<p>Let <span class="math-container">$\Delta = \lambda x.(x)x$</span> and consider <span class="math-container">$\Omega = (\Delta)\Delta$</span>. Then <span class="math-container">$\Omega$</span> is exactly the only <span class="math-container">$\lambda$</span>-term of the form <span class="math-container">$(\lambda x.t)v$</span> such that <span class="math-container">$(\lambda x.t)v=t\{v\ /\ x\}$</span>.</p>
<p>Does someone have references about this statement ? I could not find something enough relevant in my ressources or in my lectures material.</p>
<p>Thanks in advance !</p>

CC BY-SA 4.0
2021-12-14T13:13:28.913Z
I googled "lercher lambda-calculus" and found this: https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-17/issue-2/Lambda-calculus-terms-that-reduce-to-themselves/10.1305/ndjfl/1093887539.full  Judging from the first few lines of the paper, it looks like it's what you're looking for, right?
Damiano Mazza
CC BY-SA 4.0
2021-12-14T21:49:02.410Z
@DamianoMazza Indeed that's it thank you !
Maman
<reference-request><lambda-calculus>
Are there any references for this theorem of Lercher?
Maman
# Are there any references for this theorem of Lercher?

(Asked by: username_0 on 2021-12-13)

Let $\Delta = \lambda x.(x)x$ and consider $\Omega = (\Delta)\Delta$. Then $\Omega$ is exactly the only $\lambda$-term of the form $(\lambda x.t)v$ such that $(\lambda x.t)v=t\{v\ /\ x\}$.

Does someone have references about this statement ? I could not find something enough relevant in my ressources or in my lectures material.

Thanks in advance !

**Tags:** reference-request, lambda-calculus
> **Comments:**
> **username_1**: I googled "lercher lambda-calculus" and found this: https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-17/issue-2/Lambda-calculus-terms-that-reduce-to-themselves/10.1305/ndjfl/1093887539.full  Judging from the first few lines of the paper, it looks like it's what you're looking for, right?  
> **username_0**: @DamianoMazza Indeed that's it thank you !  

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## 0 answers

