author  nipkow 
Fri, 24 Nov 2000 16:49:27 +0100  
changeset 10519  ade64af4c57c 
parent 8844  db71c334e854 
child 14348  744c868ee0b7 
permissions  rwrr 
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(* Title: HOL/Power.thy 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1997 University of Cambridge 
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The (overloaded) exponentiation operator, ^ :: [nat,nat]=>nat 
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Also binomial coefficents 
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*) 
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Power = Divides + 
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consts 
7843  12 
binomial :: "[nat,nat] => nat" (infixl "choose" 65) 
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primrec (power) 
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"p ^ 0 = 1" 
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"p ^ (Suc n) = (p::nat) * (p ^ n)" 
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5183  18 
primrec 
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binomial_0 "(0 choose k) = (if k = 0 then 1 else 0)" 
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binomial_Suc "(Suc n choose k) = 
4628  22 
(if k = 0 then 1 else (n choose (k  1)) + (n choose k))" 
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end 
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