Irrelevance, Heterogeneous Equality, and Call-by-value Dependent Type Systems Vilhelm Sjoberg¨ Chris Casinghino Ki Yung Ahn University of Pennsylvania University of Pennsylvania Portland State University
[email protected] [email protected] [email protected] Nathan Collins Harley D. Eades III Peng Fu Portland State University University of Iowa University of Iowa
[email protected] [email protected] [email protected] Garrin Kimmell Tim Sheard Aaron Stump University of Iowa Portland State University University of Iowa
[email protected] [email protected] [email protected] Stephanie Weirich University of Pennsylvania
[email protected] We present a full-spectrum dependently typed core language which includes both nontermination and computational irrelevance (a.k.a. erasure), a combination which has not been studied before. The two features interact: to protect type safety we must be careful to only erase terminating expressions. Our language design is strongly influenced by the choice of CBV evaluation, and by our novel treatment of propositional equality which has a heterogeneous, completely erased elimination form. 1 Introduction The Trellys project is a collaborative effort to design a new dependently typed programming language. Our goal is to bridge the gap between ordinary functional programming and program verification with dependent types. Programmers should be able to port their existing functional programs to Trellys with minor modifications, and then gradually add more expressive types as appropriate. This goal has implications for our design. First, and most importantly, we must consider nonter- mination and other effects. Unlike Coq and Agda, functional programming languages like OCaml and Haskell allow general recursive functions, so to accept functional programs ‘as-is’ we must be able to turn off the termination checker.