src/HOL/UNITY/Comp.thy
author paulson
Mon Oct 05 10:27:04 1998 +0200 (1998-10-05)
changeset 5612 e981ca6f7332
parent 5597 a12b25c53df1
child 6012 1894bfc4aee9
permissions -rw-r--r--
Finished proofs to end of section 5.1 of Chandy and Sanders
     1 (*  Title:      HOL/UNITY/Comp.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1998  University of Cambridge
     5 
     6 Composition
     7 
     8 From Chandy and Sanders, "Reasoning About Program Composition"
     9 *)
    10 
    11 Comp = Union +
    12 
    13 constdefs
    14 
    15   (*Existential and Universal properties.  I formalize the two-program
    16     case, proving equivalence with Chandy and Sanders's n-ary definitions*)
    17 
    18   ex_prop  :: 'a program set => bool
    19    "ex_prop X == ALL F G. F:X | G: X --> (F Join G) : X"
    20 
    21   strict_ex_prop  :: 'a program set => bool
    22    "strict_ex_prop X == ALL F G. (F:X | G: X) = (F Join G : X)"
    23 
    24   uv_prop  :: 'a program set => bool
    25    "uv_prop X == SKIP: X & (ALL F G. F:X & G: X --> (F Join G) : X)"
    26 
    27   strict_uv_prop  :: 'a program set => bool
    28    "strict_uv_prop X == SKIP: X & (ALL F G. (F:X & G: X) = (F Join G : X))"
    29 
    30   (*Ill-defined programs can arise through "Join"*)
    31   welldef :: 'a program set  
    32    "welldef == {F. Init F ~= {}}"
    33 
    34   component :: ['a program, 'a program] => bool
    35    "component F H == EX G. F Join G = H"
    36 
    37   guarantees :: ['a program set, 'a program set] => 'a program set (infixl 65)
    38    "X guarantees Y == {F. ALL H. component F H --> H:X --> H:Y}"
    39 
    40   refines :: ['a program, 'a program, 'a program set] => bool
    41 			("(3_ refines _ wrt _)" [10,10,10] 10)
    42    "G refines F wrt X ==
    43       ALL H. (F Join H) : welldef Int X --> G Join H : welldef Int X"
    44 
    45   iso_refines :: ['a program, 'a program, 'a program set] => bool
    46 			("(3_ iso'_refines _ wrt _)" [10,10,10] 10)
    47    "G iso_refines F wrt X ==
    48       F : welldef Int X --> G : welldef Int X"
    49 
    50 end