symbolic algebra

SICP §2.5's generic arithmetic dispatches add, sub, and mul across a tower of scheme-numbers, rationals, and polynomials through apply-generic: a table keyed by operation and argument type. The table below is not a case statement rendered as a picture – it is the actual runtime state the trace runs against. Click a cell to remove it and re-run the trace: watch apply-generic fail with "no method" or fall back to coercion, then click it again to reinstall the entry and watch the same operation succeed.

Toggle coercion off and a mixed-type operation (a number plus a polynomial) fails outright instead of raising the number up the tower one level at a time (ex. 2.84) – num -> rational -> polynomial, never skipping a level. Toggle representation between sparse and dense term lists (ex. 2.89/2.90) to see add-terms and mul-terms run genuinely different algorithms over the same polynomials; the cost-comparison table re-runs the same operation both ways purely to compare call counts, without changing which representation drives the step-by-step trace above it. Toggle drop (ex. 2.85) to watch a result simplify to the lowest type that still represents the same value – a polynomial with no terms drops to the number

1. Different-variable polynomials (ex. 2.92) either nest the

alphabetically-later variable inside the earlier one, or fail, depending on that toggle.

The pure dispatch engine lives in wal-sh.tools.symbolic-algebra.core (host-neutral .cljc, tested on the JVM with test.check): coercion raises exactly one tower level per retry, sparse and dense term lists agree on every result even though their internal operation counts differ, drop never changes the value a term represents, and a missing dispatch entry always surfaces as a reported error, never a silent wrong answer or an unhandled exception. The browser adapter is wal-sh.tools.symbolic-algebra.browser. Build: gmake tools-cljs; debug in isolation: gmake dev-tool TOOL=symbolic-algebra.