Higher Order Functions Considered Unnecessary for Higher Order Programming Goguen

https://cseweb.ucsd.edu/~goguen/pps/utyop.pdf

Higher Order Functions Considered Unnecessary for Higher Order Programming

It is often claimed that the essence of functional programing is the use of functions as values,  i.e., of higher order functions, and many interacting examples have been given showing the power  of this approach. Unfortunately, the logic of higher order functions is diffcult, and in particular,  higher order unifcation is undecidable. Moreover (and closely related), higher order expressions  are notoriously diffcult for humans to read and write correctly. However, this paper shows that  typical higher order programming examples can be captured with just frst order functions, by the  systematic use of parameterized modules, in a style that we call parameterized programming.  This has the advantages that correctness proofs can be done entirely within frst order logic, and  that interpreters and compilers can be simpler and more effcient.
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Let us consider this last example more carefully. ...
To summarize, the difference between parameterized programming and higher order functional programming is essentially the difference between programming in the large and programming in the small. Parameterized programming does not just combine functions, it combines modules. ... Finally, note the experience of many programmers, not just naive ones, that higher order notation can be very difficult to understand and to use.