Mathematica Tutorial

Collecting Expressions During Evaluation

In many computations one is concerned only with the final result of evaluating the expression given as input. But sometimes one also wants to collect expressions that were generated in the course of the evaluation. You can do this using Sow and Reap.

Sow[val]	sow the value val for the nearest enclosing Reap
Reap[expr]	evaluate expr, returning also a list of values sown by Sow

Using Sow and Reap.

Here the output contains only the final result.

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Here two intermediate results are also given.

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This computes a sum, collecting all terms that are even.

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Like Throw and Catch, Sow and Reap can be used anywhere in a computation.

This defines a function that can do a Sow.

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This nests the function, reaping all cases below 1/2.

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Sow[val,tag]	sow val with a tag to indicate when to reap
Sow[val,{tag₁,tag₂,...}]	sow val for each of the tag_i
Reap[expr,form]	reap all values whose tags match form
Reap[expr,{form₁,form₂,...}]	make separate lists for each of the form_i
Reap[expr,{form₁,...},f]	apply f to each distinct tag and list of values