31 10 19 Types and Finding Intermediate Functions

How will type statements for functions in algorithm writer work, given that the functions will take functions of functions, etc. as arguments?  Should there be two and more versions of a function given that a function may sometimes take a certain set of functions, and other times another set of functions?  There are functions that take "any" type of (number of functions as) input.  Should functions be written to sometimes call functions if they are available, otherwise call a base case (with a different type statement)?

Type statements for functions which take functions as input can contain the types of called functions (rather than needing internal type statements).  This means functions can be plugged in and played with.

There are so many algorithm ideas and they each have to be unique, so a functional algorithm writer may not be used for anything apart from generation of algorithms.  Sentence decomposition can lead to natural use of the functional syntax.  

Newly needed intermediate, etc. functions may be developed now given below (not after) specs (of function name).  This would require a separate algorithm.

Program finder can be used in string and list finders to write new functions.

One-line aLgorithmic functions can be read quickly.