tiny-datalog

A logic engine small enough to read in an afternoon, and a course that builds it up from nothing.

What is Datalog?

A query language from the early 1980s, with three properties worth memorising:

• Declarative. You state what follows from what, never how to compute it. No loops, no ordering, no stopping condition.
• Recursive. Rules may refer to themselves, so "at any depth" questions are the native shape rather than something bolted on.
• Terminating. Every program finishes. Always. That is a theorem, not a convention.

Datalog is useful when a query is recursive and SQL is fighting you, or when a rule set has grown past the point where anyone can review it. Here is what that buys you.

You deploy 12 services, sitting on 160 packages joined by 292 dependency edges. A CVE (Common Vulnerabilities and Exposures entry, a published security flaw) lands on one package. Which services are exposed?

You write down facts, things simply true:

depends(pkg4, pkg13).             % pkg4 pulls in pkg13
service(pkg4).                    % pkg4 is something we deploy
vulnerable(pkg21, cve_2026_0001). % pkg21 has the CVE

...and rules for deriving new facts. :- means "if", the comma means "and", capitals are variables:

% programs/supply-chain.dl
uses(X, Y) :- depends(X, Y).                  % you use what you depend on
uses(X, Z) :- depends(X, Y), uses(Y, Z).      % ...and whatever that uses

exposed(S, C) :- service(S), uses(S, L), vulnerable(L, C).

The middle rule reads X uses Z if X depends on Y and Y uses Z. It refers to itself, and that is the whole trick: applied over and over it walks the graph to any depth, without you saying how deep or when to stop.

$ python3 datalog.py -q 'exposed(S, C)' programs/supply-chain.dl
?- exposed(S, C)
   exposed(pkg0, cve_2026_0001).
   exposed(pkg4, cve_2026_0001).
   exposed(pkg5, cve_2026_0001).
   exposed(pkg8, cve_2026_0001).
   (4 answers)

Four of twelve, and nothing you can see in the file says which four. The 292 edges you stated imply 8,457 uses facts, and the answer lives in those. Ask why, and you get the derivation the answer came out of, which is also the remediation path:

$ python3 datalog.py --explain 'exposed(pkg4, cve_2026_0001)' programs/supply-chain.dl
?- explain exposed(pkg4, cve_2026_0001)
   exposed(pkg4, cve_2026_0001)   [via exposed(S, C) :- service(S), uses(S, L), vulnerable(L, C).]
     service(pkg4)   (base fact)
     uses(pkg4, pkg21)   [via uses(X, Z) :- depends(X, Y), uses(Y, Z).]
       depends(pkg4, pkg13)   (base fact)
       uses(pkg13, pkg21)   [via uses(X, Y) :- depends(X, Y).]
         depends(pkg13, pkg21)   (base fact)
     vulnerable(pkg21, cve_2026_0001)   (base fact)

When tomorrow's CVE arrives, the engine repairs those 8,457 facts instead of recomputing them:

$ python3 incremental.py programs/supply-chain.dl -u 'vulnerable(pkg100, cve_2026_0002).'
materialised: 8766 facts
vulnerable(pkg100, cve_2026_0002).
  -> {'inserted': 1, 'derived': 12} in 0.034s
  (a from-scratch rebuild of this program: 0.822s)

Nothing to install:

git clone https://github.com/andrewgoodchild/tiny-datalog && cd tiny-datalog
python3 tests.py        # 254 tests, ~12s

Why the language choice decides what you can ask later

Frontier language models are getting good at reasoning and logic. They have been trained on every logic trope in the canon, they can usually spot a contradiction in prose, and when they meet more data than fits in a context window they do the sensible thing: they write a program to solve it.

So the question was never whether to run code. It is what the code should be, and that choice decides which questions you can still ask afterwards.

Rules that encode policy tend to outlive the query that prompted them. They get reviewed, audited, inherited by someone who did not write them, and changed under pressure. Sooner or later somebody asks why a particular decision came out the way it did, and somebody else asks whether the rules are even coherent before trusting any answer at all.

(The sign-off case has its own demonstration: lesson 17 writes a lending policy badly twice, and --explain names which of two rules wrongly let a suspended staff member borrow — three lines, no debugger.)

Both are questions about the rules, not about a run, and most languages cannot answer them. Datalog can, because it gave things up:

(Containment and equivalence become undecidable once recursion is involved — Shmueli, 1993, which is why containment.py handles conjunctive queries and refuses the rest. Lesson 16 covers the boundary.)

