Improve functions intro.

Add `λ', sugared/unsugared examples, optionals, keywords.

racket.html.markdown

@@ -204,44 +204,71 @@ m ; => '#hash((b . 2) (a . 1) (c . 3))  <-- no `d'
 ;; 3. Functions
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
-;; Use lambda to create new functions.
-;; A function always returns its last statement.
+;; Use `lambda' to create functions.
+;; A function always returns the value of its last expression
 (lambda () "Hello World") ; => #<procedure>
+;; Can also use a unicode `λ'
+(λ () "Hellow World")     ; => same function
 
-;; (You need extra parens to call it)
+;; Use parens to call all functions, including a lambda expression
 ((lambda () "Hello World")) ; => "Hello World"
+((λ () "Hello World"))      ; => "Hello World"
 
 ;; Assign a function to a var
 (define hello-world (lambda () "Hello World"))
 (hello-world) ; => "Hello World"
 
-;; You can shorten this to:
+;; You can shorten this using the function definition syntatcic sugae:
 (define (hello-world2) "Hello World")
 
-;; The () is the list of arguments for the function.
+;; The () in the above is the list of arguments for the function
 (define hello
   (lambda (name)
     (string-append "Hello " name)))
 (hello "Steve") ; => "Hello Steve"
+;; ... or equivalently, using a sugared definition:
+(define (hello2 name)
+  (string-append "Hello " name))
 
-;; You can have multi-variadic functions, too
-(define hello2
+;; You can have multi-variadic functions too, using `case-lambda'
+(define hello3
   (case-lambda
     [() "Hello World"]
     [(name) (string-append "Hello " name)]))
-(hello2 "Jake") ; => "Hello Jake"
-(hello2) ; => "Hello World"
+(hello3 "Jake") ; => "Hello Jake"
+(hello3) ; => "Hello World"
+;; ... or specify optional arguments with a default value expression
+(define (hello4 [name "World"])
+  (string-append "Hello " name))
 
 ;; Functions can pack extra arguments up in a list
 (define (count-args . args)
   (format "You passed ~a args: ~a" (length args) args))
 (count-args 1 2 3) ; => "You passed 3 args: (1 2 3)"
+;; ... or with the unsugared `lambda' form:
+(define count-args2
+  (lambda args
+    (format "You passed ~a args: ~a" (length args) args)))
 
 ;; You can mix regular and packed arguments
 (define (hello-count name . args)
   (format "Hello ~a, you passed ~a extra args" name (length args)))
 (hello-count "Finn" 1 2 3)
 ; => "Hello Finn, you passed 3 extra args"
+;; ... unsugared:
+(define hello-count2
+  (lambda (name . args)
+    (format "Hello ~a, you passed ~a extra args" name (length args))))
+
+;; And with keywords
+(define (hello-k #:name [name "World"] #:greeting [g "Hello"] . args)
+  (format "~a ~a, ~a extra args" g name (length args)))
+(hello-k)                 ; => "Hello World, 0 extra args"
+(hello-k 1 2 3)           ; => "Hello World, 3 extra args"
+(hello-k #:greeting "Hi") ; => "Hi World, 0 extra args"
+(hello-k #:name "Finn" #:greeting "Hey") ; => "Hey Finn, 0 extra args"
+(hello-k 1 2 3 #:greeting "Hi" #:name "Finn" 4 5 6)
+                                         ; => "Hi Finn, 6 extra args"
 
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 ;; 4. Equality