On Effect Analysis for Programs with Callbacks

We introduce a precise interprocedural effect analysis for programs with mutable state, dynamic object allocation, and dynamic dispatch. Our analysis is precise even in the presence of dynamic dispatch where the context-insensitive estimate on the number of targets is very large. This feature makes our analysis appropriate for programs that manipulate first-class functions (callbacks). We first present a framework in which programs are enriched with special effect statements, and define the semantics of both program and effect statements as relations on states. Our framework defines a program composition operator that is sound with respect to relation composition. Computing the summary of a procedure then consists of composing all its program statements to produce a single effect statement. We propose a strategy for applying the composition operator in a way that balances precision and efficiency. We instantiate this framework with a domain for tracking read and write effects, where relations on program states are abstracted as graphs. We implemented the analysis as a plugin for the Scala compiler. We analyzed the Scala standard library containing 58K methods and classified them into several categories according to their effects. Our analysis proves that over one half of all methods are pure. We also analyze how context sensitivity and composition operator application strategies impact the analysis precision and performance

Deductive Synthesis and Repair

In this thesis, we explore techniques for the development of recursive functional programs over unbounded domains that are proved correct according to their high-level specifications. We present algorithms for automatically synthesizing executable code, starting from the speci- fication alone. We implement these algorithms in the Leon system. We augment relational specifications with a concise notation for symbolic tests, which are are helpful to characterize fragments of the functionsâ behavior. We build on our synthesis procedure to automatically repair invalid functions by generating alternative implementations. Our approach therefore formulates program repair in the framework of deductive synthesis and uses the existing program structure as a hint to guide synthesis. We rely on user-specified tests as well as automatically generated ones to localize the fault. This localization enables our procedure to repair functions that would otherwise be out of reach of our synthesizer, and ensures that most of the original behavior is preserved. We also investigate multiple ways of enabling Leon programs to interact with external, un- trusted code. For that purpose, we introduce a precise inter-procedural effect analysis for arbitrary Scala programs with mutable state, dynamic object allocation, and dynamic dispatch. We analyzed the Scala standard library containing 58000 methods and classified them into sev- eral categories according to their effects. Our analysis proves that over one half of all methods are pure, identifies a number of conditionally pure methods, and computes summary graphs and regular expressions describing the side effects of non-pure methods. We implement the synthesis and repair algorithms within the Leon system and deploy them as part of a novel interactive development environment available as a web interface. Our implementation is able to synthesize, within seconds, a number of useful recursive functions that manipulate unbounded numbers and data structures. Our repair procedure automatically locates various kinds of errors in recursive functions and fixes them by synthesizing alternative implementations

An independent axiomatisation for free short-circuit logic

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the equational logic in which compound statements are evaluated from left to right, while atomic evaluations are not memorised throughout the evaluation, i.e., evaluations of distinct occurrences of an atom in a compound statement may yield different truth values. We provide a simple semantics for free SCL and an independent axiomatisation. Finally, we discuss evaluation strategies, some other SCLs, and side effects.Comment: 36 pages, 4 tables. Differences with v2: Section 2.1: theorem Thm.2.1.5 and further are renumbered; corrections: p.23, line -7, p.24, lines 3 and 7. arXiv admin note: substantial text overlap with arXiv:1010.367

