sicp-ex-1.10


Using the substitution model, we can determine the values of the given expressions.

  
 (A 1 10) 
  
 (A 0 (A 1 9)) 
  
 (A 0 (A 0 (A 1 8))) 
  
 (A 0 (A 0 (A 0 (A 1 7)))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 1 6))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 5)))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 4))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 3)))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 2))))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 1)))))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 2))))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 4)))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 8))))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 16)))))) 
  
 (A 0 (A 0 (A 0 (A 0 (A 0 32))))) 
  
 (A 0 (A 0 (A 0 (A 0 64)))) 
  
 (A 0 (A 0 (A 0 128))) 
  
 (A 0 (A 0 256)) 
  
 (A 0 512) 
  
 1024 
  
 (A 2 4) 
 (A 1 (A 2 3)) 
 (A 1 (A 1 (A 2 2))) 
 (A 1 (A 1 (A 1 (A 2 1)))) 
 (A 1 (A 1 (A 1 2))) 
 (A 1 (A 1 (A 0 (A 1 1)))) 
 (A 1 (A 1 (A 0 2))) 
 (A 1 (A 1 4)) 
 (A 1 (A 0 (A 1 3))) 
 (A 1 (A 0 (A 0 (A 1 2)))) 
 (A 1 (A 0 (A 0 (A 0 (A 1 1))))) 
 (A 1 (A 0 (A 0 (A 0 2)))) 
 (A 1 (A 0 (A 0 4))) 
 (A 1 (A 0 8)) 
 (A 1 16) 
 (A 0 (A 1 15)) 
 (A 0 (A 0 (A 1 14))) 
 (A 0 (A 0 (A 0 (A 1 13)))) 
 (A 0 (A 0 (A 0 (A 0 (A 1 12))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 11)))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 10))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 9)))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 8))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 7)))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 6))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 5)))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 4))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 3)))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 2))))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 1)))))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 2))))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 4)))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 8))))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 16)))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 32))))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 64)))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 128))))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 256)))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 512))))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 1024)))))) 
 (A 0 (A 0 (A 0 (A 0 (A 0 2048))))) 
 (A 0 (A 0 (A 0 (A 0 4096)))) 
 (A 0 (A 0 (A 0 8192))) 
 (A 0 (A 0 16384)) 
 (A 0 32768) 
 65536 
  
 (A 3 3) 
  
 (A 2 (A 3 2)) 
  
 (A 2 (A 2 (A 3 1))) 
  
 (A 2 (A 2 2)) 
  
 ... 
  
 (A 2 4) 
  
 ... 
  
 65536 
  

The procedures f, g, h will respectively compute (mathematical formulae given in LaTeX notation):

(f n): 2n
(g n): 2^{n}
(h n): 2^2^… (n times)


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