src/HOLCF/Porder.thy
author regensbu
Thu, 29 Jun 1995 16:28:40 +0200
changeset 1168 74be52691d62
parent 297 5ef75ff3baeb
child 1274 ea0668a1c0ba
permissions -rw-r--r--
The curried version of HOLCF is now just called HOLCF. The old uncurried version is no longer supported
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     1
(*  Title: 	HOLCF/porder.thy
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     2
    ID:         $Id$
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     3
    Author: 	Franz Regensburger
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
297
5ef75ff3baeb Franz fragen
nipkow
parents: 243
diff changeset
    12
consts	
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    13
	"<|"	::	"['a set,'a::po] => bool"	(infixl 55)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    14
	"<<|"	::	"['a set,'a::po] => bool"	(infixl 55)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    15
	lub	::	"'a set => 'a::po"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    16
	is_tord	::	"'a::po set => bool"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    17
	is_chain ::	"(nat=>'a::po) => bool"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    18
	max_in_chain :: "[nat,nat=>'a::po]=>bool"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    19
	finite_chain :: "(nat=>'a::po)=>bool"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    20
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    21
defs
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    22
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    23
(* class definitions *)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    24
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    25
is_ub		"S  <| x == ! y.y:S --> y<<x"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    26
is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    27
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    28
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    29
(* Arbitrary chains are total orders    *)                  
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    30
is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    31
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    32
(* Here we use countable chains and I prefer to code them as functions! *)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    33
is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
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
(* finite chains, needed for monotony of continouous functions *)
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    36
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    37
max_in_chain_def "max_in_chain i C == ! j. i <= j --> C(i) = C(j)" 
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    38
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    39
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
    40
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    41
rules
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    42
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    43
lub		"lub(S) = (@x. S <<| x)"
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
end 
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    46
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 297
diff changeset
    47