Programming Language Theory: Difference between revisions
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*<tt>K ≡ λx, y. x</tt> (generation of constant functions) | *<tt>K ≡ λx, y. x</tt> (generation of constant functions) | ||
*<tt>S ≡ λx, y, z. (x z (y z))</tt> (generalized function application) | *<tt>S ≡ λx, y, z. (x z (y z))</tt> (generalized function application) | ||
====Grammar==== | |||
<pre>C-term ::= C-app | C-prim | var | |||
C-app ::= C-term C-term</pre> | |||
====Fixed-Point Combinators==== | ====Fixed-Point Combinators==== | ||
For a function F, its set of ''fixed points'' are those inputs which map to themselves. The ''fixed-point combinators'' compute the fixed points of their inputs. Curry's ''Y-combinator'' was the first: | For a function F, its set of ''fixed points'' are those inputs which map to themselves. The ''fixed-point combinators'' compute the fixed points of their inputs. Curry's ''Y-combinator'' was the first: | ||