src/HOLCF/Porder.thy
changeset 1479 21eb5e156d91
parent 1274 ea0668a1c0ba
child 2278 d63ffafce255
equal deleted inserted replaced
1478:2b8c2a7547ab 1479:21eb5e156d91
     1 (*  Title: 	HOLCF/porder.thy
     1 (*  Title:      HOLCF/porder.thy
     2     ID:         $Id$
     2     ID:         $Id$
     3     Author: 	Franz Regensburger
     3     Author:     Franz Regensburger
     4     Copyright   1993 Technische Universitaet Muenchen
     4     Copyright   1993 Technische Universitaet Muenchen
     5 
     5 
     6 Conservative extension of theory Porder0 by constant definitions 
     6 Conservative extension of theory Porder0 by constant definitions 
     7 
     7 
     8 *)
     8 *)
     9 
     9 
    10 Porder = Porder0 +
    10 Porder = Porder0 +
    11 
    11 
    12 consts	
    12 consts  
    13 	"<|"	::	"['a set,'a::po] => bool"	(infixl 55)
    13         "<|"    ::      "['a set,'a::po] => bool"       (infixl 55)
    14 	"<<|"	::	"['a set,'a::po] => bool"	(infixl 55)
    14         "<<|"   ::      "['a set,'a::po] => bool"       (infixl 55)
    15 	lub	::	"'a set => 'a::po"
    15         lub     ::      "'a set => 'a::po"
    16 	is_tord	::	"'a::po set => bool"
    16         is_tord ::      "'a::po set => bool"
    17 	is_chain ::	"(nat=>'a::po) => bool"
    17         is_chain ::     "(nat=>'a::po) => bool"
    18 	max_in_chain :: "[nat,nat=>'a::po]=>bool"
    18         max_in_chain :: "[nat,nat=>'a::po]=>bool"
    19 	finite_chain :: "(nat=>'a::po)=>bool"
    19         finite_chain :: "(nat=>'a::po)=>bool"
    20 
    20 
    21 defs
    21 defs
    22 
    22 
    23 (* class definitions *)
    23 (* class definitions *)
    24 
    24 
    25 is_ub		"S  <| x == ! y.y:S --> y<<x"
    25 is_ub           "S  <| x == ! y.y:S --> y<<x"
    26 is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
    26 is_lub          "S <<| x == S <| x & (! u. S <| u  --> x << u)"
    27 
    27 
    28 
    28 
    29 (* Arbitrary chains are total orders    *)                  
    29 (* Arbitrary chains are total orders    *)                  
    30 is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
    30 is_tord         "is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
    31 
    31 
    32 (* Here we use countable chains and I prefer to code them as functions! *)
    32 (* Here we use countable chains and I prefer to code them as functions! *)
    33 is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
    33 is_chain        "is_chain(F) == (! i.F(i) << F(Suc(i)))"
    34 
    34 
    35 (* finite chains, needed for monotony of continouous functions *)
    35 (* finite chains, needed for monotony of continouous functions *)
    36 
    36 
    37 max_in_chain_def "max_in_chain i C == ! j. i <= j --> C(i) = C(j)" 
    37 max_in_chain_def "max_in_chain i C == ! j. i <= j --> C(i) = C(j)" 
    38 
    38 
    39 finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain i C)"
    39 finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain i C)"
    40 
    40 
    41 rules
    41 rules
    42 
    42 
    43 lub		"lub(S) = (@x. S <<| x)"
    43 lub             "lub(S) = (@x. S <<| x)"
    44 
    44 
    45 (* start 8bit 1 *)
    45 (* start 8bit 1 *)
    46 (* end 8bit 1 *)
    46 (* end 8bit 1 *)
    47 
    47 
    48 end 
    48 end