Can somebody refer me to peer-reviewed papers studying the advantages or disadvantages of writing code in a functional style? Are there papers which discuss the applications of Lambda Calculus in fields such as Machine Learning, Language Design, etc.?
There is a famous paper "Why Functional Programming Matters" by John Hughes. The main argument of this paper is the modularity of functional programs.
Also, the work by Chris Okasaki about functional data structures is very interesting. The article "Red-Black Trees in a Functional Setting" provides a very clear implementation of red-black trees using functional programming language, which is much simpler than their imperative implementation in the book "Introduction to Algorithms" by Tomas H. Cormen et al.
a semifamous high quality, free reference in this area is Structure and intepretation of computer programs by Abelson and Sussman, MIT professors, some more info on wikipedia. they advocate functional programming as a way of understanding the theory and abstraction of programming such that understanding of functional programming will help one understand/apply the same principles in any language. they make some effort to discriminate it from/juxtapose it with what is called "imperative style" but without side-by-side comparisons.