(define sent
   [Input Proof] <- (vp (np [Input [[sent --> np vp] | Proof]]))
   _ -> (fail))

(define np
   [Input Proof] <- (n (det [Input [[np --> det n] | Proof]]))
   [Input Proof] <- (name [Input [[np --> name] | Proof]])
   _ -> (fail))

(define name
  [["John" | Input] Proof] -> [Input [[name --> "John"] | Proof]]
  [["Bill" | Input] Proof] -> [Input [[name --> "Bill"] | Proof]]
   _ -> (fail))

 (define det
  [["the" | Input] Proof] -> [Input [[det --> "the"] | Proof]]
  [["a" | Input] Proof] -> [Input [[det --> "a"] | Proof]]
  [["that" | Input] Proof] -> [Input [[det --> "that"] | Proof]]
  [["this" | Input] Proof] -> [Input [[det --> "this"] | Proof]]
  _ -> (fail))
 
(define n
  [["ball" | Input] Proof] -> [Input [[n --> "ball"] | Proof]]
  [["girl" | Input] Proof] -> [Input [[n --> "girl"] | Proof]]
   _ -> (fail))

(define vp
   [Input Proof] <- (np (vtrans [Input [[vp --> vtrans np] | Proof]]))
   [Input Proof] <- (vp [Input [[vp --> vintrans] | Proof]])
   _ -> (fail))

(define vtrans
  [["kicks" | Input] Proof] -> [Input [[vtrans --> "kicks"] | Proof]]
  [["likes" | Input] Proof] -> [Input [[vtrans --> "likes"] | Proof]]
   _ -> (fail))

(define vintrans
  [["jumps" | Input] Proof] 
   -> [Input [[vintrans --> "jumps"] | Proof]]
  _ -> (fail))  
 
(define parse
   Sentence -> (let Parse (sent [Sentence []]) 
                          (if (parsed? Parse) 
                              (output_parse Parse) 
                              ungrammatical))) 

(define parsed?
   [[] _] -> true
    _ -> false)

(define output_parse
   [_ Parse_Rules] -> (reverse Parse_Rules))
   
(parse ["the" "girl" "likes" "the" "ball"])

(parse ["the" "cat" "likes" "the" "girl"])