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Realizability i n terpretations of logics are given by s a ying what it means for computational objects of some kind to realize logical formulae. The computational objects in question might b e d r a wn from an untyped universe of computation, such a s a partial combinatory algebra, or they might b e t yped objects such as terms of a PCF-style programming language. In some instances, one can show that a particular untyped realizability i n terpretation matches a particular typed one, in thedoi:10.1016/s1571-0661(04)00105-7 fatcat:6zp5v23rfjhkdow3vy7yyhaojy