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In this paper, we study strong normalization of a core language based on System Fω which supports programming with finite and infinite structures. Building on our prior work, finite data such as finite lists and trees are defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. In this work, we take a type-based approach to strong normalization by tracking sizedoi:10.1145/2500365.2500591 dblp:conf/icfp/AbelP13 fatcat:4nifaqt3irbizkeg2hnlhdzp74