A Dependent Type Theory with Abstractable Names

Dependent Types and Fibred Computational Effects

“…In contrast, the existing work on combining dependent types with first-class computational e↵ects has concerned only particular kinds of e↵ects (e.g., [7,26,28,37]). Other authors have used dependent types in existing languages to represent e↵ects using DSLs (e.g., [5,13,23]).…”

“…We do not know a general denotational semantics for such types, though there may be one (there is one for local names [28]). Pragmatically, the situation depends on the nature of the computational e↵ects considered.…”

“…Pragmatically, the situation depends on the nature of the computational e↵ects considered. For e↵ects not requiring interaction with the program runtime, such as local names [28] or general recursion [7], one need not restrict M , as computing A(M ) then only depends on static information. However, this does not work well in general, as some e↵ects, e.g., I/O, do crucially depend on interaction with the program runtime, and so then will the computation of A(M ).…”

Typed Nominal Rewriting

“…Nominal terms are given sorts in [69] where atoms inhabit base atom sorts and term-formers yield terms of base 'data' sorts. The authors are unaware of any other approaches to type systems for nominal terms directly but a number of systems of nominal abstract syntax, a more fundamental approach to the incorporation of the ideas of nominal sets to syntax, have been typed including such as [11,13,25,59,60,65]. As with sorted nominal terms, atoms in such systems are either typed with a single type or restricted to a certain set of base types.…”

A nominal exploration of intuitionism

“…As opposed to the systems mentioned above, this system has ordinary non-bunched contexts. FreshMLTT [64] is a dependent type theory that has name-abstraction and nameconcretion operators, as well as a name-swapping operator and a fresh operator νà la Odersky, which allow them to derive expressive name-concretion rules.…”