The Scott model of PCF in univalent type theory

Abstract We develop the Scott model of programming language PCF in univalent type theory. Moreover, we work constructively and predicatively. To account for non-termination PCF, use lifting monad (also known as partial map classifier monad) from topos theory, which has been extended to theory by Escardó Knapp. Our results show that is a viable approach partiality can be constructed predicative constructive setting. Other approaches either require some form choice or quotient inductive-inductive types. one do without these extensions.