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In asynchronous games, Melli{\`e}s proved that innocent strategies arepositional: their behaviour only depends on the position, not the temporalorder used to reach it. This insightful result shaped our understanding of thelink between dynamic (i.e. game) and static (i.e. relational) semantics. Inthis paper, we investigate the positionality of innocent strategies in thetraditional setting of Hyland-Ong-Nickau-Coquand pointer games. We show thatthough innocent strategies are not positional, total finite innocent strategiesstill enjoy a key consequence of positionality, namely positional injectivity:they are entirely determined by their positions. Unfortunately, this does nothold in general: we show a counterexample if finiteness and totality arelifted. For finite partial strategies we leave the problem open; we showhowever the partial result that two strategies with the same positions musthave the same P-views of maximal length.

Positional Injectivity for Innocent Strategies