This paper sketches a foundation for programming with higher-order abstract syntax and explicit substitutions based on contextual modal type theory [NPP05]. Contextual modal types not only allows us to cleanly separate the representation of data objects from computation, but allow us to recurse over data objects with free variables. In this paper, we extend these ideas even further by adding fi...

The applicability of term rewriting to program transformation is limited by the lack of control over rule application and by the context-free nature of rewrite rules. The first problem is addressed by languages supporting user-definable rewriting strategies. The second problem is addressed by the extension of rewriting strategies with scoped dynamic rewrite rules. Dynamic rules are defined at r...

Curry is a multi-paradigm declarative language covering functional, logic, and concurrent programming paradigms. Curry’s operational semantics is based on lazy reduction of expressions extended by a possibly non-deterministic binding of free variables occurring in expressions. Moreover, constraints can be executed concurrently which provides for concurrent computation threads that are synchroni...

Many term calculi, like λ-calculus or π-calculus, involve binders for names, and the mathematics of bound variable names is subtle. Schönfinkel introduced the SKI combinator calculus in 1924 to clarify the role of quantified variables in intuitionistic logic by eliminating them. Yoshida demonstrated how to eliminate the bound names coming from the input prefix in the asynchronous π-calculus, bu...