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ACM SIGPLAN 2013 Workshop on Partial Evaluation and Program Manipulation

The list of accepted papers and their abstracts are shown below, in no particular order.
**Regular Research Papers:**

- Jeroen Weijers, Jurriaan Hage and Stefan Holdermans.
**Security Type Error Diagnosis for Higher-Order, Polymorphic Languages**

**Abstract:**We combine the type error slicing and heuristics based approaches to type error diagnostic improvement within the context of type based security analysis on a let-polymorphic call by value lambda calculus extended with lists, pairs and the security specific constructs declassify and protect. We define and motivate four classes of heuristics that help diagnose inconsistencies among the constraints, and show their effect on a selection of security incorrect programs.

- Marco Servetto and Elena Zucca.
**A meta-circular language for active libraries**

**Abstract:**We present a new Java-like language design coupling disciplined meta-programming features with a composition language. That is, programmers can write meta-expressions that combine class definitions, on top of a small set of composition operators, inspired by the seminal Bracha's Jigsaw framework. Moreover, such operators are deep, that is, they allow to manipulate (e.g., rename or duplicate) a nested class at any level of depth.

This provides an effective language support for active libraries: namely, a (library) class can provide a method returning a customized version of a class, depending, e.g., on the execution platform. Since a class can contain nested classes, a whole library can be generated in this way. That is, deep operators allows the programmer to better exploit meta-programming capabilities, leading to a "meta-programming in the large" style.

We adopt a mixed typechecking technique, which provides a good compromise between meta-programming systems with extreme expressiveness and no static type checking, and those with strong type system and only limited meta-programming capability. In particular, our technique ensures an important property, called meta-level soundness, stating that typing errors never originate from already compiled (meta-)code, that is, programmers can safely use (active) libraries.

- Álvaro García-Pérez and Pablo Nogueira.
**A Syntactic and Functional Correspondence between Reduction Semantics and Reduction-Free Full Normalisers**

**Abstract:**Olivier Danvy and others have shown the syntactic correspondence between reduction semantics (a small-step semantics) and abstract machines, as well as the functional correspondence between reduction-free normalisers (a big-step semantics) and abstract machines. The correspondences are established by program-transformation (so-called interderivation) techniques. A reduction semantics and a reduction-free normaliser are interderivable when the abstract machine obtained from them is the same. However, the correspondences fail when the underlying reduction strategy is hybrid, i.e., relies on another sub-strategy. Hybridisation is an essential structural property of full-reducing and complete strategies. Hybridisation is unproblematic in the functional correspondence. But in the syntactic correspondence the refocusing and inlining-of-iterate-function steps become context sensitive, preventing the refunctionalisation of the abstract machine. We show how to solve the problem and showcase the interderivation of normalisers for normal order, the standard, full-reducing and complete strategy of the pure lambda calculus. Our extension makes it possible to interderive, rather than contrive, full-reducing abstract machines. As expected, the machine we obtain is a variant of Pierre Crégut's full Krivine machine KN.

- Qiang Sun, Yuting Chen and Jianjun Zhao.
**Constraint-Based Locality Analysis for X10 Programs**

**Abstract:**X10, a HPC (High Performance Computing) programming language proposed by IBM, supports a PGAS (Partitioned Global Address Space) programming model offering a shared address space. The address space can be further partitioned into several logical locations where objects and activities (or threads) will be dynamically created. An analysis of locations can help to check the safety of object accesses through exploring which objects and activities may reside in which locations, while in practice the objects and activities are usually designated at runtime and their locations may also vary under different environments. In this paper, we propose a constraint-based locality analysis method called Leopard for X10. Leopard calculates the points-to relations for analyzing the objects and activities in a program and uses a place constraint graph to analyze their locations. We have developed a tool to support Leopard, and conducted an experiment to evaluate its effectiveness and efficiency. The experimental results show that Leopard can calculate the locations of objects and activities precisely.

