Lambda the Ultimate

From the other thread, I read Relations as First-Class Citizen from which I wonder: If we are seeking good support for compositionality, how might a declarative/calculus approach go wrong? What is it about SQL or Make or whatever else (e.g. random thing IBM's Collage) that might contribute to compositional frustration?

While the declarative style of programming of SQL is very nice for solving very specific and well isolated sub-problems in your requirements & design space, it is of almost no aid for putting the architectural pieces together. Yet, putting the pieces together is something software engineers do every single day. And so is writing algorithms. Exposing a relational algebra therefore appears more natural when it comes to software development, and when it comes to manipulating data vs. querying database. To be fair, libraries such as ARel, Sequel, and jOOQ already show the way: they provide an API that is closer to relational algebra than relational calculus. Alf and Axiom simply go further this path by abstracting from SQL and choosing a sound algebra known as Tutorial D as a better inspiration than SQL towards the same objective.

An algebra is about providing operators for putting operands together, a calculus simply is not.