Question

In Mathematica the command Select only lets define a selection criterion for each element of a list on its own.

I want to specify a criterion that is dependend of a function of the previous and/or next element and a function on all elements, respectively. The first and last element cannot be tested that way, but they should be selected anyway.

Doing that iteratively probably would not be a problem, I want to try it functional first.

I would imaging using it somehow like that:

Select[list,FirstQ||LastQ,Func1[#-1,#]&&Func2[#,#1]&&Func3[list]&]

Answer 1

I suggest using the Partition function. To get each element of a list grouped with its immediate neighbors you can do this

Partition[{a,b,c,d,e}, 3, 1]

to get this:

{{a,b,c}, {b,c,e}, {c,d,e}}

Knowing that, we can make a “select with neighbors” function that roughly matches your spec:

SelectWN[list_, firstq_, lastq_, trinaryfunc_] := Join[
  If[firstq, {First@list}, {}], 
  Select[Partition[list, 3, 1], trinaryfunc@@#&][[All,2]], 
  If[lastq, {Last@list}, {}]]

Note that in the arguments to trinaryfunc, #2 is the list element itself, #1 is the left neighbor, and #3 is the right neighbor.
It would be nice to generalize this to use any number of neighbors, not just the immediate neighbors, but then you’d want a better way to refer to them than the analog of {#1, #2, #3}.