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28
Algo/CM/CM du 04 octobre.md
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@ -28,4 +28,30 @@ That an consistency, because the two `nth`axioms are contradictory
The completeness is when we have enough axioms for our abstract type
To use partial operations we have to create some preconditions
To use partial operations we have to create some preconditions
```
Types
vector
Uses
integer, element, boolean
Operations
Vect: integer x integer -> vector /* internal operation */
Modify : vector x integer x element -> vector /*internal operation*/
Nth: vector x integer -> element /* Observers */
isint: vector x integer -> boolean
Lowerlimit: vector -> integer /* Observers */
Upperlimit: vector -> integer /* Observers */
Preconditions
nth(v,i) is-defined-iaoi lowerlimit(v) =< (i) =< upperlimit(v) & isinit(v,i) = true
Axioms
lowerlimit(v) =< i =< upperlimit(v) -> nth(modify(v,i,e), i) = e
lowerlimit(v) =< i =< upperlimit(v) & lowerlimit(v) =< j =< upperlimit(v) & i≠j -> nth(modifiy(v,i,e), j) = nth(v,j)
isinit(vect(i,j),k)= false
lowerlimit(v) =< i =< upperlimit(v) -> isinit(modifiy(v,i,e),i)= true
... (all the other axioms)
```
Here, `nth`is a partial operation and `isinit` is a auxiliary operation