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How can I publish my database with asp like DSN-less style.
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Your question is not very clear.
Is your data in DBF/DBC? SQL-Server or similar?
When you say publish, do you meant Web pages in the Internet?
Wen you say ASP-like you mean using ASP or using VFP would also do/be more desirable?

If you want to publish in the web you can certainly use ASP and write DSN-less accesses using a ConnectionString. If you are going against SQL/Server data or similar you can also use an OleDB provider instead of ODBC and acess the data through ADO. In VFP you will not have an OleDB provider until VFP7 (unless you have one of the VFP7 Betas that come with an OleDB provider).

If you are talking about VFP data (DBF) and want to use VFP code instead of ASP+VBS there are several tools on the market to do that, like Web Connect, Axtive FoxPro Pages and FoxWeb.