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    \$\begingroup\$ This construction doesn't work directly; SKI aren't Turing complete in a strongly typed language like Haskell. However, I believe you can use the same technique to define fix, and SKI + fix is Turing complete, even in a strongly typed language. \$\endgroup\$ Commented Feb 21, 2017 at 5:03
  • \$\begingroup\$ Oh, so you prefix those definitions at the beginning of each program? \$\endgroup\$ Commented Feb 21, 2017 at 12:34
  • \$\begingroup\$ @PyRulez: yes. Per our defaults I assume that it is enough to be able to construct functions with the given character set - a full program is not required. \$\endgroup\$ Commented Feb 21, 2017 at 16:44
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    \$\begingroup\$ You should probably replace (==) so that it wouldn't clash with the default equality operator \$\endgroup\$ Commented Feb 24, 2017 at 9:33
  • \$\begingroup\$ @proudhaskeller: yes, if you actually want to program it would be better to rename (==), but the above code is just a prove of turing completeness. \$\endgroup\$ Commented Feb 24, 2017 at 19:25