Typed self-evaluation via intensional type functions

Abstract

Many popular languages have a self-interpreter, that is, an interpreter for the language written in itself. So far, work on polymorphically-typed self-interpreters has concentrated on self-recognizers that merely recover a program from its representation. A larger and until now unsolved challenge is to implement a polymorphicallytyped self-evaluator that evaluates the represented program and produces a representation of the result. We present F µi ω , the first λcalculus that supports a polymorphically-typed self-evaluator. Our calculus extends Fω with recursive types and intensional type functions and has decidable type checking. Our key innovation is a novel implementation of type equality proofs that enables us to define a versatile representation of programs. Our results establish a new category of languages that can support polymorphically-typed selfevaluators.

Incorporating quotation and evaluation into Church's type theory

“…Nevertheless these representations were only partially typed. The finally tagless approach to embedded representations [29] kicked off a series of papers on typed selfrepresentation [4,5,18,19,20,21,81,107] which eventually succeeded at providing elegant solutions.…”