September 2017 Update

Task/Y-combinator/Lambdatalk/y-combinator.lambdatalk

@@ -0,0 +1,42 @@
+1) defining the Ycombinator
+{def Y
+ {lambda {:f :n}
+  {:f :f :n}}}
+
+2) defining non recursive functions
+2.1) factorial
+{def almost-fac
+ {lambda {:f :n}
+  {if {= :n 1}
+   then 1
+   else {* :n {:f :f {- :n 1}}}}}}
+
+2.2) fibonacci
+{def almost-fibo
+ {lambda {:f :n}
+  {if {<   :n 2}
+   then 1
+   else {+ {:f :f {- :n 1}} {:f :f {- :n 2}}}}}}
+
+3) testing
+{Y almost-fac 6}
+-> 720
+{Y almost-fibo 8}
+-> 34
+
+We could also forget the Ycombinator and names:
+
+1) fac:
+{{lambda {:f :n} {:f :f :n}}
+ {lambda {:f :n}
+  {if {= :n 1}
+   then 1
+   else {* :n {:f :f {- :n 1}}}}} 6}
+-> 720
+
+2) fibo:
+{{lambda {:f :n} {:f :f :n}}
+ {{lambda {:f :n}
+  {if {<   :n 2} then 1
+   else {+ {:f :f {- :n 1}} {:f :f {- :n 2}}}}}} 8}
+-> 34