We introduce a notion of guarded recursive (g.r.) datatype constructors, generalizing the notion of recursive datatypes in functional programming languages such as ML and Haskell....
The search for an expressive calculus of datatypes in which canonical algorithms can be easily written and proven correct has proved to be an enduring challenge to the theoretical ...
We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arise...
Abstract. For nested or heterogeneous datatypes, terminating recursion schemes considered so far have been instances of iteration, excluding efficient definitions of fixed-point ...
We describe the operational and denotational semantics of a small imperative language in type theory with inductive and recursive definitions. The operational semantics is given b...