The PS4 uses a couple APIs for game graphics, GNM and GNMX[1]. I've heard that their shader language is similar to GLSL (corrected by lunixbochs). The menus are built in WebGL running inside a stripped-down Webkit browser. Developers are unable to use WebGL for games, but it isn't out of the question that will be supported in the future.
[1] https://en.wikipedia.org/wiki/PlayStation_4_system_software