vault backup: 2023-10-04 11:26:19

Algo/CM/CM du 04 octobre.md

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+An abstract type have a signature, which contains types, uses and operations, and have some axioms. 
+
+An axiom let us determine the value of the application of the observers with the internal operations (in the example below, the operation modify). An axiom must be precise. 
+
+```
+Types
+	vector
+Uses
+	integer, element
+Operations
+	Modify : vector x integer x element -> vector /*internal operation*/
+	Nth: vector x integer -> element /* Observers */
+	Lowerlimit: vector -> integer /* Observers */
+	Upperlimit: vector -> integer /* Observers */
+
+Axioms
+	lowerlimit(v) =< i =< upperlimit(v) -> nth(modify(v,i,e), i) = e
+```
+In this example, the axiom explain that it check nth position in the modified vector