dxo: A System for Relational Algebra and Differentiation
We present dxo, a relational system for algebra and differentiation, written in miniKanren. dxo operates over math expressions, represented as s-expressions. dxo supports addition, multiplication, exponentiation, variables (represented as tagged symbols), and natural numbers (represented as little-endian binary lists). We show the full code for dxo, and describe in detail the four main relations that compose dxo. We present example problems dxo can solve by combining the main relations. Our differentiation relation, do
, can differentiate polynomials, and by running backwards, can also integrate. Similarly, our simplification relation, simpo
, can simplify expressions that include addition, multiplication, exponentiation, variables, and natural numbers, and by running backwards, can complicate any expression in simplified form. Our evaluation relation, evalo
, takes the same types of expressions as simpo
, along with an environment associating variables with natural numbers. By evaluating the expression with respect to the environment, evalo
can produce a natural number; by running backwards, evalo
can generate expressions (or the associated environments) that evaluate to a given value. reordero
also takes the same types of expressions as simpo
, and relates reordered expressions.
Thu 27 AugDisplayed time zone: Eastern Time (US & Canada) change
15:30 - 17:10 | Afternoon SessionminiKanren at miniKanren Chair(s): Nada Amin Harvard University, Weixi Ma Indiana University | ||
15:30 20mTalk | mediKanren: A System for Bio-medical Reasoning miniKanren Michael Patton University of Alabama at Birmingham, Gregory Rosenblatt University of Alabama at Birmingham, USA, William E. Byrd University of Alabama at Birmingham, USA, Matthew Might University of Alabama at Birmingham | Harvard Medical School Link to publication | ||
15:50 20mTalk | Relational Synthesis for Pattern Matching miniKanren Dmitrii Kosarev JetBrains Research, Saint Petersburg State University, Dmitri Boulytchev St. Petersburg State University, St. Petersburg, Russia Link to publication | ||
16:10 20mTalk | Some Novel miniKanren Synthesis Tasks miniKanren Link to publication | ||
16:30 20mTalk | A Relational Interpreter for Synthesizing JavaScript miniKanren Artem Chirkov University of Toronto Mississauga, Gregory Rosenblatt University of Alabama at Birmingham, USA, Matthew Might University of Alabama at Birmingham | Harvard Medical School, Lisa Zhang University of Toronto Mississauga Link to publication | ||
16:50 20mTalk | dxo: A System for Relational Algebra and Differentiation miniKanren Link to publication |