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I would like to dedicate a small machine to exclusively running a Mathematica kernel and use that kernel to read http requests arriving on port 80, treat them and send http responses back without any web server or extra software of any kind. Requests are to be treated in sequence (only 1 connection shall be supported at a time). Clearly webMathematica is an overkill here. Any ideas?

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This usage is not permitted by the Mathematica licence: you need webMathematica, even if technically you don't. Practically speaking, it's not possible with no extra software at all since Mathematica has no facilities to work with TCP sockets, but you can use Java, a .Net language, or C to fill in the gaps. –  Oleksandr R. Jun 27 '13 at 21:56
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It seems to me that using Mathematica to answer http requests is already "overkill." –  bill s Jun 28 '13 at 6:11
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From Oleksandr's comment:

This usage is not permitted by the Mathematica license: you need webMathematica, even if technically you don't. Practically speaking, it's not possible with no extra software at all since Mathematica has no facilities to work with TCP sockets, but you can use Java, a .Net language, or C to fill in the gaps.

The specific statement can be found in the Mathematica License Agreement, under Prohibited Uses, section f:

allowing access to the Product by any user other than Licensee, including, without limitation, access to the Product via a web server, which is only allowed pursuant to a valid webMathematica™ license agreement;

and section j:

using a password, activation key, or other means of accessing the Software other than as specifically authorized by WRI;

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