Adjust old type checker to new syntax, and refactor lambda lifter to use typed AST

sample-programs/basic-1

@@ -1,2 +1,3 @@
 
-f = \x. x+1;
+f : Int -> Int;
+f = \x:Int. x+1;

sample-programs/basic-10

@@ -0,0 +1,3 @@
+
+main : Int -> Int -> Int;
+main x y = (x : Int) + y;

sample-programs/basic-2

@@ -1,4 +1,7 @@
-add x = \y. x+y;
 
-main = (\z. z+z) ((add 4) 6);
+add : Int -> Int -> Int;
+add x = \y:Int. x+y;
+
+main : Int;
+main = (\z:Int. z+z) ((add 4) 6);
 

sample-programs/basic-3

@@ -1,2 +1,3 @@
 
-main = (\x. x+x+3) ((\x. x) 2)
+main : Int;
+main = (\x:Int. x+x+3) ((\x:Int. x) 2);

sample-programs/basic-4

@@ -1,2 +1,7 @@
 
-f x = let g = (\y. y+1) in g (g x)
+f : Int -> Int;
+f x = let 
+        g : Int -> Int;
+        g = (\y:Int. y+1);
+      in 
+        g (g x);

sample-programs/basic-5

@@ -1,9 +1,14 @@
+id : Int -> Int;
 id x = x;
 
+add : Int -> Int -> Int;
 add x y = x + y;
 
+double : Int -> Int;
 double n = n + n;
 
-apply f x = \y. f x y;
+apply : (Int -> Int -> Int) -> Int -> Int -> Int;
+apply f x = \y:Int. f x y;
 
-main = apply (id add) ((\x. x + 1) 1) (double 3);
+main : Int;
+main = apply add ((\x:Int. x + 1) 1) (double (id 3));

sample-programs/basic-6

@@ -1,3 +1,4 @@
 
 
-f = \x.\y. x+y
+f : Int -> Int -> Int;
+f = \x:Int.\y:Int. x+y;

sample-programs/basic-7

@@ -1,5 +1,8 @@
+add : Int -> Int -> Int;
 add x y = x + y;
 
+apply : (Int -> Int) -> Int -> Int;
 apply f x = f x;
 
+main : Int;
 main = apply (add 4) 6;

sample-programs/basic-8

@@ -1,2 +1,7 @@
 
-f x = let double = \y. y+y in (\x. x+y) 4;
+f : Int -> Int;
+f x = let 
+        double : Int -> Int;
+        double = \y:Int. y+y 
+      in 
+        double (x + 4);

sample-programs/basic-9

@@ -1,4 +1,5 @@
 
 
 
-main = (\f.\x.\y. f x + f y) (\x. x+x) ((\x. x+1) ((\x. x+3) 2)) 4
+main : Int;
+main = (\f:Int -> Int.\x:Int.\y:Int. f x + f y) (\x:Int. x+x) ((\x:Int. x+1) ((\x:Int. x+3) 2)) 4