Program reasoning consists of the tasks of automatically and statically verifying correctness and inferring properties of programs. Program synthesis is the task of automatically generating programs. Both program reasoning and synthesis are theoretically undecidable, but the results in this dissertation show that they are practically tractable. We show that there is enough structure in programs written by human developers to make program reasoning feasible, and additionally we can leverage program reasoning technology for automatic program synthesis. This dissertation describes expressive and efficient techniques for program reasoning and program synthesis. Our techniques work by encoding the underlying inference tasks as solutions to satisfiability instances. A core ingredient in the reduction of these problems to finite satisfiability instances is the assumption of templates. Templates are user-provided hints about the structural form of the desired artifact, e.g., invariant, pre- and postcondition templates for reasoning; or program templates for synthesis. We propose novel algorithms, parameterized by suitable templates, that reduce the inference of these artifacts to satisfiability. We show that fixed-point computation—the key technical challenge in program reasoning— is encodable as SAT instances. We also show that program synthesis can be viewed as generalized

Examples are often a natural way to specify computational structures such as programs, queries, and sequences. Synthesizing such structures from example based specification has applications in automating end-user programming and in building intelligent tutoring systems. Synthesis from examples involves addressing two key technical challenges: (i) design of an efficient search algorithm – these algorithms have been based on various paradigms including versionspace algebras, SAT/SMT solvers, numerical methods, and even exhaustive search, (ii) design of a user interaction model to deal with the inherent ambiguity in the example based specification. This paper illustrates various algorithmic techniques and user interaction models by describing inductive synthesizers for varied applications including synthesis of tricky bitvector algorithms, spreadsheet macros for automating repetitive data manipulation tasks, ruler/compass based geometry constructions, new algebra problems, sequences for mathematical intellisense, and grading of programming problems. 1.

Automated synthesis of program fragments from specifications can make programs easier to write and easier to reason about. To integrate synthesis into programming languages, software synthesis algorithms should behave in a predictable way: they should succeed for a well-defined class of specifications. We propose to systematically generalize decision procedures into synthesis procedures, and use them to compile implicitly specified computations embedded inside functional and imperative programs. Synthesis procedures are predictable, because they are guaranteed to find code that satisfies the specification whenever such code exists. To illustrate our method, we derive synthesis procedures by extending quantifier elimination algorithms for integer arithmetic and set data structures. We then show that an implementation of such synthesis procedures can extend a compiler to support implicit value definitions and advanced pattern matching. 1.

Abstract—Application Programming Interface (API) documents are a typical way of describing legal usage of reusable software libraries, thus facilitating software reuse. However, even with such documents, developers often overlook some documents and build software systems that are inconsistent with the legal usage of those libraries. Existing software verification tools require formal specifications (such as code contracts), and therefore cannot directly verify the legal usage described in natural language text in API documents against code using that library. However, in practice, most libraries do not come with formal specifications, thus hindering toolbased verification. To address this issue, we propose a novel approach to infer formal specifications from natural language text of API documents. Our evaluation results show that our approach achieves an average of 92 % precision and 93% recall in identifying sentences that describe code contracts from more than 2500 sentences of API documents. Furthermore, our results show that our approach has an average 83 % accuracy in inferring specifications from over 1600 sentences describing code contracts. I.

Program Synthesis, which is the task of discovering programs that realize user intent, can be useful in several scenarios: enabling people with no programming background to develop utility programs, helping regular programmers automatically discover tricky/mundane details, program understanding, discovery of new algorithms, and even teaching. This paper describes three key dimensions in program synthesis: expression of user intent, space of programs over which to search, and the search technique. These concepts are illustrated by brief description of various program synthesis projects that target synthesis of a wide variety of programs such as standard undergraduate textbook algorithms (e.g., sorting, dynamic programming), program inverses (e.g., decoders, deserializers), bitvector manipulation routines, deobfuscated programs, graph algorithms, text-manipulating routines, mutual exclusion algorithms, etc. Categories and Subject Descriptors D.1.2 [Programming Techniques]:

