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Scheme is based on lambda calculus, it is not lambda calculus.
In lambda calculus nor combinator logic, one can't write recursive definitions like fact x = if x=0 then 1 else x*fact (x-1)
that is the reason for a fixed point combinator. <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/201.124.239.99|201.124.239.99]] ([[User talk:201.124.239.99#top|talk]]) 13:25, 25 April 2017 (UTC)</small> <!--Autosigned by SineBot-->
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