Difference between revisions of "Arithmetic Rewrite Rules"
From Event-B
Jump to navigationJump to searchimported>Laurent (Marked SIMP_CARD_CPROD as broken because ill-defined (e.g., if S is empty, T can be infinite)) |
imported>Laurent (Marked SIMP_CARD_SETMINUS as broken (both sets could be infinite, in which case WD is not preserved).) |
||
Line 19: | Line 19: | ||
{{RRRow}}|*||{{Rulename|SIMP_CARD_POW}}||<math> \card (\pow (S)) \;\;\defi\;\; 2 ^ \card (S) </math>|| || A | {{RRRow}}|*||{{Rulename|SIMP_CARD_POW}}||<math> \card (\pow (S)) \;\;\defi\;\; 2 ^ \card (S) </math>|| || A | ||
{{RRRow}}|*||{{Rulename|SIMP_CARD_BUNION}}||<math> \card (S \bunion T) \;\;\defi\;\; \card (S) + \card (T) - \card (S \binter T) </math>|| || A | {{RRRow}}|*||{{Rulename|SIMP_CARD_BUNION}}||<math> \card (S \bunion T) \;\;\defi\;\; \card (S) + \card (T) - \card (S \binter T) </math>|| || A | ||
− | {{RRRow}}| | + | {{RRRow}}|b||{{Rulename|SIMP_CARD_SETMINUS}}||<math> \card (S \setminus T) \;\;\defi\;\; \card (S) - \card (S \binter T) </math>|| || A |
{{RRRow}}|b||{{Rulename|SIMP_CARD_CPROD}}||<math> \card (S \cprod T) \;\;\defi\;\; \card (S) * \card (T) </math>|| || A | {{RRRow}}|b||{{Rulename|SIMP_CARD_CPROD}}||<math> \card (S \cprod T) \;\;\defi\;\; \card (S) * \card (T) </math>|| || A | ||
{{RRRow}}|||{{Rulename|SIMP_CARD_CONVERSE}}||<math> \card (r^{-1} ) \;\;\defi\;\; \card (r) </math>|| || A | {{RRRow}}|||{{Rulename|SIMP_CARD_CONVERSE}}||<math> \card (r^{-1} ) \;\;\defi\;\; \card (r) </math>|| || A |
Revision as of 09:30, 8 January 2010
Name | Rule | Side Condition | A/M | |
---|---|---|---|---|
SIMP_SPECIAL_MOD_0 |
![]() |
A | ||
SIMP_SPECIAL_MOD_1 |
![]() |
A | ||
SIMP_MIN_SING |
![]() |
where ![]() |
A | |
SIMP_MAX_SING |
![]() |
where ![]() |
A | |
SIMP_MIN_NATURAL |
![]() |
A | ||
SIMP_MIN_NATURAL1 |
![]() |
A | ||
SIMP_MIN_BUNION_SING |
![]() |
A | ||
SIMP_MAX_BUNION_SING |
![]() |
A | ||
SIMP_MIN_UPTO |
![]() |
A | ||
SIMP_MAX_UPTO |
![]() |
A | ||
SIMP_LIT_MIN |
![]() |
where ![]() ![]() ![]() |
A | |
SIMP_LIT_MAX |
![]() |
where ![]() ![]() ![]() |
A | |
SIMP_LIT_MIN_UPTO |
![]() |
where ![]() |
A | |
SIMP_LIT_MAX_UPTO |
![]() |
where ![]() |
A | |
* | SIMP_SPECIAL_CARD |
![]() |
A | |
* | SIMP_CARD_SING |
![]() |
where ![]() |
A |
* | SIMP_SPECIAL_EQUAL_CARD |
![]() |
A | |
* | SIMP_CARD_POW |
![]() |
A | |
* | SIMP_CARD_BUNION |
![]() |
A | |
b | SIMP_CARD_SETMINUS |
![]() |
A | |
b | SIMP_CARD_CPROD |
![]() |
A | |
SIMP_CARD_CONVERSE |
![]() |
A | ||
SIMP_CARD_ID |
![]() |
A | ||
SIMP_CARD_LAMBDA |
![]() |
A | ||
SIMP_CARD_COMPSET |
![]() |
where ![]() ![]() |
A | |
* | SIMP_LIT_CARD_UPTO |
![]() |
where ![]() ![]() ![]() |
A |
SIMP_TYPE_CARD |
![]() |
where ![]() ![]() |
A | |
SIMP_LIT_GE_CARD_0 |
![]() |
A | ||
SIMP_LIT_LE_CARD_1 |
![]() |
A | ||
SIMP_LIT_LE_CARD_0 |
![]() |
A | ||
SIMP_LIT_GE_CARD_0 |
![]() |
A | ||
