Next: Basic Rules of Lambda
Up: Lambda Calculus and A++
Previous: Contents
Contents
New book on A++ and the Lambda Calculus available!
The syntax of lambda expressions is defined as follows:
The Lambda Calculus therefore includes three diffenrent types of lambda expressions:
 variables (referencing lambda expressions)
 lambda abstractions (defining functions)
 applications (invoking functions)
Remark:
The parentheses in the syntax of an application are not mandatory.
This results from the law of associativity for applications
introduced below.
On the basis of the syntax for lambda expressions
and a few conversion rules a primitive programming
language can be developed in a few steps.
This primitive programming language would contain

logical operations: true, false, if, not, and, or

,

list operations: cons, car, cdr, nullp, length,
insert, insertionsort, map, filter, memberp, addelt,
union

,

numerical operations: zero, one, two, zerop, add,
succ, pred, sub, mult, sum

relational operations: equalp, gtp, ltp, gep

.
Georg Loczewski
20030807