Bx Examples Repository
Title: undoableNotSimplyMatching
Version: 0.1
Type: Precise
Overview
This example was contrived to demonstrate that being undoable does not
imply being simply matching (the two properties are incomparable: both
are implied by history ignorance)
Models
$M = N = \{(x,\phi) | x \in {a,b,c}, \phi \in \{false, true\}\}$
Consistency
$R((x,\phi),(y,\psi))$ iff $x = y$
Consistency Restoration
Forward
$\overrightarrow{R}((x,\phi),(y,\psi)) = (x,\psi)$
Backward
$\overleftarrow{R}((x,\phi),(y,true)) = (y,\phi)$
$\overleftarrow{R}((x,\phi),(y,false)) = (y,\not\phi)$, if as sets, $\{x,y\} = \{a,c\}$
$\overleftarrow{R}((x,\phi),(y,false)) = (y,\phi)$, otherwise.
Properties
Correct, hippocratic, undoable. Not simply matching, hence not history ignorant.
Discussion
This is Example 7 from the paper cited below.
History ignorant bx are simply matching, by Prop. 4, Coro. 1 of that paper.
References [optional section]
Perdita Stevens, Observations relating to the equivalences induced on model sets by bidirectional transformations, EC-EASST Vol.49, Proceedings of BX 2012. TU Berlin. ISSN 1863-2122 .bib
External link: http://journal.ub.tu-berlin.de/eceasst/article/view/714/720
Author(s)
Perdita Stevens, James McKinna
