A data structure is said to be persistent when any update operation returns a new structure without altering the old version. This paper introduces a new notion of persistence, called semi-persistence, where only ancestors of the most recent version can be accessed or updated. Making a data structure semi-persistent may improve its time and space complexity. This is of particular interest in backtracking algorithms manipulating persistent data structures, where this property is usually satisfied. We propose a proof system to statically check the valid use of semi-persistent data structures. It requires a few annotations from the user and then generates proof obligations that are automatically discharged by a dedicated decision procedure. Additionally, we give some examples of semi-persistent data structures (arrays, lists and hash tables).