Being declarative, recursive and terminating is not a feature list. It is the trade that makes rules analysable, and three things follow from it:

• The artifact is reviewable by someone who is not a programmer. eligible(P) :- member(P, H), qualifying_household(H), not employed(P). is nearly the policy sentence. Loops and mutable state are not.
• Termination is a safety property, not a nicety, when the rules are going to be executed by something you do not supervise.
• Provenance and incremental maintenance come from the semantics rather than from extra code that would itself need verifying.

Every feature in this repository is a check of that kind: stratification catches circularity, --models catches contradiction and ambiguity, containment.py catches redundancy, and --explain produces the derivation somebody has to sign off on.

Two limits. An engine checks coherence, not intent: a rule set can pass every check above and still be the wrong policy. And the trade only pays when the rules genuinely outlive the query. For a one-off question, or anything arithmetic-heavy, forty lines of ordinary code is the better tool, and that covers most problems.

What else you can ask it

The worked example above is one row of a table. The full version — 20 questions, each with the command that answers it and the lesson that builds the machinery — is in getting started, beside the reading paths.

Claims you can check

Beyond the benchmarks: every shell command quoted in every lesson is executed in CI and its quoted output diffed against reality — the course cannot silently rot, which is a rarer property than anything else on this page. Every performance claim below is reproducible from the shipped generator, including the one that goes the wrong way. Timings are on an Apple M1 Pro, CPython 3.10, single core:

python3 benchmarks/generate.py chain 50  > chain50.dl
python3 benchmarks/generate.py chain 100 > chain100.dl
python3 benchmarks/generate.py chain 150 > chain150.dl

The last two are the same rewriting on the same program. Magic sets pays in proportion to how much the query's bindings prune; when demand is the whole relation the guards are pure overhead. Lesson 7 works through why.

Correctness is checked by a seeded differential fuzzer that generates stratified programs and demands semi-naive, naive, magic-sets and tabled evaluation all agree, and that incremental maintenance matches recomputation under random updates. 400 programs per run; TINY_DATALOG_FUZZ=3000 python3 tests.py DifferentialFuzzTests soaks.

Answers are also checked against engines this repository did not write. conformance/ runs the datalog-conformance corpus, harvested from Soufflé, Nemo and Crepe, through all four strategies, and its defeasible theories, from SPINdle and the papers, through defeasible.py: 195 cases pass. Every skip is named with its reason: arithmetic and 10⁵-fact joins, which this course omits on purpose, or cases written for a different logic.

Learning Datalog

lessons/ is a complete course, no prior exposure assumed, every example a runnable file, following the field's own history from 1977 to the current research threads. The field's own recent lecture notes observe that the literature advises people building Datalog engines better than people trying to use one; this course does both halves on purpose — sixteen lessons where the engine is the explanation, then a lesson on authoring rules that survive review, and one on a logic built for rules with exceptions. And it is built to be inherited: git clone, no dependencies, no hosted anything, and every quoted transcript re-verified by CI — the exercises cannot rot. (For where each technique ships — CodeQL, RDFox, Feldera, SNOMED and the rest — lesson 0 ends with the deployments.) lessons/getting-started.md has the titles and the reading order, and lessons/glossary.md defines every technical term the course uses, and lessons/references.md collects every work the lessons cite.

Three of them teach things that are hard to find taught well anywhere else, and they are the reason the course exists rather than just the engine:

• Lesson 8 proves that why-provenance cannot be specialised into derivation counts, with a program that prints the disproof: two facts with identical provenance and different counts. That settles "materialise provenance once, specialise later," which is a real design-review question with a real answer.
• Lesson 16 shows that the containment test you need for query minimisation is the search already sitting in datalog.py: _match maps a rule body into a database, find_homomorphism maps a rule body into another rule body. Same backtracking, one level up.
• Lesson 4 contrasts the two reasoners in this repository, which disagree about what absence means, and leaves you with a habit: when you see not, ask whose authority says this is absent.

Every lesson ends with exercises, and every exercise has a worked answer in exercises/ — runnable where the answer is a program, and executed by the test suite so the answers cannot rot. cases/ lets anyone add a regression test without writing Python.

What this is not, and what is missing on purpose

Not an engine to build a product on. Joins are nested-loop, stable-model search is exhaustive, evaluation is batch. For real workloads see Soufflé, clingo, RDFox or Feldera; for Datalog inside a Python application, with arithmetic and queries over SQL databases, see pyDatalog.

