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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)
The parentheses in the syntax of an application are not mandatory.
This results from the law of associativity for applications
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, insertion-sort, map, filter, memberp, addelt,
numerical operations: zero, one, two, zerop, add,
succ, pred, sub, mult, sum
relational operations: equalp, gtp, ltp, gep