Playing with LambdaAPI3

The LambdaAPI3 software is provided in source form. Experimenting it is easier using a platform like the Eclipse Platform .

In order to install the software with Eclipse you have to create a Java project, within which you import the LambdaAPI3 source directory content.

The software uses no other library than the JRE System Library, version 1.6 or later.

The main class to run is: org.xmloperator.lambda3.Test

Running Test produces this text on System.out. It covers the following topics:

Term printing
Number coding
Step by step reducing
Normal from evaluation
Term statistics

Term printing

The following informations are given for a set of combinators:

Type:	Type assignment a la Curry
Lambda:	Usual expression of a lambda-term
DeBruijn:	Expression indexed a la De Bruijn
DAG:	DAG representation
Combinat:	Abstraction elimination

[A,B,C] is a tupple. It means \x.xABC

Number coding

The following number encodings are used:

Church encoding: numbers and operators are shown preceded by a <#>.
Scott encoding: numbers and operators are shown preceded by a <@>.
Binary encoding: numbers and operators are shown preceded by a <$>.
Integer encoding: numbers and operators are shown preceded by a <_>.
Float encoding: numbers and operators are shown preceded by a <£>.

Step by step reducing

A step by step reduction is shown for a set of lambda-terms.

At each step a DAG representation of the current lambda-term is displayed, followed by a line that underscores the leftermost outermost redex of this lambda-term. The argument part of the redex is underscored differently.

Normal form evaluation

Normal form and number of steps used for obtaining it are shown for a set of lambda-terms.

Term statistics

Term statistics are compiled at the end.

For each type of Term (Variable, Constant2, Constant3, Abstraction or Application) the following countings are realized:

living instance count	A living Term has not be collected.
consumed instance count	A consumed Term has been collected.
reusable instance count	A reusable Term is ready for reusing.

Living Term counts must be zero for a full garbage collection.

Each reusable Term count is limited by the size of the corresponding reuse stack size. They can judge the correct size of these stacks.