Reddit reviews The Algebra of Programming (Prentice-hall International Series in Computer Science)

It’s not particularly trendy right now in the programming world, but algebraically deriving efficient programs from their implementations is the primary thing Richard Bird has done in his career.

It usually goes under the name Algebra of Programming and you can see it described and used in the books [Pearls of Functional Algorithm Design](Pearls of Functional Algorithm Design https://www.amazon.com/dp/0521513383/ref=cm_sw_r_cp_api_i_dmFWCbX54E4G1) and [The Algebra of Programming](The Algebra of Programming (Prentice-hall International Series in Computer Science) https://www.amazon.com/dp/013507245X/ref=cm_sw_r_cp_api_i_-fFWCbRYRZ6W8).

The basic idea is that you can specify your problem with a naive functional program and apply algebraic transformations to that program which preserve the behavior while improving the runtime.

Jeremy Gibbons is also doing exceptionally good work in this area (and presently leads the research group linked above). You can see a taste of this sort of thinking here as well.

You joke but that style is actually used in The Algebra of Programming

I don't understand what you mean. Do you mean that you think all algebras are commutative ?

We do have an algebra of programming

It's quite pricey, but I recommend
Algebra for Programming by Richard Bird and Oege de Moor. The second chapter has a brief but lucid introduction to category theory insofar as it applies to a functional language like Haskell. It doesn't cover everything like adjunctions, but it's a great start (definitely easier than Awodey unless you already know a ton of algebra). The bonus here is that you can download solutions to some exercises as well!

You may also enjoy Computational Category Theory, although the examples are in Standard ML.

Try Bird's Introduction to Functional Programming using Haskell, which this seems to be an update of! One of the best books on FP ever written IMO. And his Pearls of Functional Algorithm Design. And (it's a bit pricey though!) his Algebra of Programming.

To answer your general question: To use a parameter more than once, you need to duplicate your parameter like:
dup :: a -> (a, a)
Then you call two functions on each.

Algebra of Programming could help you.

https://www.amazon.ca/Algebra-Programming-Richard-Bird/dp/013507245X

> Desculpa, não sabes do que estás a falar.

Sinceramente, cada vez tenho menos paciência para ti.

> Programar é fácil. É apenas a definição de instruções de maneira a expressar um algoritmo.

Nunca na minha vida vi a palavra "programar" ser interpretada com esse significado. Para além qualquer curso de programação (independentemente do nível) requer que se faça mais que isso.

Quanto ao significado da palavra programar. Começando pelo básico, i.e. wikipedia.

> "Computer programming (often shortened to programming) is a process that leads from an original formulation of a computing problem to executable computer programs. Programming involves activities such as analysis, developing understanding, generating algorithms, verification of requirements of algorithms including their correctness and resources consumption, and implementation"

Se quiseres ler livros sobre o assunto, alguns clássicos são,

Systematic Programming: An Introduction - Niklaus Wirth

The Art of Computer Programming - Donald Knuth

The Science of Programming - David Gries

The Algebra of Programming - Richard Bird, Oege de Moor

The Mathematics of Programming - Tony Hoare

E porque sei que ler livros dá muito trabalho, ficam algumas quotes,

Edsger Dijkstra

> "Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians."



Tony Hoare

>"Programming is a mathematical activity. Like other branches of applied mathematics and engineering, its successful practice requires determined and meticulous application of traditional methods of mathematical understanding, calculation and proofs"