- Bruno Oliveira and Andres Loh.
**Abstract Syntax Graphs for Domain Specific Languages**

**Abstract:**This paper shows a Haskell representation for embedded domain specific languages (EDSLs) using abstract syntax graphs (ASGs). The purpose of this representation is to deal with the important problem of defining operations that require observing or preserving sharing and recursion in EDSLs in an expressive, yet easy to use way. In contrast to more conventional representations based on abstract syntax trees, ASGs represent sharing and recursion explicitly as binder constructs. We use a functional representation of ASGs based on structured graphs, where binders are encoded with parametric higher-order abstract syntax. We show how adapt to this representation to well-typed ASGs. This is especially useful for EDSLs, which often reuse the type system of the host language. We also show a type-class based encoding of (well-typed) ASGs that enables extensible and modular well-typed EDSLs while allowing the manipulation of sharing and recursion.

- Emanuele De Angelis, Fabio Fioravanti, Alberto Pettorossi and Maurizio Proietti.
**Verifying Programs via Iterated Specialization**

**Abstract:**We present a method for verifying safety properties of imperative programs by using techniques based on the specialization of constraint logic programs (CLP). We consider a class of C programs with integer variables, and we define their operational semantics as a reachability relation between memory configurations. Then we address the problem of verifying safety properties, stating that error configurations cannot be reached from initial configurations.

The reachability relation is encoded as a CLP program R, and the safety property to be verified is encoded as the negation of a predicate unsafe in R, meaning that an {error} configuration can be reached from the initial configuration.

Then, we check whether or not the safety property holds by specializing the CLP program R with respect to the given C program, initial and error configurations, so as to derive a new CLP program R_s where the evaluation of unsafe either finitely fails (safety holds) or succeeds (safety does not hold). The program specialization strategy we propose always terminates, but due to the undecidability of safety properties, it may be the case that in the residual program R_s we are not able to decide whether unsafe finitely fails or succeeds.

Then, we apply again program specialization and iterate this process in the hope of proving safety or unsafety. During the various specializations we may apply different strategies for propagating information (e.g., forward propagation from an initial configuration, or backward propagation from an error configuration) and different operators for generalizing predicate definitions (e.g., widening and convex hull).

We have implemented the various strategies using the MAP transformation system. By an experimental evaluation on various examples taken from the literature, we show that our method is competitive with respect to state-of-the-art software model checkers.

- Ryosuke Sato, Hiroshi Unno and Naoki Kobayashi.
**Towards a Scalable Software Model Checker for Higher-Order Programs**

**Abstract:**In our recent paper, we have shown how to construct a fully-automated program verification tool (so called a "software model checker") for a tiny subset of functional language ML, by combining higher-order model checking, predicate abstraction, and CEGAR. This can be viewed as a higher-order counterpart of previous software model checkers for imperative languages like BLAST and SLAM. The naive application of the proposed approach, however, suffered from scalability problems, both in terms of efficiency and supported language features. To obtain more scalable software model checkers for full-scale functional languages, we propose several optimizations and extensions of the previous approach. Among others, we introduce (i) selective CPS transformation, (ii) selective predicate abstraction, (iii) refined predicate discovery as optimization techniques, and (iv) functional encoding of recursive data structures and control operations to support a larger subset of ML. We have implemented the proposed methods, and obtained promising results.

- Dominique Devriese, Ilya Sergey, Dave Clarke and Frank Piessens.
**Fixing Idioms - A recursion primitive for applicative DSLs**

**Abstract:**In a lazy functional language, the standard encoding of recursion in DSLs uses the host language's recursion, so that DSL algorithms automatically use the host language's least fixpoints, even though many domains require algorithms to produce different fixpoints. In particular, this is the case for DSLs implemented as Applicative functors (structures with a notion of pure computations and function application). We propose a recursion primitive afix that models a recursive binder in a finally tagless HOAS encoding, but with a novel rank-2 type that allows us to specify and exploit the effects-values separation that characterizes Applicative DSLs. Unlike related approaches for Monads and Arrows, we model effectful recursion, not value recursion.

Using generic programming techniques, we define an arity-generic version of the operator to model mutually recursive definitions. We recover intuitive user syntax with a form of shallow syntactic sugar: an alet construct that syntactically resembles the let construct, which we have implemented in the GHC Haskell compiler. We describe a proposed axiom for the afix operator. We demonstrate usefulness with examples from Applicative parser combinators and functional reactive programming. We show how higher-order recursive operators like many can be encoded without special library support, unlike previous approaches, and we demonstrate an implementation of the left recursion removal transform.

