Peas will do moderately well in shade, as they prefer cool temperatures to sunlight. Of course lettuces, arugula, spinach and other greens which bolt in the sun are good shade candidates. Some root vegetables such as carrots, radishes, beets, and parsnips (which are biennial and you harvest the next year) will give you a small crop. Don't forget perennial herbs such as lemon balm, garlic chives, and Rosemary(which you may have to dig up in Fall and house indoors if your zone requires it).
What a lot of shade-locked gardeners do is plant in containers or pots that can be moved into the sun every few days. Planting in a wheelbarrow that you can wheel into the sun for a few days -- or even hours every few days -- can broaden the range of what you can successfully harvest.
A couple of things to keep in mind....do you have a septic system with leaching fields in the front yard? If yes, then don't plant in the front yard. If you run to a public sewer, this is not an issue. Does your municipality allow permanent vegetable gardens in the front yard? Some areas do frown on it (however a mobile garden gets you around this). You're going to have to build raised beds so that you don't have to disturb any tree roots when preparing your beds and to give plant roots room to grow and spread out.
Other than that, it is going to be trial and error for you finding out what works and what doesn't Happy gardening!