Probabilistic Context-Free Grammar

(define (terminal t) (lambda () t))

(define (sample thunk) (thunk))

(define D (lambda ()
            (map sample
                 (multinomial
                  (list (list (terminal 'the) ) 
                        (list (terminal 'a)))
                  (list (/ 1 2) (/ 1 2))))))
(define N (lambda ()
            (map sample 
                 (multinomial
                  (list (list (terminal 'chef)) 
                        (list (terminal 'soup)) 
                        (list (terminal 'omelet)))
                  (list (/ 1 3) (/ 1 3) (/ 1 3))))))
(define V (lambda ()
            (map sample
                 (multinomial
                  (list (list (terminal 'cooks)) 
                        (list (terminal 'works)))
                  (list (/ 1 2) (/ 1 2))))))                
(define A (lambda ()
            (map sample
                 (multinomial
                  (list (list (terminal 'diligently)))
                  (list (/ 1 1))))))
(define AP (lambda ()
             (map sample
                  (multinomial
                   (list (list A))
                   (list (/ 1 1))))))
(define NP (lambda ()
             (map sample
                  (multinomial
                   (list (list D N))
                   (list (/ 1 1))))))
(define VP (lambda ()
             (map sample
                  (multinomial
                   (list (list V AP) 
                         (list V NP))
                   (list (/ 1 2) (/ 1 2))))))
(define S (lambda ()
            (map sample 
                 (multinomial
                  (list (list NP VP))
                  (list (/ 1 1))))))
(S)

(define (terminal t) (list 'terminal t))

(define (unwrap-terminal t) (second t))

(define (tree-unfold transition start-symbol)
  (if (terminal? start-symbol)
      (unwrap-terminal start-symbol)   
      (pair start-symbol 
            (map (lambda (symbol) 
                   (tree-unfold  transition symbol)) 
                 (transition start-symbol)))))

(define (terminal? symbol)
  (if (list? symbol)
      (equal? (first symbol) 'terminal)
      false))

(define (transition nonterminal)
  (case nonterminal
        (('D) (multinomial(list (list (terminal 'the)) 
                                (list (terminal 'a)))
                          (list (/ 1 2) (/ 1 2))))
        (('N) (multinomial (list (list (terminal 'chef))
                                 (list (terminal 'soup)) 
                                 (list (terminal 'omelet)))
                           (list (/ 1 3) (/ 1 3) (/ 1 3))))
        (('V) (multinomial (list (list (terminal 'cooks)) 
                                 (list (terminal 'works)))
                           (list (/ 1 2) (/ 1 2))))                
        (('A) (multinomial (list (list (terminal 'diligently)))
                           (list (/ 1 1))))
        (('AP) (multinomial (list (list 'A))
                            (list (/ 1 1))))
        (('NP) (multinomial (list (list 'D 'N))
                            (list (/ 1 1))))
        (('VP) (multinomial (list (list 'V 'AP) 
                                  (list 'V 'NP))
                            (list (/ 1 2) (/ 1 2))))
        (('S) (multinomial (list (list 'NP 'VP))
                           (list (/ 1 1))))
        (else 'error)))


(tree-unfold transition 'S)