src/HOLCF/porder.thy
 author wenzelm Thu Aug 27 20:46:36 1998 +0200 (1998-08-27) changeset 5400 645f46a24c72 parent 297 5ef75ff3baeb permissions -rw-r--r--
```     1 (*  Title: 	HOLCF/porder.thy
```
```     2     ID:         \$Id\$
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```     3     Author: 	Franz Regensburger
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```     4     Copyright   1993 Technische Universitaet Muenchen
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```     5
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```     6 Conservative extension of theory Porder0 by constant definitions
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```     7
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```     8 *)
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```     9
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```    10 Porder = Porder0 +
```
```    11
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```    12 consts
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```    13 	"<|"	::	"['a set,'a::po] => bool"	(infixl 55)
```
```    14 	"<<|"	::	"['a set,'a::po] => bool"	(infixl 55)
```
```    15 	lub	::	"'a set => 'a::po"
```
```    16 	is_tord	::	"'a::po set => bool"
```
```    17 	is_chain ::	"(nat=>'a::po) => bool"
```
```    18 	max_in_chain :: "[nat,nat=>'a::po]=>bool"
```
```    19 	finite_chain :: "(nat=>'a::po)=>bool"
```
```    20
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```    21 rules
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```    22
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```    23 (* class definitions *)
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```    24
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```    25 is_ub		"S  <| x == ! y.y:S --> y<<x"
```
```    26 is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
```
```    27
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```    28 lub		"lub(S) = (@x. S <<| x)"
```
```    29
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```    30 (* Arbitrary chains are total orders    *)
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```    31 is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
```
```    32
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```    33 (* Here we use countable chains and I prefer to code them as functions! *)
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```    34 is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
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```    35
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```    36 (* finite chains, needed for monotony of continouous functions *)
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```    37
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```    38 max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)"
```
```    39
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```    40 finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
```
```    41
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```    42 end
```