very sophisticated, extravagant, not too fast

This is derived from the Paper "Can Programming be Liberated from the von Neumann Style?" of John Backus 1978. Please refer to this document to fully understand this piece of Code. In essence, the function IP is constructed by function composition of some 1-parameter-functions, that are generated by function calls.

insert and alpha2 are taken from backus' papers. The first one is a function that generates closures, that act like reduce and the second generates closures that act like mapcar -.

transpose simply computes the transposed matrix of a matrix, given in list representation, e.g. ((1 2) (a b)) --> ((1 a) (2 b))