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Louis Gallet 2023-10-04 11:26:19 +02:00
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2
.obsidian/workspace.json vendored
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@ -158,6 +158,7 @@
}, },
"active": "325e43e04f9c035d", "active": "325e43e04f9c035d",
"lastOpenFiles": [ "lastOpenFiles": [
"Algo/CM/CM du 27 septembre.md",
"Algo/CM/CM du 04 octobre.md", "Algo/CM/CM du 04 octobre.md",
"Algo/Séminaire/Remediation.md", "Algo/Séminaire/Remediation.md",
"Algo/Courses/Chapter 6 - Lists.md", "Algo/Courses/Chapter 6 - Lists.md",
@ -168,7 +169,6 @@
"Algo/Séminaire/Exercices seminaire.md", "Algo/Séminaire/Exercices seminaire.md",
"Algo/Séminaire/Chapter 3 - Case analysis.md", "Algo/Séminaire/Chapter 3 - Case analysis.md",
"Algo/Courses", "Algo/Courses",
"Algo/CM/CM du 27 septembre.md",
"Algo/Séminaire/Chapter 5 - Recursivity.md", "Algo/Séminaire/Chapter 5 - Recursivity.md",
"COM-ADMR/Séjour international EPITA.md", "COM-ADMR/Séjour international EPITA.md",
"Algo/CM", "Algo/CM",

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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