tutorial

Wile algebra tutorial

Runnable walkthrough of (wile algebra ...) -- a self-verifying tutorial that doubles as an acceptance-test surface. Every chapter is a plain Scheme file: read it, run it, modify it.

How to run

Run a single chapter:

wile --file examples/algebra/tutorial/chapters/01-getting-started.scm

Run every chapter and every quick-tour file (enforced by CI):

make tutorial-test

Each file prints ok lines for successful checks and exits non-zero on any mismatch. No special test harness -- just wile --file <path>.

Reading order

The deep chapters build on each other. Work through them in order:

Chapter	Topic	Sub-libraries
chapters/01-getting-started.scm	Monoids from scratch	monoid
chapters/02-structures.scm	Lattice to ring to field tower	lattice, semiring, group, ring, differential, boolean
chapters/03-rewriting-basics.scm	Axioms, normalizers, traces	rewrite
chapters/04-boolean-simplifier.scm	Boolean vs Heyting simplification	boolean, heyting, symbolic, rewrite
chapters/05-symbolic-differentiation.scm	Polynomial calculus + hand-written S-expression differentiator	polynomial, differential, ring
chapters/06-graph-algorithms.scm	BFS, isomorphism, Tutte, Hopcroft-Karp	combinatorial-graph
chapters/07-group-actions.scm	Orbits, stabilizers, Burnside	group
chapters/08-lattice-presets.scm	Canonical lattices, Birkhoff	lattice, incidence
chapters/09-dataflow-analysis.scm	MFP solver, sign domain	dataflow, abstract-domain, lattice
chapters/10-unification.scm	Syntactic and AC unification	unification
chapters/11-equivalence-discovery.scm	Sub-theory comparison	rewrite, symbolic, boolean

The quick-tour files in quick-tour/ cover the sub-libraries not featured in a deep chapter. Read them a la carte.

Quick tour	Library
quick-tour/setoid.scm	setoid
quick-tour/partial-order.scm	order
quick-tour/closure.scm	closure
quick-tour/category.scm	category
quick-tour/galois.scm	galois
quick-tour/fca.scm	fca
quick-tour/graph.scm	graph (abstract, distinct from combinatorial-graph)
quick-tour/interval.scm	interval
quick-tour/matrix.scm	matrix
quick-tour/pareto.scm	pareto
quick-tour/matching.scm	matching (two-sided / stable marriage)
quick-tour/sat.scm	sat
quick-tour/cfl.scm	cfl (context-free-language reachability)

How it works

• lib/check.scm provides five helpers: check=, check-approx=, check-true, check-false, check-error. Each prints ok on pass and raises an error (non-zero exit) on fail.
• Chapters include lib/check.scm via (include "../lib/check.scm").
• Some chapters include "try this yourself" exercises as commented check= lines -- uncomment, guess the value, run the file.

See also

• docs/algebra/overview.md -- design philosophy and structure hierarchy.
• docs/algebra/reference.md -- complete API reference.
• docs/algebra/tutorial.md -- tutorial index with chapter prerequisites graph.