legal theory : Who should the rule in favor of and under what legal theory?

legal theory

Bill saves the life of Fred’s wife Sally when she slips and falls off the
deck of an aquarium into a shark infested fool. Bill dives into the water and saves hers life. Sally orally promises to leave Bill $10,000 in her will. However upon the death of Sally she had no property except for the home she shared with her husband jointly).After Sally dies, Fred signed and delivered to Bill the following instrument: “In consideration of Bill saving my wife’s life and his agreement to bring no claims against my estate based on her will, I hereby promise to pay Bill $10,000.” Upon Fred’s death, Bill filed a claim for $10,000. Fred’s executor contested the claim on the ground that the promise to pay was enforceable.

Who should the rule in favor of and under what legal theory? Fully
explain citing all sources utilized.