- Axel Simon.
**Deriving a Complete Type Inference for Hindley-Milner and Vector Sizes using Expansion**

**Abstract:**Type inference and program analysis both infer static properties about a program. Yet, they are constructed using very different techniques. We reconcile both approaches by deriving a type inference from a denotational semantics using abstract interpretation. We observe that completeness results in the abstract interpretation literature can be used to derive type inferences that are abstract-complete, a property akin to the inference of principal typings. The resulting algorithm is similar to that of Milner-Mycroft, that is, it infers Hindley-Milner types while allowing for polymorphic recursion. Instead of type schemes, it uses*expansion*to instantiate types. Since our expansion operator is agnostic to the abstract domain, we are able to apply it not only to types. We illustrate this by inferring the size of vector types using systems of linear equalities.

- Francisco Javier López-Fraguas and Enrique Martin-Martin.
**Typing as Functional-Logic Evaluation**

**Abstract:**We present a transformational approach to type inference for functional logic programs. More concretely, we give a wide set of examples showing how, given a functional logic program P, we can synthesize a remarkably simple and natural functional logic program P' such that the evaluation of expressions with respect to P' corresponds to typing the expressions in the original P. We start developing those ideas for the case of type inference with standard Hindley-Milner types, and after that we consider some variations, like local definitions with different degrees of polymorphism, existential types, or type checking in presence of polymorphic recursion. For the basic case of Hindley-Milner types we provide also a formalization of the transformation and proofs of its adequacy. Besides its potential applicability to the implementation of different type systems, or to the educational use of the synthesized typing programs to explain different type inference/checking processes, the paper demonstrates vividly the expressive power of functional logic languages, as well as some of their limitations to the purpose of metaprogramming, that we have overcome by providing a suitable set of metalogical functions to inspect, classify and manipulate expressions according to their structure, similar to well known Prolog metapredicates for such purposes.

- Kostis Sagonas, Josep Silva and Salvador Tamarit.
**Precise Explanation of Success Typing Errors**

**Abstract:**Nowadays, many dynamic languages come with (some sort of) type inference in order to detect type errors statically. Often, in order not to unnecessarily reject programs which are allowed under a dynamic type discipline, their type inference algorithms are based on non-standard (i.e., not Hindley-Milner based) type inference techniques and employ aggressive forwards and backwards propagation of subtype constraints. Although such analyses are effective in locating real errors, the type errors they report are often extremely difficult for programmers to follow and convince themselves that something should be changed in their programs.

We have observed this phenomenon in the context of Erlang: for a number of years now its implementation comes with a static analysis tool called Dialyzer which, among other software discrepancies, detects definite type errors (i.e., code points that will result in a runtime error if executed) by inferring success typings.

In this work, we extend the analysis that infers success typings, with infrastructure that maintains additional information that can be used to provide precise (i.e., minimal) explanations about the cause of a discrepancy reported by Dialyzer using program slicing.

An interesting aspect of the information that our analysis gathers is that it is not useful only for explaining definite type errors but also places in the code containing unreachable statements, dead code, etc., i.e. discrepancies which would normally be undetected by most type inference, static analysis, or testing techniques.

We have implemented the techniques we describe in a publicly available development branch of Dialyzer.

- Bruno Martinez, Marcos Viera and Alberto Pardo.
**Just Do It While Compiling!: Fast Extensible Records in Haskell**

**Abstract:**The library for strongly typed heterogeneous collections HList provides an implementation of extensible records in Haskell that needs only a few common extensions of the language. In HList, records are represented as linked lists of label-value pairs with a look-up operation that is linear-time in the number of fields. In this paper, we use type-level programming techniques to develop a more efficient representation of extensible records for HList. We propose two internal encodings for extensible records that improve lookup at runtime without needing a total order on the labels. One of the encodings performs lookup in constant time but at a cost of linear time insertion. The other one performs lookup in logarithmic time while preserving the fast insertion of simple linked lists. Through staged compilation, the required slow search for a field is moved to compile time in both cases.

- María Alpuente, Marco A. Feliú and Alicia Villanueva.
**Automatic Inference of Specifications using Matching Logic**

**Abstract:**Formal specifications can be used for various software engineering activities ranging from finding errors to documenting software and automatic test-case generation. Automatically discovering specifications for heap-manipulating programs is a challenging task. In this paper, we propose a technique for automatically inferring formal specifications from code which is based on the symbolic execution and automated reasoning tandem "Matching Logic / K framework". We implemented our technique for a fragment of C, called KernelC^{?}, in the automated tool KingSpec^{?}, which generates axioms that describe the precise input/output behavior of C routines that handle pointer-based structures, i.e., result values and state change. These specifications can be written either in Matching Logic itself, which is useful for further automated analysis within the K formal environment, or in sugared axiomatic form, which favors better human inspection. Since we rely on rewriting logic K semantics specification of programming languages, our approach can be easily extended to any language for which a formal semantics in K is given.

