| author | paulson |
| Wed, 13 Dec 2000 12:46:47 +0100 | |
| changeset 10662 | cf6be1804912 |
| parent 10045 | c76b73e16711 |
| permissions | -rw-r--r-- |
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c76b73e16711
New theories: construction of hypernaturals, nonstandard extensions,
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(* Title : Series.thy |
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c76b73e16711
New theories: construction of hypernaturals, nonstandard extensions,
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Author : Jacques D. Fleuriot |
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New theories: construction of hypernaturals, nonstandard extensions,
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Copyright : 1998 University of Cambridge |
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New theories: construction of hypernaturals, nonstandard extensions,
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Description : Finite summation and infinite series |
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*) |
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Series = SEQ + Lim + |
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consts sumr :: "[nat,nat,(nat=>real)] => real" |
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primrec |
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sumr_0 "sumr m 0 f = #0" |
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sumr_Suc "sumr m (Suc n) f = (if n < m then #0 |
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else sumr m n f + f(n))" |
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constdefs |
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sums :: [nat=>real,real] => bool (infixr 80) |
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"f sums s == (%n. sumr 0 n f) ----> s" |
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summable :: (nat=>real) => bool |
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"summable f == (EX s. f sums s)" |
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suminf :: (nat=>real) => real |
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"suminf f == (@s. f sums s)" |
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end |
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