Rodolfo Hansen
A collection of slides I have generated for some of the talks / workshops I have created.
Introduction to FP
(a C++ perspective).
Let's replace FP with just two restrictions:
Avoid throwing exceptions.
Avoid mutations.
How do we phase out or limit exceptions, global state, and loops?
A convincing demonstration of correctness being impossible as long as the mechanism is regarded as a black box, our only hope lies in not regarding the mechanism as a black box.
Why would we do this?
The good compiler is a actually a proof assistant; so you can leverage types as propositions.
... Proof Assistant? ...
Types ≃ Propositions ≃ Objects
Terms ≃ Proofs ≃ Morphisms
Curry-Howard(-Lambek) Correspondance.
//In other words:
struct True; // not true: Boolean
We can prove logical statements by constructing elements of types
https://github.com/DanielKrawisz/Truth
Types ≃ Propositions
If you can define the method, you found the proof...
template <typename A, typename B>
struct And {
A fst;
B snd;
};
template <typename A, typename B>
union Or {
A fst;
B snd;
};
template <typename A, typename B>
B Implies(in: A);Types ≃ Propositions
Updated for C++ 17
template<typename A, typename B>
using And = std::tuple<A, B>;
template<typename A, typename B>
using Or = std::variant<A, B>;
template<typename A, typename B>
using Implies = std::function<B(A)>;What are we looking to write more of:
- Total Functions
- Referential Transparency
- Proovable Termination
Why: Determinism
Total Functions
Avoid exceptions
int decode(std::string& s);
tl::expected<int, internal_error>
decode(std::string& s);Total Functions
Restrict input values
void open(std::string& filename, std::string& mode);
tl::expected<fstream, io_exception>
open(std::string& filename, mode_enum mode);Referential Transparency
Avoid mutation
int x = 5;
x = 3;
const int y = 5;
y = 3; // Exception
if (x = 1) // Oops
std::fstream fs;
fs.open("w")
fs.open("y") // OopsReferential Transparency
Decouple evaluation
IO<Tiemstamp> systemTime;
systemTime()
doSomething()
sleep(1)
systemTime()
doSomethingElse()Termination
Avoid recursion
int use(int a) { return use(a); };
int sum(int... nums) = { return (... + nums); };Termination
Avoid loops
int use(int a) { while (true) { ... }; return a; };
mlib::lazylist<int> fib = mlib::lazylist::single<int>(0)
.scanLeft(1)([] (int a, int b) { return a + b; });This subset of your code composes!
Category Theory is the study of composition.
The code your write this ways obeys the laws of category theory.
Introduction to FP
By Rodolfo Hansen
Introduction to FP
Let the compiler prove itself to you
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