Soft typing of general first-order languages

The aim of the paper is to describe an extension of the notion of soft typing which increases its usefulness in software engineering. Our soft typing concept is general enough to be integrated into a wide variety of normal languages, including formalizations of mathematics, with a view to increasing reasoning productivity in the development of verified software. Specifically the paper extends the concept of soft typing to general first order languages in a parametric many sorted framework. Conventionally static and dynamic type checking are treated rather separately and so do not achieve the full potential of the typing concept. Soft typing embeds both static and dynamic type checking within a uniform framework, to provide a more efficient and flexible type checking method. For example soft typing allows incremental type extensions within a theory to be justified by discharging appropriate proof obligations within that theory. Incremental static and dynamic checking is also supported