iOS SQL Database access from Javascript

You would have to build your own bridge or use one of the many HTML-based app frameworks available for iOS (PhoneGap, Appcelerator, etc).

If you want to go down the path of building your own bridge, you should check out UIWebView's -stringByEvaluatingJavaScriptFromString:, and the combination of UIWebView's -loadRequest and UIWebViewDelegate's webView:shouldStartLoadWithRequest:navigationType: using a custom protocol (e.g., com.mycompany.myapp.1.0://) that you check for in the delegate method.

EDIT:

Here's some sample code:

Your HTML should have something like this:

<a href="myapp://doQuery?arg1=a&arg2=b">Do Query</a>

or:

<a href="#" onclick:"javascript:doQuery();">Do Query</a>
<script>
  function doQuery() {
    window.location = "myapp://doQuery";
  }
</script>

Then your webview delegate can capture a click there by:

- (BOOL)webView:(UIWebView *)webView shouldStartLoadWithRequest:(NSURLRequest *)req (UIWebViewNavigationType)navType {
  if ([[req URL] scheme] == @"myapp:") {
    if ([[req URL] host] == @"doQuery") {
      // Do the query here.
      [webView stringByEvaluatingJavaScriptFromString:[NSString stringWithFormat:@"latestResult = %@; queryReturned(latestResult);", queryResultAsJSON]];
    } else if ([[req URL] host] == @"doSomethingElse") {
      // Do something else.
    }
    return NO;
  }
  return YES;
}