It's all Geek to me?
Jacob Fugal
lukfugl at gmail.com
Wed Feb 21 12:49:46 MST 2007
On 2/21/07, Steve <smorrey at gmail.com> wrote:
> But what the heck does it mean to "contain the lambda calculus properly"?
Distilled from http://en.wikipedia.org/wiki/Lambda_calculus#Formal_definition,
the calculus is defined as:
* A set of identifiers
* A grammar over those identifiers for forming lambda expressions
* A set of equivalence relations for determining if two lambda
expressions are "equal"
My interpretation of a language X "containing" the calculus would be that:
1) For any expression A in X, there is at least one lambda expression
A' that represents the same calculation as A. We'll call A' equivalent
to A.
and
2) For any two expressions A and B in X, the A and B are equivalent if
and only if A' and B' are equivalent for all (A', B') where A' is a
lambda expression to A and B' is a lambda expression equivalent to B.
In more informal language: "X contains the lambda calculus if
translating a program in X into the lambda calculus and then
manipulating the translated program according to the rules of the
lambda calculus will always leave the result of the program
unchanged."
Jacob Fugal
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