src/HOLCF/Porder.thy
author wenzelm
Fri, 10 Oct 1997 19:02:28 +0200
changeset 3842 b55686a7b22c
parent 2640 ee4dfce170a0
child 4721 c8a8482a8124
permissions -rw-r--r--
fixed dots;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
1479
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
     1
(*  Title:      HOLCF/porder.thy
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     2
    ID:         $Id$
1479
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
     3
    Author:     Franz Regensburger
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     4
    Copyright   1993 Technische Universitaet Muenchen
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     5
297
5ef75ff3baeb Franz fragen
nipkow
parents: 243
diff changeset
     6
Conservative extension of theory Porder0 by constant definitions 
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     7
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     8
*)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     9
297
5ef75ff3baeb Franz fragen
nipkow
parents: 243
diff changeset
    10
Porder = Porder0 +
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    11
1479
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    12
consts  
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    13
        "<|"    ::      "['a set,'a::po] => bool"       (infixl 55)
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    14
        "<<|"   ::      "['a set,'a::po] => bool"       (infixl 55)
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    15
        lub     ::      "'a set => 'a::po"
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    16
        is_tord ::      "'a::po set => bool"
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    17
        is_chain ::     "(nat=>'a::po) => bool"
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    18
        max_in_chain :: "[nat,nat=>'a::po]=>bool"
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    19
        finite_chain :: "(nat=>'a::po)=>bool"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    20
2394
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    21
syntax
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    22
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    23
  "@LUB"	:: "(('b::term) => 'a) => 'a"	(binder "LUB " 10)
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    24
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    25
translations
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    26
3842
b55686a7b22c fixed dots;
wenzelm
parents: 2640
diff changeset
    27
  "LUB x. t"	== "lub(range(%x. t))"
2394
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    28
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    29
syntax (symbols)
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    30
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    31
  "LUB "	:: "[idts, 'a] => 'a"		("(3\\<Squnion>_./ _)"[0,10] 10)
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    32
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    33
defs
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    34
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    35
(* class definitions *)
3842
b55686a7b22c fixed dots;
wenzelm
parents: 2640
diff changeset
    36
is_ub           "S  <| x == ! y. y:S --> y<<x"
1479
21eb5e156d91 expanded tabs
clasohm
parents: 1274
diff changeset
    37
is_lub          "S <<| x == S <| x & (! u. S <| u  --> x << u)"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    38
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    39
(* Arbitrary chains are total orders    *)                  
2394
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    40
is_tord         "is_tord S == ! x y. x:S & y:S --> (x<<y | y<<x)"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    41
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    42
(* Here we use countable chains and I prefer to code them as functions! *)
3842
b55686a7b22c fixed dots;
wenzelm
parents: 2640
diff changeset
    43
is_chain        "is_chain F == (! i. F(i) << F(Suc(i)))"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    44
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    45
(* finite chains, needed for monotony of continouous functions *)
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    46
max_in_chain_def "max_in_chain i C == ! j. i <= j --> C(i) = C(j)" 
2394
91d8abf108be adaptions for symbol font
oheimb
parents: 2291
diff changeset
    47
finite_chain_def "finite_chain C == is_chain(C) & (? i. max_in_chain i C)"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    48
2640
ee4dfce170a0 Changes of HOLCF from Oscar Slotosch:
slotosch
parents: 2394
diff changeset
    49
lub_def          "lub S == (@x. S <<| x)"
1274
ea0668a1c0ba added 8bit pragmas
regensbu
parents: 1168
diff changeset
    50
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    51
end 
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    52
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    53