Deliberate omissions, because saying why teaches more than lacking them quietly:

• Arithmetic and comparisons. A built-in isn't a relation you can enumerate, so it must be evaluated the moment its operands bind — which entangles correctness with join order and forces terms to become trees. Lesson 14 is the whole story, including what to do instead.
• Indexes and join planning. Every join is a nested loop so the algorithms stay one-screen readable. It is also why the magic-sets timing above goes the way it does.
• ⊤ and role hierarchies in the classifier — what ships is EL⊥ (disjointness and unsatisfiability detection included). SNOMED needs ELH (EL plus role hierarchies) with right identities, which is what the ELK and Snorocket reasoners implement and this does not.
• A REPL (interactive prompt). Run a file, or call it from Python.

Aggregation used to be on this list; lesson 13 is what promoting an omission into a feature looks like.

Using it in your own project

The engine is on PyPI, with no dependencies beyond the standard library:

pip install tiny-datalog

from tiny_datalog import run_program, explain

engine = run_program(open("supply-chain.dl").read())
for answer in engine.query("exposed(S, C)"):
    print(answer)                     # {'S': 'pkg0', 'C': 'cve_2026_0001'}
print("\n".join(explain(engine, "exposed", ("pkg0", "cve_2026_0001"))))

Facts can come straight from Python data (a CSV file, a database query) instead of program text. Each row is checked as if it had been parsed:

rules = """
uses(X, Y) :- depends(X, Y).
uses(X, Z) :- depends(X, Y), uses(Y, Z).
exposed(S, C) :- service(S), uses(S, L), vulnerable(L, C).
"""
engine = run_program(rules, facts={
    "depends": [("app", "lib"), ("lib", "core")],
    "service": ["app"],                         # one-column rows may be bare
    "vulnerable": [("core", "cve_2026_0001")],
})
engine.query("exposed(S, C)")       # [{'S': 'app', 'C': 'cve_2026_0001'}]

The command-line interface installs too, as tiny-datalog (and tiny-datalog-semiring, -tabling, -incremental, -subsumption, -containment, -defeasible, -prolog for the satellites):

tiny-datalog -q 'exposed(S, C)' supply-chain.dl

The course material — lessons, programs, exercises — is not part of the installed package; clone the repository for that.

Layout

tiny_datalog/   the engine and its satellites — the code you read:
  datalog.py    the core: AST, parser, safety checks, stratification,
                the semi-naive evaluator, and the CLI
  magic.py      the magic-sets rewriting (a program-to-program pass)
  semantics.py  grounding, stable models, the well-founded model
  semiring.py   semiring-valued evaluation (costs, counts, provenance,
                probabilities)
  incremental.py  insertions + DRed deletions over a live materialisation
  prolog.py     top-down SLD resolution with function symbols
  tabling.py    tabled top-down evaluation (iterative QSQR)
  subsumption.py  KL-ONE-style EL classifier, compiled to Datalog
  containment.py  query containment and minimisation by homomorphism
  defeasible.py   defeasible logic: exceptions, priorities, defeaters
*.py            three-line launchers, so `python3 datalog.py ...` works
                straight from a checkout with nothing installed
programs/       teaching programs, numbered by the lesson that uses
                them (00-* are the README's examples)
lessons/        getting started, glossary, and lessons 0–19
exercises/      worked answers, verified by the test suite
cases/          golden test cases — add one without writing Python
conformance/    the external datalog-conformance corpus (Soufflé, Nemo,
                Crepe, SPINdle), run against every evaluation strategy
benchmarks/     scaled input generators (chain/tree/clique/grid)
tests.py        254 tests: every shipped program and exercise answer is
                executed, a conformance suite runs every query through
                every applicable strategy, and a seeded fuzzer checks
                the same property on random programs

The code is part of the course: comments explain the algorithms as they happen, and the lessons that introduce machinery end with an Under the hood section reading the piece of the implementation they used.

How big is it, honestly

The evaluator is about 850 lines (tiny_datalog/datalog.py, up to the command-line interface), the CLI, --explain and why-not another 600, and the nine satellite modules about 2,900. Call it 4.3k lines of toolkit and 2.7k of tests, roughly a quarter of it commentary.

"Tiny" is a claim about the evaluator, and about each satellite module singly: none of the nine exceeds 500 lines, which a test asserts. It is not a claim about the repository, which is ten modules because it teaches ten things.

There is no dead code to golf away (checked); shrinking further means deleting either a technique or an explanation.

License

MIT.