What is Reddit's opinion of The Algebra of Programming (Prentice-hall International Series in Computer Science)?

From 3.5 billion Reddit comments

• Monoids (and comonoids) show up everywhere. (Finite) lists are free monoids. A variety of interesting structures are monoidal: bloom filters, hyperloglog, dependency graphs, etc. Monoids can be used to reason about and implement, e.g., stream processing and data parallelization. They also form the abstract basis of linear algebra, which is ofc useful in a variety of ways, including numerical analysis.

• Recursion schemes (folds, unfolds, etc) have (relatively) simple algebraic interpretations (as cata- and anamorphisms, respectively)

• Many concepts from category theory (which is just the abstract algebra of abstract functions) also show up frequently. Naturality is implied by parametricity, so (covariant) polymorphic functions are automatically natural transformations. This makes it very easy to reason about the behavior of parametric polymorphism.

Monads also feature prominenty, even if they are implicit in the imperative structure rather than explicit in the type system. This shouldn't be too surprising: natural transformations give rise to adjunctions which give rise to monads.

• The (Curry-Howard) correspondence between types, proofs, and categories is useful for reasoning about the denotations of programs.

There's a lot more as well. Richard Bird has written <u>The Algebra of Programming</u> on the subject, which is a great read – if somewhat pricey.