Typed self-interpretation by pattern matching

Abstract

Self-interpreters can be roughly divided into two sorts: self-recognisers that recover the input program from a canonical representation, and self-enactors that execute the input program. Major progress for statically-typed languages was achieved in 2009 by Rendel, Ostermann, and Hofer who presented the first typed selfrecogniser that allows representations of different terms to have different types. A key feature of their type system is a type:type rule that renders the kind system of their language inconsistent.In this paper we present the first statically-typed language that not only allows representations of different terms to have different types, and supports a self-recogniser, but also supports a selfenactor. Our language is a factorisation calculus in the style of Jay and Given-Wilson, a combinatory calculus with a factorisation operator that is powerful enough to support the pattern-matching functions necessary for a self-interpreter. This allows us to avoid a type:type rule. Indeed, the types of System F are sufficient. We have implemented our approach and our experiments support the theory.

Control Flow Analysis for SF Combinator Calculus

“…SF-calculus is structure complete, in the sense that it can pattern match over normal forms of terms (those having no redexes) and distinguish between any two different terms in normal form. In particular, for any two such terms t 1 and t 2 , there is a term e such that we have e t 1 → * S and e t 2 → * F. Adding System F types to SF-calculus (and giving names to some other combinators), the resulting calculus can encode and type an interpreter for its own language [12]. Thus it presents a promising theoretical foundation for reasoning about programs that transform other programs, for example by means of partial evaluation.…”