newt/playground/samples/Tour.newt

/-
  Ok, so this is newt, a dependent typed programming language that
  I am implementing to learn how they work.  It targets javascript
  and borrows a lot of syntax from Idris and Agda.

  This page is a very simple web playground based on the monaco editor.
  It runs newt, compiled by Idris2, in a web worker.

  Block comments follow Lean because they're easier to type on a
  US keyboard.

  The output, to the right, is somewhat noisy and obtuse. You'll see
  INFO and sometimes ERROR messages that show up in the editor view
  on hover.  I'm emitting INFO for solved metas.

  The Day1.newt and Day2.newt are last year's advent of code, translated
  from Lean.

-/

-- One-line comments begin with two hyphens

-- every file begins with a `module` declaration
-- it must match the filename
module Tour

-- We can import other modules, with a flat namespace and no cycles,
-- diamonds are ok

-- commented out until we preload other files into the worker
-- import Lib

-- We're calling the universe U and are doing type in type for now

-- Inductive type definitions are similar to Idris, Agda, or Haskell
data Nat : U where
  Z : Nat
  S : Nat -> Nat

-- Multiple names are allowed on the left:
data Bool : U where
  True False : Bool

-- function definitions are equations using dependent pattern matching
plus : Nat -> Nat -> Nat
plus Z m = m
plus (S n) m = S (plus n m)

-- we can also have case statements on the right side
-- the core language includes case statements
-- here `\` is used for a lambda expression:
plus' : Nat -> Nat -> Nat
plus' = \ n m => case n of
    Z => m
    S n => S (plus n m)

-- We can define operators, currently only infix
-- and we allow unicode and letters in operators
infixl 2 _≡_

-- Here is an equality, like Idris, everything goes to the right of the colon
-- Implicits are denoted with braces `{ }`
-- unlike idris, you have to declare all of your implicits
data _≡_ : {A : U} -> A -> A -> U where
  Refl : {A : U} {a : A} -> a ≡ a

-- And now the compiler can verify that 1 + 1 = 2
test : plus (S Z) (S Z) ≡ S (S Z)
test = Refl

-- Ok now we do typeclasses.  There isn't any sugar, but we have
-- search for implicits marked with double brackets.

-- Let's say we want a generic `_+_` operator
infixl 7 _+_

-- We don't have records yet, so we define a single constructor
-- inductive type. Here we also use `∀ A.` which is sugar for `{A : _} ->`
data Plus : U -> U where
  MkPlus : ∀ A. (A -> A -> A) -> Plus A

-- and the generic function that uses it
-- the double brackets indicate an argument that is solved by search
_+_ : ∀ A. {{_ : Plus A}} -> A -> A -> A
_+_ {{MkPlus f}} x y = f x y

-- The typeclass is now defined, search will look for functions in scope
-- that return a type matching (same type constructor) the implicit
-- and only have implicit arguments (inspired by Agda).

-- We make an instance `Plus Nat`
PlusNat : Plus Nat
PlusNat = MkPlus plus

-- and it now finds the implicits, you'll see the solutions to the
-- implicits if you hover over the `+`.
two : Nat
two = S Z + S Z

-- We can leave a hole in an expression with ? and the editor will show us the
-- scope and expected type (hover to see)
foo : Nat -> Nat -> Nat
foo a b = ?

-- Newt compiles to javascript, there is a tab to the right that shows the
-- javascript output. It is not doing erasure (or inlining) yet, so the
-- code is a little verbose.

-- We can define native types:

ptype Int : U
ptype String : U
ptype Char : U

-- The names of these three types are special, primitive numbers, strings,
-- and characters inhabit them, respectively. We can match on primitives, but
-- must provide a default case:

isVowel : Char -> Bool
isVowel 'a' = True
isVowel 'e' = True
isVowel 'i' = True
isVowel 'o' = True
isVowel 'u' = True
isVowel _ = False

-- And primitive functions have a type and a javascript definition:

pfunc plusInt : Int -> Int -> Int := "(x,y) => x + y"
pfunc plusString : String -> String -> String := "(x,y) => x + y"

-- We can make them Plus instances:

PlusInt : Plus Int
PlusInt = MkPlus plusInt

PlusString : Plus String
PlusString = MkPlus plusString

concat : String -> String -> String
concat a b = a + b

-- Now we define Monad

data Monad : (U -> U) -> U where
  MkMonad : {m : U -> U} ->
            ({a : U} -> a -> m a) ->
            ({a b : U} -> m a -> (a -> m b) -> m b) ->
            Monad m

pure : ∀ m. {{Monad m}} -> {a : U} -> a -> m a
pure {{MkMonad p _}} a = p a

-- we can declare multiple infix operators at once
infixl 1 _>>=_ _>>_

_>>=_ : ∀ m a b. {{Monad m}} -> m a -> (a -> m b) -> m b
_>>=_ {{MkMonad _ b}} ma amb = b ma amb

_>>_ :  ∀ m a b. {{Monad m}} -> m a -> m b -> m b
ma >> mb = ma >>= (λ _ => mb)

-- That's our Monad typeclass, now let's make a List monad

infixr 3 _::_
data List : U -> U where
  Nil : ∀ A.  List A
  _::_ : ∀ A. A -> List A -> List A

infixr 7 _++_
_++_ : ∀ a.  List a -> List a -> List a
Nil ++ ys = ys
(x :: xs) ++ ys = x :: (xs ++ ys)

bindList : ∀ a b. List a -> (a -> List b) -> List b
bindList Nil f = Nil
bindList (x :: xs) f = f x ++ bindList xs f

-- Both `\` and `λ` work for lambda expressions:
MonadList : Monad List
MonadList = MkMonad (λ a => a :: Nil) bindList

-- We'll want Pair below too.  `,` has been left for use as an operator.
-- Also we see that → can be used in lieu of ->
infixr 1 _,_ _×_
data _×_ : U → U → U where
  _,_ : ∀ A B. A → B → A × B

-- The _>>=_ operator is used for desugaring do blocks

prod : ∀ A B. List A → List B → List (A × B)
prod xs ys = do
  x <- xs
  y <- ys
  pure (x, y)