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...Higher order causal stream functions in sig from first principles baltasar trancon y widemann markus lepper technische universitat ilmenau semantics gmbh berlin abstract the programming language is a total functional clocked syn chronous data ow its core has been designed to admit concise coalgebraic universal coalgebra an expressive oretical framework for behavioral but traditionally phrased categorical and generally considered inaccessible present paper we rephrase concepts relevant basic mathematical notation demonstrate how features characteristic of paradigms namely sequential parallel composition applicative style delay apply are shaped naturally by semantic structure thus serves two purposes as gentle self contained applied introduc tion explication denotational operational design introduction streams ubiquitous fundamental even more so realms reactive oriented computation foundations terms coinduction have proposed almost twenty years ago remain woefully obscure general communi...