Abstract A reversible programming language supports deterministic forward and backward
computation. We formalize the programming language Janus and prove its reversibility. We
provide a program inverter for the language and implement a self-interpreter that achieves

Abstract We formalize a technique introduced by Böhm and Piperno to solve systems of
recursive equations in lambda calculus without the use of the fixed point combinator and
using only normal forms. To this aim we introduce the notion of a canonical algebraic term

… 3.8 A partial evaluator should be "strong enough" in the following sense. Partial evaluation
of a self-interpreter for the subject language with respect to a program should be able to yield
essentially the same program as output: P= L mix (self-interpreter, P) …

… Page 227. 217 1.2 The partial evaluator The partial evaluator consists of two parts: a meta-circular
self-interpreter to perform the static parts of the program, and a specializer that unfolds non- static
goals or specializes them with respect to their static arguments …

… ' Write F'/(M) for the set of free variables of M. A K-term M is closed if' FV(M) = Q. the set of closed
7»-terms is denoted by A". 2 Definition (i) An interpreter (or evaluator) is an (external) Function
E: A—>A such that EUM“) E M. (ii) A self-interpreter is a ?»~term E such that for Me …

… September 2, 1994 Abstract We start by giving a compact representation schema for -terms and
show how this leads to an exceedingly small and elegant self-interpreter … 12 Page 13. Appendix
A: proof of correctness for the self-interpreter We will prove Theorem 1 E dMe!!M …

… The exe- cution of p (on a C machine) on input d1, ..., dn is written [[p]]C (d1, ... , dn) ⇒ d, where
d is the result (if any). Suppose sint is a self-interpreter for C, taking as input a program p and
its input data di, and yield as result a value d as normal execution of p would …

… Experience from the "Mix" project has shown that successful specialization of a self- interpreter
(an interpreter written in the same langu- age as it interprets) is a first step towards self- application …
An autoprojector is a "self- specializer", and thus a "smart" self-interpreter …

… interferes. Let sint be a self-interpreter for C. In languages like Scheme, programs
are legal data objects and can be given directly to a self-interpreter, but in C, a
suitable program representation must be devised. Furthermore …

Abstract According to conventional wisdom, a self-interpreter for a strongly normalizing
lambda-calculus is impossible. We call this the normalization barrier. The normalization
barrier stems from a theorem in computability theory that says that a total universal function