Inductive datatypes provide mechanisms to define finite data such as finite lists and trees via
constructors and allow programmers to analyze and manipulate finite data via pattern …

This paper explores a new point in the design space of functional programming: functional
programming with dependently-typed higher-order data structures described in the logical …

An old and celebrated analogy says that writing programs is like proving theorems. This
analogy has been productive in both directions, but in particular has demonstrated …

We show how to combine a general purpose type system for an existing language with
support for programming with binders and contexts by refining the type system of ML with a …

Recent work on higher-dimensional type theory has explored connections between Martin-
Löf type theory, higher-dimensional category theory, and homotopy theory. These …

This paper re-examines the presentation of datatypes in dependently typed languages,
addressing in particular the issue of what it means for one datatype to be in various ways …

Relational descriptions have been used in formalizing diverse computational notions,
including, for example, operational semantics, typing, and acceptance by non-deterministic …

Higher-order abstract syntax provides a convenient way of embedding domain-specific
languages, but is awkward to analyse and manipulate directly. We explore the boundaries of …

Modern proof assistants such as Coq and Isabelle provide high degrees of expressiveness
and assurance because they support formal reasoning in higher-order logic and supply …

14. ABSTRACT A logical framework and its implementation should serve as a flexible tool
for specifying, simulating, and reasoning about formal systems. When the formal systems we …