Statically typed programming languages allow earlier error checking, better enforcement of disciplined programming styles, and generation of more efficient object code than languages where all type consistency checks are performed at run time. However, even in statically typed languages, there is often the need to deal with data whose type cannot be determined at compile time. To handle such situations safely, we propose to add a type Dynamic whose values are pairs of a value v and a type tag T where v has the type denoted by T. Instances of Dynamic are built with an explicit tagging construct and inspected with a type safe typecase construct. This paper explores the syntax, operational semantics, and denotational semantics of a simple language including the type Dynamic. We give examples of how dynamically typed values can be used in programming. Then we discuss an operational semantics for our language and obtain a soundness theorem. We present two formulations of the denotational s...

There are situations in programmingwhere some dynamic typing is needed, even in the presence of advanced static type systems. We investigate the interplay of dynamic types with other advanced type constructions, discussing their integration into languages with explicit polymorphism (in the style of system F ), implicit polymorphism (in the style of ML), abstract data types, and subtyping.