src/HOLCF/Fix.thy
author wenzelm
Sat, 03 Nov 2001 01:41:26 +0100
changeset 12030 46d57d0290a2
parent 10834 a7897aebbffc
child 14981 e73f8140af78
permissions -rw-r--r--
GPLed;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
2640
ee4dfce170a0 Changes of HOLCF from Oscar Slotosch:
slotosch
parents: 2275
diff changeset
     1
(*  Title:      HOLCF/Fix.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: 1410
diff changeset
     3
    Author:     Franz Regensburger
12030
wenzelm
parents: 10834
diff changeset
     4
    License:    GPL (GNU GENERAL PUBLIC LICENSE)
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     5
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
     6
definitions for fixed point operator and admissibility
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
Fix = Cfun3 +
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    10
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    11
consts
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    12
1990
9e23119c0219 added comment on is_flat
oheimb
parents: 1825
diff changeset
    13
iterate	:: "nat=>('a->'a)=>'a=>'a"
9e23119c0219 added comment on is_flat
oheimb
parents: 1825
diff changeset
    14
Ifix	:: "('a->'a)=>'a"
9e23119c0219 added comment on is_flat
oheimb
parents: 1825
diff changeset
    15
fix	:: "('a->'a)->'a"
2841
c2508f4ab739 Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents: 2640
diff changeset
    16
adm		:: "('a::cpo=>bool)=>bool"
1990
9e23119c0219 added comment on is_flat
oheimb
parents: 1825
diff changeset
    17
admw		:: "('a=>bool)=>bool"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    18
5192
704dd3a6d47d Adapted to new datatype package.
berghofe
parents: 4721
diff changeset
    19
primrec
704dd3a6d47d Adapted to new datatype package.
berghofe
parents: 4721
diff changeset
    20
  iterate_0   "iterate 0 F x = x"
10834
a7897aebbffc *** empty log message ***
nipkow
parents: 5192
diff changeset
    21
  iterate_Suc "iterate (Suc n) F x  = F$(iterate n F x)"
5192
704dd3a6d47d Adapted to new datatype package.
berghofe
parents: 4721
diff changeset
    22
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 1150
diff changeset
    23
defs
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    24
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3326
diff changeset
    25
Ifix_def      "Ifix F == lub(range(%i. iterate i F UU))"
1168
74be52691d62 The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents: 1150
diff changeset
    26
fix_def       "fix == (LAM f. Ifix f)"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    27
4721
c8a8482a8124 renamed is_chain to chain, is_tord to tord, replaced chain_finite by chfin
oheimb
parents: 3842
diff changeset
    28
adm_def       "adm P == !Y. chain(Y) --> 
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3326
diff changeset
    29
                        (!i. P(Y i)) --> P(lub(range Y))"
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    30
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3326
diff changeset
    31
admw_def      "admw P == !F. (!n. P (iterate n F UU)) -->
1479
21eb5e156d91 expanded tabs
clasohm
parents: 1410
diff changeset
    32
                            P (lub(range (%i. iterate i F UU)))" 
243
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    33
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    34
end
c22b85994e17 Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff changeset
    35