I wonder whether there is any relationship between lambda calculus and phonology (study of phonemes). Specifically, how one would use the concepts of lambda calculus (typed or untyped) in the study of phonology of a particular natural language, like English, German, or Finnish? It would be much appreciated, if you could mention some introductory texts, papers, books, etc. about this.
This is just a long comment (too many words to fit in a comment box).
Gérard Huet is, among other things, an expert in $\lambda$-calculus who worked worked a lot on the computational processing of Sanskrit, including its phonological aspects. I remember him once giving a talk in Marseilles entitled Des Lambdas et des Aums ("Lambdas and Oms") but unfortunately I do not recall whether he made any explicit connection between the two (it was a very informal talk in honor of Per Martin-Löf, who was to receive a doctorate honoris causa from the University of Aix-Marseille 2 a few days later. All this was nearly 16 years ago).
I browsed a bit his web page (linked above), there's a lot of material on the computational analysis of Sanskrit (including phonetics) but none of it seems to mention the $\lambda$-calculus (there's some OCaml programming at best). Since, as I said, Huet knows the $\lambda$-calculus extremely well, my guess is that had he seen any connection between the latter and Sanskrit phonology, he would have stressed it. But certainly the best is just to ask him directly! I'm sure he'll be glad to tell you.
PS: perhaps a little bit of motivation/background to your question wouldn't hurt. Why do you think there should be any relationship between $\lambda$-calculus and phonology? I guess I can vaguely understand the motivation behind a computational approach to phonology, but why the $\lambda$-calculus?