Differences between version 9 and revision by previous author of LambdaCalculus.
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| Newer page: | version 9 | Last edited on Friday, October 24, 2003 7:02:11 pm | by CarstenKlapp | Revert |
| Older page: | version 6 | Last edited on Friday, October 24, 2003 2:04:52 pm | by StuartYeates | Revert |
@@ -1,13 +1,13 @@
-A conceptual model of computers based on defining and evaluating functions. Of current ProgrammingLanguages, [LISP], [Scheme], [Haskell] and other FunctionalLanguages best expose this conceptual model.
+A conceptual model of computers based on defining and evaluating functions. Of the
current ProgrammingLanguages, [LISP], [Scheme], [Haskell] and other FunctionalLanguages best expose this conceptual model.
-One of the fundamental proofs in ComputerScience is that any result calculatable
in LambdaCalculus is calculatable
on a FiniteStateMachine.
+One of the fundamental proofs in ComputerScience is that any result calculable
in LambdaCalculus is calculable
on a FiniteStateMachine.
(From memory:)
-LambdaCalculus is based on the idea that you have two types of rewrite rules, one where you change the names of variables, and one where you replace a variable with it's
expansion. And thats
it.
+LambdaCalculus is based on the idea that you have two types of rewrite rules, one where you change the names of variables, and one where you replace a variable with its
expansion. And that's
it.
-For instance, if we define "one" as a function which outputs it's
argument once, we have:
+For instance, if we define "one" as a function which outputs its
argument once, we have:
one = λx(x)
then the successor function might be defined as
@@ -17,22 +17,22 @@
two = successor one
two = λx.y(x y y) λx(x)
now we do an alpha reduction (rename some variables)
two = λx.y(x y y) λz(z)
-now we do a beta reduction (replace x with it's
value (λz(z))
+now we do a beta reduction (replace x with its
value (λz(z))
two = λy(λz(z) y y)
and a beta reduction on z
two = λy(y y)
-we now have a function that outputs it's
argument twice.
+we now have a function that outputs its
argument twice.
Three is obvious
three = sucessor two
which eventually expands to
three = λx(x x x)
-Addiction
is easy
+Addition
is easy
addition = λx.y.z(x z y z)
five = add two three
five = λx.y.z(x z y z) λa(a a) λa(a a a)
five = λz(Λa(a a) z λa(a a a) z)
five = λz(z z z z z)