**Tool Demonstration Papers:**

- Martin Sulzmann, Jürgen Nicklisch and Axel Zechner.
**Traceability and Correctness of EDSL Abstractions**

**Abstract:**EDSLs (embedded domain-specific languages) are in particular suitable for agile software projects. New abstractions can be coded quickly and easily in the EDSLs host language and are automatically transformed to the basic primitives of the EDSLs. In the context of formal software certification, it is paramount that these abstractions are*correct*and that the low-level code resulting from the EDSL primitives can be*traced*to some higher-level artifacts, let it be some concrete programming abstractions, software requirements etc. We have built an EDSL-based toolchain for implementing and testing mission critical applications which supports measures to guarantee traceability and correctness of EDSL abstractions. We give an overview of our approach and practical experiences applying the EDSLs in the industrial context.

- Marco Comini and Luca Torella.
**Automatic inference of term equivalence in (left-linear) Term Rewriting Systems**

**Abstract:**This paper presents a technique to automatically infer algebraic property-oriented specifications from Term Rewriting Systems. Namely, given the source code of a TRS we infer a specification which consists of a set of equations relating (nested) terms (operation calls) that rewrite to the same set of values.

In this paradigm there are several additional issues which arises with respect to the (first order) functional programming case, because free variables are admitted in queries and non-constructor-based rules are allowed.

The (glass-box) semantic-based inference method that we propose can cope with this issues and achieves, to some extent, the correctness of the inferred specification, differently from other (black-box) approaches based on testing techniques.

To experiment on the validity of our proposal we have considered an instance of the proposed method employing a novel (condensed) semantics for left-linear TRSs and we have implemented a "proof of concept" prototype in Haskell which is available online.

**Short Papers:**

- Michael Carbin, Deokhwan Kim, Sasa Misailovic and Martin Rinard.
**Verified Integrity Properties for Safe Approximate Program Transformations**

**Abstract:**Approximate computations (for example, video, audio, and image processing computations, machine learning computations, and many scientific computations) have the freedom to generate a range of acceptable results. Approximate program transformations (for example, task skipping and loop perforation) exploit this freedom to produce computations that can execute at a variety of points in an underlying accuracy versus performance trade-off space. One potential concern is that these transformations may change the semantics of the program and therefore cause the program to crash, perform an illegal operation, or otherwise violate its integrity.

We investigate verifying integrity properties -- key correctness properties that the transformed computation must respect -- to safely apply approximate program transformations. We present our experience developing and evaluating a compiler that verifies integrity properties of computations expressed as `for' loops, then leverages these verified properties to safely apply transformations that perforate the loops.

- Baris Aktemur, Yukiyoshi Kameyama, Oleg Kiselyov and Chung‐chieh Shan.
**Shonan Challenge for Generative Programming (Short Position Paper)**

**Abstract:**The appeal of generative programming is "abstraction without guilt": eliminating the vexing trade-off between writing high-level code and highly-performant code. Generative programming also promises to formally capture the domain-specific knowledge and heuristics used by high-performance computing (HPC) experts. How far along are we in fulfilling these promises? To gauge our progress, a recent Shonan Meeting on "bridging the theory of staged programming languages and the practice of high-performance computing" proposed to use a set of benchmarks, dubbed "Shonan Challenge".

Shonan Challenge is a collection of crisp problems posed by HPC and domain experts, for which efficient implementations are known but were tedious to write and modify. The challenge is to generate a similar efficient implementation from the high-level specification of a problem, performing the same optimizations, but automatically. It should be easy to adjust optimizations and the specification, maintaining confidence in the generated code.

We describe our initial set of benchmarks and provide two solutions to one of the problems. We hope that the Shonan Challenge will clarify the state of the art and stimulate the theory and technology of staging just as the POPLmark challenge did for meta-theory mechanization. Since each Shonan Challenge problem is a kernel of a significant HPC application, each solution has an immediate practical application.