v0.0.9: change how functions work

spec.md

@@ -10,6 +10,8 @@ Most important ones:
 - `List[T]`: (linked-) list of `T`
 - `Char`: unicode codepoint
 - `Unit`: nothing
+- `i -> o`: function
+- `template a, b: t`
 
 Advanced (uncommon) types:
 - `Int8`, `Int16`, ...
@@ -18,23 +20,43 @@ Advanced (uncommon) types:
 
 ## Functions
 ```
+# the type of msg is: List[Char] -> List[Char]
 def msg(username: List[Char]) : List[Char] {
   "Hello, " ++ username ++ "!"   # last expr is returned
 }
 
+# the type of main is: Unit -> Unit
 def main() {
   print("hi")
 }
 main()
 ```
 
+## Anonymus functions
+```
+The type of List.map is List[t] -> (t -> t) -> List[t]
+List.map(li, x:Num -> x * 2)
+```
+
 ## Simple, forward type-inference
 ```
 def zero ()  : Flt32 {
-  3.1       # error: got Num, but expected F32
+  3.1       # error: got Num, but expected Flt32
 }
 ```
 
+## Partial function applications
+```
+# type of add is   Num -> Num -> Num
+def add(a: Num, b: Num) : Num {
+  a + b
+}
+
+let a = add(1)   # type of a is   Num -> Num
+let b = a(2)     # type of b is   Num
+# b is 3
+```
+
 ## Bindings
 ```
 let name = "Max"
@@ -134,12 +156,15 @@ def add(a: Num, b: Num) -> _ {
 
 ## templated generics
 ```
+# Type of add is:   template a, b: a -> b -> _
 def [a,b] add(a: a, b: b) -> _ {
   a + b
 }
 
 add(1,2)
 
+add(1)(2)  # error: partial function application of templated functions not allowed
+
 add(1,"2")    # error: in template expansion of add[Num,List[Char]]: No definition for `Num + List[Char]`
 ```