named variables. Before the summation is carried out, a named variable, in this case is assigned the (vertex) value of the argument passed. When the summands are evaluated, the function argument is the traversed cell incident to the initial vertex. However, the named variable can be accessed in analogy to an unnamed variable. A formulation of (2.51) using only functional expressions and named variables is
Compared to the lambda function which is known from the lambda calculus [67,68], the order of the function remains unchanged, whereas named variables obtain a certain value. An appropriate formulation can also be obtained by the lambda function, where the use of named variables can be avoided. For the sake of clarity and conciseness it turned out to be more appropriate to use this formulation.
The summation can be further simplified by collapsing the formalism to a common summation symbol. The notation can be written shorter, without loss of generality. This reasoning can of course be applied to all accumulation mechanisms.