Verification by Reduction to Functional Programs

In this thesis, we explore techniques for the development and verification of programs in a high-level, expressive, and safe programming language. Our programs can express problems over unbounded domains and over recursive and mutable data structures. We present an implementation language flexible enough to build interesting and useful systems. We mostly maintain a core shared language for the specifications and the implementation, with only a few extensions specific to expressing the specifications. Extensions of the core shared language include imperative features with state and side effects, which help when implementing efficient systems. Our language is a subset of the Scala programming language. Once verified, programs can be compiled and executed using the existing Scala tools. We present algorithms for verifying programs written in this language. We take a layer-based approach, where we reduce, at each step, the program to an equivalent program in a simpler language. We first purify functions by transforming away mutations into explicit return types in the functions' signatures. This step rewrites all mutations of data structures into cloning operations. We then translate local state into a purely functional code, hence eliminating all traces of imperative programming. The final language is a functional subset of Scala, on which we apply verification. We integrate our pipeline of translations into Leon, a verifier for Scala. We verify the core functional language by using an algorithm already developed inside Leon. The program is encoded into equivalent first-order logic formulas over a combination of theories and recursive functions. The formulas are eventually discharged to an external SMT solver. We extend this core language and the solving algorithm with support for both infinite-precision integers and bit-vectors. The algorithm takes into account the semantics gap between the two domains, and the programmer is ultimately responsible to use the proper type to represent the data. We build a reusable interface for SMT-LIB that enables us to swap solvers transparently in order to validate the formulas emitted by Leon. We experiment with writing solvers in Scala; they could offer both a better and safer integration with the rest of the system. We evaluate the cost of using a higher-order language to implement such solvers, traditionally written in C/C++. Finally, we experiment with the system by building fully working and verified applications. We rely on the intersection of many features including higher-order functions, mutable data structures, recursive functions, and nondeterministic environment dependencies, to build concise and verified applications

Programming with Specifications

This thesis explores the use of specifications for the construction of correct programs. We go beyond their standard use as run-time assertions, and present algorithms, techniques and implementations for the tasks of 1) program verification, 2) declarative programming and 3) software synthesis. These results are made possible by our advances in the domains of decision procedure design and implementation. In the first part of this thesis, we present a decidability result for a class of logics that support user-defined recursive function definitions. Constraints in this class can encode expressive properties of recursive data structures, such as sortedness of a list, or balancing of a search tree. As a result, complex verification conditions can be stated concisely and solved entirely automatically. We also present a new decision procedure for a logic to reason about sets and constraints over their cardinalities. The key insight lies in a technique to decompose con- straints according to mutual dependencies. Compared to previous techniques, our algorithm brings significant improvements in running times, and for the first time integrates reasoning about cardinalities within the popular DPLL(T ) setting. We integrated our algorithmic ad- vances into Leon, a static analyzer for functional programs. Leon can reason about constraints involving arbitrary recursive function definitions, and has the desirable theoretical property that it will always find counter-examples to assertions that do not hold. We illustrate the flexibility and efficiency of Leon through experimental evaluation, where we used it to prove detailed correctness properties of data structure implementations. We then illustrate how program specifications can be used as a high-level programming construct ; we present Kaplan, an extension of Scala with first-class logical constraints. Kaplan allows programmers to create, manipulate and combine constraints as they would any other data structure. Our implementation of Kaplan illustrates how declarative programming can be incorporated into an existing mainstream programming language. Moreover, we examine techniques to transform, at compile-time, program specifications into efficient executable code. This approach of software synthesis combines the correctness benefits of declarative programming with the efficiency of imperative or functional programming

Effect Analysis for Programs with Callbacks

We introduce a precise interprocedural effect analysis for programs with mutable state, dynamic object allocation, and dynamic dispatch. Our analysis is precise even in the presence of dynamic dispatch where the context-insensitive estimate on the number of targets is very large. This feature makes our analysis appropriate for programs that manipulate first-class functions (callbacks). We present a framework in which programs are enriched with special effect statements, and define the semantics of both program and effect statements as relations on states. Our framework defines a program composition operator that is sound with respect to relation composition. Computing the summary of a procedure then consists of composing all its program statements to produce a single effect statement. We propose a strategy for applying the composition operator in a way that balances precision and efficiency. We instantiate this framework with a domain for tracking read and write effects, where relations on program states are abstracted as graphs. We implemented the analysis as a plugin for the Scala compiler. We analyzed the Scala standard library containing 58000 methods and classified them into several categories according to their effects. Our analysis proves that over one half of all methods are pure, identifies a number of conditionally pure methods, and computes summary graphs and regular expressions describing the side effects of non-pure methods