"Jerzy" == Jerzy Karczmarczuk [EMAIL PROTECTED] writes:
Somebody tried to suggest that lambda provides a kind of logarithm...
In defense of it I can offer the following laws, which follow from
the eta-rule of lambda calculus. Just regard log_x ... as alternative
notation for \ x - ...
Laszlo Nemeth wrote:
I somehow managed to delete Hans's earlier post in which he gives the
definitions for + and ^. So I wanted to fetch them from the
archive...which was last updated on the 28 May. Is the archive broken
or just rarely updated?
Thanks,
Laszlo Nemeth
Somebody tried to
"Hans" == Hans Aberg [EMAIL PROTECTED] writes:
In real life though, it is very difficult to translate an arbitrarily given
lambda expression into a combination of the given primitive set.
I cannot resist illustrating Hans's point. This is the sort of thing
that comes up...
(((V
At 13:39 +0100 1999/06/03, Jerzy Karczmarczuk wrote:
... I don't understand
the Hans remark about making from +, * etc. the primitive basis
for the set theory. What's so primitive about them?
A set of lambda expressions is called primitive if all other lambda
expressions can be generated from it
At 13:46 +0100 1999/06/03, Peter Hancock wrote:
Just regard log_x ... as alternative
notation for \ x - ...
log_x (a * b) = log_x a + log_x b
log_x 1 = 0
log_x x = 1
log_x (a ^ b) = (log_x a) * b , x not free in b .
These are interesting relations in some sense, even though it is
Jerzy Karczmarczuk wrote:
6. Subtraction. Largo.
According to some folklore Church himself thought for some time
that it is not possible to define the subtraction using pure
lambdas.
In fact it is possible to subtract Church numerals (but never
getting negative numbers, of
At 15:37 +0100 1999/06/03, Peter Hancock wrote:
By the way, I'm not wild about Hans's term "constant variables". In
Church's lambda-I calculus, you aren't allowed abstractions where the
bound variable doesn't occur in the body. It would be better to
distinguish linear (exactly once), affine (at
