sugar in samples

port/Prelude.newt

@@ -60,45 +60,28 @@ infixr 2 _,_
 data _×_ : U → U → U where
   _,_ : {A B} → A → B → A × B
 
-
 infixl 6 _<_
-data Ord : U → U where
-  MkOrd : {A} → (A → A → Bool) → Ord A
+class Ord a where
+  _<_ : a → a → Bool
 
-_<_ : {A} {{Ord A}} → A → A → Bool
-_<_ {{MkOrd cmp}} a b = cmp a b
-
-cmpNat : Nat → Nat → Bool
-cmpNat Z Z = True
-cmpNat Z m = False
-cmpNat n Z = True
-cmpNat (S n) (S m) = True
-
-OrdNat : Ord Nat
-OrdNat = MkOrd cmpNat
+instance Ord Nat where
+  _ < Z = False
+  Z < S _ = True
+  S n < S m = n < m
 
 -- Monad
 
--- TODO sugar for if then else (mixfix is too eager)
-
--- TODO stack with Applicative, etc?
-
-data Monad : (U -> U) -> U where
-  MkMonad : { M : U -> U } ->
-            (bind : {A B : U} -> (M A) -> (A -> M B) -> M B) ->
-            (pure : {A : U} -> A -> M A) ->
-            Monad M
+class Monad (m : U → U) where
+  bind : {a b} → m a → (a → m b) → m b
+  pure : {a} → a → m a
 
 infixl 1 _>>=_ _>>_
-_>>=_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> (m a) -> (a -> m b) -> m b
-_>>=_ {a} {b} {m} {{MkMonad bind' _}}  ma amb = bind' {a} {b} ma amb
+_>>=_ : {m} {{Monad m}} {a b} -> (m a) -> (a -> m b) -> m b
+ma >>= amb = bind ma amb
 
-_>>_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> m a -> m b -> m b
+_>>_ :  {m} {{Monad m}} {a b} -> m a -> m b -> m b
 ma >> mb = mb
 
-pure : {a : U} {m : U -> U} {{_ : Monad m}} -> a -> m a
-pure {_} {_} {{MkMonad _ pure'}} a = pure' a
-
 -- Equality
 
 infixl 1 _≡_
@@ -114,89 +97,47 @@ sym : {A : U} -> {a b : A} -> a ≡ b -> b ≡ a
 sym Refl = Refl
 
 -- Functor
-data Functor : (U → U) → U where
-  MkFunctor : {m : U → U} → ({a b : U} → (a → b) → m a → m b) → Functor m
 
-map : {m} {{Functor m}} → {a b} → (a → b) → m a → m b
-map {{MkFunctor f}} ma = f ma
+class Functor (m : U → U) where
+  map : {a b} → (a → b) → m a → m b
 
 infixr 4 _<$>_
-_<$>_ : {f : U → U} {{Functor f}} {a b} → (a → b) → f a → f b
+_<$>_ : {f} {{Functor f}} {a b} → (a → b) → f a → f b
 f <$> ma = map f ma
 
-
-mapMaybe : {a b} → (a → b) → Maybe a → Maybe b
-mapMaybe f Nothing = Nothing
-mapMaybe f (Just a) = Just (f a)
-
-FunctorMaybe : Functor Maybe
-FunctorMaybe = MkFunctor mapMaybe
-
-
-
--- Idris is lazy in second arg, we don't have that.
-data Alternative : (U → U) → U where
-  MkAlt : {m : U → U} →
-          ({a} → m a → m a → m a) →
-          Alternative m
+instance Functor Maybe where
+  map f Nothing = Nothing
+  map f (Just a) = Just (f a)
 
 infixr 2 _<|>_
-_<|>_ : {m : U → U} {{Alternative m}} → {a} → m a → m a → m a
-_<|>_ {m} {{MkAlt f}} {a} x y = f x y
+class Alternative (m : U → U) where
+  _<|>_ : {a} → m a → m a → m a
 