Abstract. Symbolic reasoning is in the core of many software development tools such as: bug-finders, test-case generators, and verifiers. Of renewed interest is the use of symbolic reasoning for synthesing code, loop invariants and ranking functions. Satisfiability Modulo Theories (SMT) solvers have been the focus of increased recent attention thanks to technological advances and an increasing number of applications. In this paper we review some of these applications that use software verifiers as bug-finders “on steroids ” and suggest that new model finding techniques are needed to increase the set of applications supported by these solvers. 1

We describe the design of a string programming/expression language that supports restricted forms of regular expressions, conditionals and loops. The language is expressive enough to represent a wide variety of string manipulation tasks that end-users struggle with. We describe an algorithm based on several novel concepts for synthesizing a desired program in this language from input-output examples. The synthesis algorithm is very efficient taking a fraction of a second for various benchmark examples. The synthesis algorithm is interactive and has several desirable features: it can rank multiple solutions and has fast convergence, it can detect noise in the user input, and it supports an active interaction model wherein the user is prompted to provide outputs on inputs that may have multiple computational interpretations. The algorithm has been implemented as an interactive add-in for Microsoft Excel spreadsheet system. The prototype tool has met the golden test- it has synthesized part of itself, and has been used to solve problems beyond authors ’ imagination.

In this paper, we present a novel program synthesis approach that is inspired by symbolic testing. We symbolically execute an unknown template program and constrain the program’s behavior over each executed path. As more paths are explored the space of candidate programs narrows until only the valid ones remain. Instead of randomly picking paths, we find that is possible and more efficient to direct path exploration over the unknown template program using a novel technique that parameterizes the symbolic executor by the remaining candidate solutions. We call this approach Pathbased Inductive Synthesis (PINS). We apply PINS to the problem of automatic program inversion. The specification for inversion is implicit as the combination of the original program and the inverse is the identity transform. We observe that an inverse is typically related to the original program and so the space of possible inverses can be inferred by automatically mining the original program for expressions, predicates, and control flow. Using PINS, we show we can synthesize inverses for compressors (e.g., LZ77), packers (e.g., UUEncode), and arithmetic transformers (e.g., image rotations). PINS synthesizes these inverses in a median time of 40 seconds and an average time of 293 seconds, demonstrating the viability of our testing-inspired synthesis approach. 1.

In this paper, we study the problem of automatically solving ruler/compass based geometry construction problems. We first introduce a logic and a programming language for describing such constructions and then phrase the automation problem as a program synthesis problem. We then describe a new program synthesis technique based on three key insights: (i) reduction of symbolic reasoning to concrete reasoning (based on a deep theoretical result that reduces verification to random testing), (ii) extending the instruction set of the programming language with higher level primitives (representing basic constructions found in textbook chapters, inspired by how humans use their experience and knowledge gained from chapters to perform complicated constructions), and (iii) pruning the forward exhaustive search using a goal-directed heuristic (simulating backward reasoning performed by humans). Our tool can successfully synthesize constructions for various geometry problems picked up from high-school textbooks and examination papers in a reasonable amount of time. This opens up an amazing set of possibilities in the context of making classroom teaching interactive.

Abstract. Program verification is the task of automatically generating proofs for a program’s compliance with a given specification. Program synthesis is the task of automatically generating a program that meets a given specification. Both program verification and program synthesis can be viewed as search problems, for proofs and programs, respectively. For these search problems, we present approaches based on user-provided insights in the form of templates. Templates are hints about the syntactic forms of the invariants and programs, and help guide the search for solutions. We show how to reduce the template-based search problem to satisfiability solving, which permits the use of off-the-shelf solvers to efficiently explore the search space. Template-based approaches have allowed us to verify and synthesize programs outside the abilities of previous verifiers and synthesizers. Our approach can verify and synthesize difficult algorithmic textbook programs (e.g., sorting, and dynamic programming-based algorithms, etc.), and difficult arithmetic programs. 1