Implement Applicative Parser

app/Parser.hs

@@ -1,6 +1,7 @@
 module Parser where
 
-import qualified Lexer
+import qualified Lexer as L
+import Control.Applicative as Applicative
 
 type AST = Expr
 
@@ -18,3 +19,21 @@ data Factor = Integer Int
             | Parantheses Expr
             | NegFactor Factor
             deriving Show
+
+type Tokens = [L.Token]
+newtype Parser a = Parser {
+    runParser :: Tokens -> Maybe (Tokens, a)
+}
+
+instance Functor Parser where
+    fmap f (Parser p) = Parser $ \input -> case p input of
+        Nothing -> Nothing
+        Just (rest, a) -> Just (rest, f a)
+
+instance Applicative Parser where
+    pure x = Parser $ \input -> Just (input, x)
+    (<*>) (Parser fParser) (Parser a) = Parser $ \input -> case fParser input of
+        Nothing -> Nothing
+        Just (rest, f) -> case a rest of
+            Nothing -> Nothing
+            Just (rest', x) -> Just (rest', f x)