An Introduction to Functional Programming Through Lambda Calculus

- 99 -For example:1::(2::(3::(4::[]))) == 1::2::3::4::[] == [1,2,3,4]6.7. Lists and evaluationIt is important to note that we have adopted tacitly a weaker form of β reduction with lists because we are notevaluating fully the expressions corresponding to list representations. A list of the form:::is shorthand for:CONS which is a function application and should, strictly speaking, be evaluated.Here, we have tended to use a modified form of applicative order where we evaluate the arguments and to get values and but do not then evaluate theresulting function application:any further.CONS Similarly, a list of the form:[,]has been evaluated to:[,]but no further even though it is equivalent to:CONS (CONS NIL)This should be born in brain until we discuss evaluation in more detail in chapter 9.6.8. Deletion from a listTo add a new value to an unordered list we CONS it on the front. To delete a value, we must then search the list untilwe find it. Thus, if the list is empty then the value is not in it so return the empty list:DELETE X [] = []It is common in list processing to return the empty list if list access fails.Otherwise, if the first value in the list is the required value then return the rest of the list:DELETE X (H::T) = T if X HOtherwise, join the first value onto the result of deleting the required value from the rest of the list:DELETE X (H::T) = H::(DELETE X T) if NOT ( X H)