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--
made tutorial first;
     1 (*  Title: 	HOLCF/porder.thy
     2     ID:         $Id$
     3     Author: 	Franz Regensburger
     4     Copyright   1993 Technische Universitaet Muenchen
     5 
     6 Conservative extension of theory Porder0 by constant definitions 
     7 
     8 *)
     9 
    10 Porder = Porder0 +
    11 
    12 consts	
    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 
    21 rules
    22 
    23 (* class definitions *)
    24 
    25 is_ub		"S  <| x == ! y.y:S --> y<<x"
    26 is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
    27 
    28 lub		"lub(S) = (@x. S <<| x)"
    29 
    30 (* Arbitrary chains are total orders    *)                  
    31 is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
    32 
    33 (* Here we use countable chains and I prefer to code them as functions! *)
    34 is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
    35 
    36 (* finite chains, needed for monotony of continouous functions *)
    37 
    38 max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)" 
    39 
    40 finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
    41 
    42 end