In 1996 DC Keenan wrote "To dissect a mockingbird" [1] giving a graphical notation for lambda calculus, expressing it in pictures with an evocative semantics. 28 years later the linked piece gives a categorical string-diagram version. Applications arise when you are interested in mappings that have extra behavior other than that of functions, as in probabilistic programming, automatic differentiation.
In 1996 DC Keenan wrote "To dissect a mockingbird" [1] giving a graphical notation for lambda calculus, expressing it in pictures with an evocative semantics. 28 years later the linked piece gives a categorical string-diagram version. Applications arise when you are interested in mappings that have extra behavior other than that of functions, as in probabilistic programming, automatic differentiation.
[1] https://dkeenan.com/Lambda/