Abstract. Pattern matching is advantageous for understanding and reasoning about function definitions, but it tends to tightly couple the interface and implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to abstract datatypes based on a rightinvertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation (implemented as abstract datatypes), while maintaining simple and sound reasoning.

A termination preserving supercompiler for a call-by-value language sometimes fails to remove intermediate structures that a supercompiler for a call-by-name language would remove. This discrepancy in power stems from the fact that many function bodies are either non-linear in use of an important variable or often start with a pattern match on their first argument and are therefore not strict in all their arguments. As a consequence, intermediate structures are left in the output program, making it slower. We present a revised supercompilation algorithm for a call-by-value language that propagates let-bindings into case-branches and uses termination analysis to remove dead code. This allows the algorithm to remove all intermediate structures for common examples where previous algorithms for call-by-value languages had to leave the intermediate structures in place.

We describe a transformation which takes a higher-order program, and produces an equivalent first-order program. Unlike Reynoldsstyle defunctionalisation, it does not introduce any new data types, and the results are more amenable to subsequent analysis operations. We can use our method to improve the results of existing analysis operations, including strictness analysis, pattern-match safety and termination checking. Our transformation is implemented, and works on a Core language to which Haskell programs can be reduced. Our method cannot always succeed in removing all functional values, but in practice is remarkably successful. D.3 [Software]: Program-

Partial evaluation [10] aims at specializing programs w.r.t. part of their input data (the static data). Partial evaluation may proceed either online or offline. Online techniques implement a single, monolithic procedure that specializes the program while dynamically checking that the termination of the process is kept.

There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting to prove termination of most functions defined in Haskell programs. In particular, we show how termination techniques for ordinary rewriting can be used to handle those features of Haskell which are missing in term rewriting (e.g., lazy evaluation, polymorphic types, and higher-order functions). We implemented our results in the termination prover AProVE and successfully evaluated them on existing Haskell-libraries.

Disjunctive well-foundedness (used in Terminator), size-change termination, and well-quasi-orders (used in supercompilation and term-rewrite systems) are examples of techniques that have been successfully applied to automatic proofs of program termination and online termination testing, respectively. Although these works originate in different communities, there is an intimate connection between them – they rely on closely related principles and both employ similar arguments from Ramsey theory. At the same time there is a notable absence of these techniques in programming systems based on constructive type theory. In this paper we’d like to highlight the aforementioned connection and make the core ideas widely accessible to theoreticians and Coq programmers, by offering a Coq development which culminates in some novel tools for performing induction. The benefit is nice composability properties of termination arguments at the cost of intuitive and lightweight user obligations. Inevitably, we have to present some Ramsey-like arguments: Though similar proofs are typically classical, we offer an entirely constructive development standing on the shoulders of Veldman and Bezem, and Richman and Stolzenberg. 1.