Editing Loop invariant (section)

==Use of loop invariants==

A loop invariant can serve one of the following purposes:
# purely documentary 
# to be checked within in the code, e.g. by an assertion call
# to be verified based on the [[Hoare logic|Floyd–Hoare approach]]

For 1., a natural language comment (like <code>// m equals the maximum value in a[0...i-1]</code> in the [[#Informal example|above]] example) is sufficient.

For 2., programming language support is required, such as the [[C (programming language)|C]] library [[assert.h]], or the [[#Eiffel|above]]-shown <code>invariant</code> clause in Eiffel. Often, run-time checking can be switched on (for debugging runs) and off (for production runs) by a compiler or a runtime option.{{citation needed|reason=hope that C's or/and Eiffel assert.h supports that?|date=May 2016}}

For 3., some tools exist to support mathematical proofs, usually based on the [[#Floyd–Hoare logic|above]]-shown Floyd–Hoare rule, that a given loop code in fact satisfies a given (set of) loop invariant(s).

The technique of [[abstract interpretation]] can be used to detect loop invariant of given code automatically. However, this approach is limited to very simple invariants (such as <code>0<=i && i<=n && i%2==0</code>).