We address the problem of performing semantic transformations on strings, which may represent a variety of data types (or their combination) such as a column in a relational table, time, date, currency, etc. Unlike syntactic transformations, which are based on regular expressions and which interpret a string as a sequence of characters, semantic transformations additionally require exploiting the semantics of the data type represented by the string, which may be encoded as a database of relational tables. Manually performing such transformations on a large collection of strings is error prone and cumbersome, while programmatic solutions are beyond the skill-set of end-users. We present a programming by example technology that allows end-users to automate such repetitive tasks. We describe an expressive transformation language for semantic manipulation that combines table lookup operations and syntactic manipulations. We then present a synthesis algorithm that can learn all transformations in the language that are consistent with the user-provided set of input-output examples. We have implemented this technology as an add-in for the Microsoft Excel Spreadsheet system and have evaluated it successfully over several benchmarks picked from various Excel help-forums. 1.

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.

We propose computer-assisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the form Left-hand-side-term = Righthand-side-term), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in making examinations where they need to test students on problems similar to what they taught in class, and students in generating practice problems tailored to their specific needs. Our first insight is that we can generalize p syntactically to a query Q that implicitly represents a set of problems [[Q]] (which includes p). Our second insight is that we can explore the space of problems [[Q]] automatically, use classical results from polynomial identity testing to generate only those problems in [[Q]] that are correct, and then use pruning techniques to generate only unique and interesting problems. Our third insight is that with a small amount of manual tuning on the query Q, the user can interactively guide the computer to generate problems of interest to her. We present the technical details of the above mentioned steps, and also describe a tool where these steps have been implemented. We also present an empirical evaluation on a wide variety of problems from various sub-fields of algebra including polynomials, trigonometry, calculus, determinants etc. Our tool is able to generate a rich corpus of similar problems from each given problem; while some of these similar problems were already present in the textbook, several were new! 1