Automatic synthesis of specifications for first order curry programs

Bacci, Giovanni; Comini, Marco; Feliú, Marco A.; Villanueva, Alicia

doi:10.1145/2370776.2370781

Cited by 9 publications

(15 citation statements)

References 18 publications

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“…Hence, a Curry function is evaluated lazily and may be non-deterministic when defined by overlapping rules. As discussed in [7], the combination of these features raises new issues for defining the equivalence of expressions. Actually, three different notions of equivalence can be distinguished:1.…”

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confidence: 99%

“…By contrast, the expression x evaluates to the single result {} x without instantiating the free variable x. Due to these differences, Bacci et al [7] state that ground equivalence is "the (only possible) equivalence notion used in the pure functional paradigm." As we will see later, this is not true since contextual equivalence is also relevant in non-strict functional languages.…”

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confidence: 99%

“…The previous example shows that the evaluation of ground equivalent expressions might result in answers with different degrees of instantiation. However, the presence of logic variables and non-determinism might also lead to different results when ground equivalent expressions are put in some context as the following contrived example shows [7] (a more natural example will be shown later). Below we show the evaluations of k (f x) x and k (g x) x in which the subscript of "→" shows the binding of the step:…”

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Equivalence Checking of Non-deterministic Operations

Antoy

Hanus²

2018

Functional and Logic Programming

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Checking the semantic equivalence of operations is an important task in software development. For instance, regression testing is a routine task performed when software systems are developed and improved, and software package managers require the equivalence of operations in different versions of a package within the same major number version. A solid foundation is required to support a good automation of this process. It has been shown that the notion of equivalence is not obvious when non-deterministic features are present. In this paper, we discuss a general notion of equivalence in functional logic programs and develop a practical method to check it. Our method is integrated in a property-based testing tool which is used in a software package manager to check the semantic versioning of software packages. MotivationFunctional logic languages combine the most important features of functional and logic programming in a single language (see [4,20] for recent surveys). In this paper we consider Curry [24], a contemporary functional logic language that conceptually extends Haskell with common features of logic programming. Hence, a Curry function is evaluated lazily and may be non-deterministic when defined by overlapping rules. As discussed in [7], the combination of these features raises new issues for defining the equivalence of expressions. Actually, three different notions of equivalence can be distinguished:1. Ground equivalence: Two expressions are equivalent if they produce the same results when their variables are replaced by ground terms. 2. Computed-result equivalence: Two expressions are equivalent if they produce the same outcomes, i.e., variables in expressions are considered as free variables which might be instantiated during the evaluation process. 3. Contextual equivalence: Two expressions are equivalent if they produce the same outcomes in all possible contexts.⋆ This is an extended version of a paper appeared in → denotes the reflexive and transitive closure of this reduction relation. The equivalence of this rewrite relation and CRWL is shown in [28]. Equivalent OperationsAs discussed above, equivalence of operations can be defined in different ways. Ground equivalence and computed result equivalence only compare the values of applications. This is too weak since some operations have no finite values.Example 3. Consider the following operations that generate infinite lists of numbers: ints1 n = n : ints1 (n+1) ints2 n = n : ints2 (n+2)Lemma 2. Let x be an integer and rs and xs lists of integers such that x ≤ z for all z ∈ rs. Then, for some list of integers r, minRest x rs xs * → (m, r) with m ≤ z for all z ∈ (x : rs++xs) and perm (x : rs++xs) * → m : r (where rs++xs denotes the concatenation of the lists rs and xs).Proof. We assume that x ≤ z for all z ∈ rs. We prove the lemma by induction on the length of the list xs.Base case: xs = []:Since minRest x rs [] *

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Equivalence Checking of Non-deterministic Operations

Antoy

Hanus²

2018

Functional and Logic Programming

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“…It is an adaptation for the TRS paradigm of ideas from [2] for the Functional Logic paradigm. This adaptation is not straightforward, since the Functional Logic paradigm is quite similar to the Functional paradigm, but considerably different from the TRS paradigm.…”

Section: Many Notions Of Equivalencementioning

confidence: 99%

“…This operation, denoted addEC (t, s, m) is the most delicate part of the method. If we would not consider the generation of "permuted" equations like f (x, y) = f (y, x), then the whole activity would just boil down to look for the presence of s in some equivalence class and then updating the classification accordingly (like in [2]). Handling of permutations cannot be done by naïvely adding all (different) permutations of s. In this way we would generate many redundant equations.…”

Section: Deriving Specifications From Trssmentioning

confidence: 99%

Automatic Inference of Term Equivalence in Term Rewriting Systems

Comini

Torella

EPiC Series in Computing

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In this paper we propose a method to automatically infer algebraic property-oriented specifications from Term Rewriting Systems. Namely, having three semantics with suitable properties, given the source code of a TRS we infer a specification which consists of a set of most general equations relating terms that rewrite, for all possible instantiations, to the same set of constructor terms.The semantic-based inference method that we propose can cope with non-constructorbased TRSs, and considers non-ground terms. Particular emphasis is put on avoiding the generation of "redundant" equations that can be a logical consequence of other ones.

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Symbolic Abstract Contract Synthesis in a Rewriting Framework

Alpuente

Pardo

Villanueva

2017

Logic-Based Program Synthesis and Transformation

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We propose an automated technique for inferring software contracts from programs that are written in a non-trivial fragment of C, called KernelC, that supports pointer-based structures and heap manipulation. Starting from the semantic definition of KernelC in the K framework, we enrich the symbolic execution facilities recently provided by K with novel capabilities for assertion synthesis that are based on abstract subsumption. Roughly speaking, we define an abstract symbolic technique that explains the execution of a (modifier) C function by using other (observer) routines in the same program. We implemented our technique in the automated tool KindSpec 2.0, which generates logical axioms that express pre-and post-condition assertions by defining the precise input/output behavior of the C routines.

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Automatic synthesis of specifications for first order curry programs

Cited by 9 publications

References 18 publications

Equivalence Checking of Non-deterministic Operations

Equivalence Checking of Non-deterministic Operations

Automatic Inference of Term Equivalence in Term Rewriting Systems

Symbolic Abstract Contract Synthesis in a Rewriting Framework

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