Newtonian program analysis via tensor product

Recently, Esparza et al. generalized Newton’s method—a numerical-analysis algorithm for finding roots of real-valued functions—to a method for finding fixed-points of systems of equations over semirings. Their method provides a new way to solve interprocedural dataflow-analysis problems. As in its real-valued counterpart, each iteration of their method solves a simpler “linearized” problem. One of the reasons this advance is exciting is that some numerical analysts have claimed that “‘all’ effective and fast iterative [numerical] methods are forms (perhaps very disguised) of Newton’s method.” However, there is an important difference between the dataflow-analysis and numerical-analysis contexts: when Newton’s method is used on numerical-analysis problems, multiplicative commutativity is relied on to rearrange expressions of the form “c ∗ X + X ∗ d” into “(c + d) ∗ X.” Such equations correspond to path problems described by regular languages. In...

• Type: Journal
• Year: 2016
• Where: POPL
• Authors: Thomas W. Reps, Emma Turetsky, Prathmesh Prabhu
• Keywords: POPL 2016, Programming Languages