* | SIMP_LIT_GT_CARD_0 |
![]() |
A | |
* | SIMP_LIT_LT_CARD_0 |
![]() |
A | |
* | SIMP_LIT_EQUAL_CARD_1 |
![]() |
A | |
SIMP_CARD_NATURAL |
![]() |
A | ||
SIMP_CARD_NATURAL1 |
![]() |
A | ||
SIMP_LIT_IN_NATURAL |
![]() |
where ![]() |
A | |
SIMP_SPECIAL_IN_NATURAL1 |
![]() |
A | ||
SIMP_LIT_IN_NATURAL1 |
![]() |
where ![]() ![]() |
A | |
SIMP_LIT_UPTO |
![]() |
where ![]() ![]() ![]() |
A | |
SIMP_LIT_IN_MINUS_NATURAL |
![]() |
where ![]() ![]() |
A | |
SIMP_LIT_IN_MINUS_NATURAL1 |
![]() |
where ![]() |
A | |
DEF_IN_NATURAL |
![]() |
where ![]() ![]() |
A | |
DEF_IN_NATURAL1 |
![]() |
where ![]() ![]() |
A | |
SIMP_SPECIAL_KBOOL_BTRUE |
![]() |
A | ||
SIMP_SPECIAL_KBOOL_BFALSE |
![]() |
A | ||
* | SIMP_LIT_EQUAL_KBOOL_TRUE |
![]() |
A | |
* | SIMP_LIT_EQUAL_KBOOL_FALSE |
![]() |
A | |
DEF_EQUAL_MIN |
![]() |
where ![]() ![]() |
M | |
DEF_EQUAL_MAX |
![]() |
where ![]() ![]() |
M | |
* | SIMP_SPECIAL_PLUS |
![]() |
A | |
* | SIMP_SPECIAL_MINUS_R |
![]() |
A | |
* | SIMP_SPECIAL_MINUS_L |
![]() |
A | |
* | SIMP_MINUS_MINUS |
![]() |
A | |
* | SIMP_MINUS_UNMINUS |
![]() |
where ![]() |
M |
* | SIMP_MULTI_MINUS |
![]() |
A | |
* | SIMP_MULTI_MINUS_PLUS_L |
![]() |
M | |
* | SIMP_MULTI_MINUS_PLUS_R |
![]() |
M | |
* | SIMP_MULTI_MINUS_PLUS_PLUS |
![]() |
M | |
* | SIMP_MULTI_PLUS_MINUS |
![]() |
M | |
* | SIMP_MULTI_ARITHREL_PLUS_PLUS |
![]() |
where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_PLUS_R |
![]() |
where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_PLUS_L |
![]() |
where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_MINUS_MINUS_R |
![]() |
where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_MINUS_MINUS_L |
![]() |
where the root relation (![]() ![]() |
M |
* | SIMP_SPECIAL_PROD_0 |
![]() |
A | |
* | SIMP_SPECIAL_PROD_1 |
![]() |
A | |
* | SIMP_SPECIAL_PROD_MINUS_EVEN |
![]() |
if an even number of ![]() |
A |
* | SIMP_SPECIAL_PROD_MINUS_ODD |
![]() |
if an odd number of ![]() |
A |
SIMP_LIT_MINUS |
![]() |
where ![]() |
A | |
SIMP_LIT_MINUS_MINUS |
![]() |
where ![]() |
A | |
* | SIMP_LIT_EQUAL |
![]() |
where ![]() ![]() |
A |
* | SIMP_LIT_LE |
![]() |
where ![]() ![]() |
A |
* | SIMP_LIT_LT |
![]() |
where ![]() ![]() |
A |
* | SIMP_LIT_GE |
![]() |
where ![]() ![]() |
A |
* | SIMP_LIT_GT |
![]() |
where ![]() ![]() |
A |
* | SIMP_DIV_MINUS |
![]() |
A | |
SIMP_SPECIAL_DIV_1 |
![]() |
A | ||
* | SIMP_SPECIAL_DIV_0 |
![]() |
A | |
* | SIMP_SPECIAL_EXPN_1_R |
![]() |
A | |
* | SIMP_SPECIAL_EXPN_1_L |
![]() |
A | |
* | SIMP_SPECIAL_EXPN_0 |
![]() |
A | |
* | SIMP_MULTI_LE |
![]() |
A | |
* | SIMP_MULTI_LT |
![]() |
A | |
* | SIMP_MULTI_GE |
![]() |
A | |
* | SIMP_MULTI_GT |
![]() |
A | |
* | SIMP_MULTI_DIV |
![]() |
A | |
* | SIMP_MULTI_DIV_PROD |
![]() |
A | |
SIMP_MULTI_MOD |
![]() |
A | ||
DISTRI_PROD_PLUS |
![]() |
M | ||
DISTRI_PROD_MINUS |
![]() |
M | ||
DERIV_NOT_EQUAL |
![]() |
![]() ![]() |
M |