Assuming "correct behavior" mean no bottom, and follow monad law, yes.

The html based prolog thing you mention is probably eve.

Right, http://witheve.com/

I must say the first idea is brilliant... (Despite morally disputable)

The map can be combined together with short cut fusion, so a map to create new array, get the avg, and another map to get p value further 'combination' is theoretically possible but I dont know if they will be done.