-altMaybe : {a} → Maybe a → Maybe a → Maybe a
-altMaybe Nothing x = x
-altMaybe (Just x) _ = Just x
-
-AltMaybe : Alternative Maybe
-AltMaybe = MkAlt altMaybe
+instance Alternative Maybe where
+  Nothing <|> x = x
+  Just x <|> _ = Just x
 
 -- Semigroup
 
 infixl 8 _<+>_
-data Semigroup : U → U where
-  MkSemi : {a} → (a → a → a) → Semigroup a
-
-_<+>_ : {a} {{Semigroup a}} → a → a → a
-_<+>_ {{MkSemi op}} x y = op x y
-
+class Semigroup a where
+  _<+>_ : a → a → a
 
 infixl 7 _+_
-data Add : U → U where
-  MkAdd : {A} → (A → A → A) → Add A
-
-_+_ : {A} {{Add A}} → A → A → A
-_+_ {{MkAdd add}} x y  = add x y
+class Add a where
+  _+_ : a → a → a
 
 infixl 8 _*_
-data Mul : U → U where
-  MkMul : {A} →
-          (A → A → A) →
-          Mul A
+class Mul a where
+  _*_ : a → a → a
 
-_*_ : {A} {{Mul A}} → A → A → A
-_*_ {{MkMul mul}} x y  = mul x y
-
-
--- TODO codata/copatterns might be nice here?
--- AddNat : AddNat
--- AddNat .add Z m = m
--- AddNat .add (S n) m = S (self .add n m)
-
-addNat : Nat → Nat → Nat
-addNat Z m = m
-addNat (S n) m = S (addNat n m)
-
-AddNat : Add Nat
-AddNat = MkAdd addNat
-
-mulNat : Nat → Nat → Nat
-mulNat Z _ = Z
-mulNat (S n) m = m + mulNat n m
-
-MulNat : Mul Nat
-MulNat = MkMul mulNat
+instance Add Nat where
+  Z + m = m
+  S n + m = S (n + m)
 
+instance Mul Nat where
+  Z * _ = Z
+  S n * m = m + n * m
 
 -- TODO Sub
 infixl 7 _-_
@@ -205,6 +146,9 @@ Z - m = Z
 n - Z = n
 S n - S m = n - m
 
+infixr 7 _++_
+class Concat a where
+  _++_ : a → a → a
 
 ptype String
 ptype Int
@@ -217,6 +161,12 @@ pfunc length : String → Nat := "(s) => {
   return rval
 }"
 
+
+
+pfunc sconcat : String → String → String := "(x,y) => x + y"
+instance Concat String where
+  _++_ = sconcat
+
 data Unit : U where
   MkUnit : Unit
 
@@ -239,8 +189,7 @@ pfunc aempty : {a : U} -> Unit -> Array a := "() => []"
 pfunc fastConcat : List String → String := "(xs) => listToArray(undefined, xs).join('')"
 pfunc replicate : Nat -> Char → String := "() => abort('FIXME replicate')"
 
-
-
+-- I don't want to use an empty type because it would be a proof of void
 ptype World
 
 data IORes : U -> U where
@@ -249,16 +198,15 @@ data IORes : U -> U where
 IO : U -> U
 IO a = World -> IORes a
 
--- TODO - if I move w to the left, I get "extra pattern variable"
--- because I'm not looking instide the IO b type, probably should force it.
-iobind : {a b : U} -> IO a -> (a -> IO b) -> IO b
-iobind ma mab = \ w => case ma w of
-  (MkIORes a w) => mab a w
-
-iopure : {a : U} -> a -> IO a
-iopure a = \ w => MkIORes a w
-
-IOMonad : Monad IO
-IOMonad = MkMonad iobind iopure
+instance Monad IO where
+  bind ma mab = \ w => case ma w of
+    MkIORes a w => mab a w
+  pure a = \ w => MkIORes a w
 
 pfunc putStrLn : String -> IO Unit := "(s) => (w) => console.log(s)"
+
+class Show a where
+  show : a → String
+
+instance Show String where
+  show a = a