Hornet

Horn clauses via Expression Trees — a Prolog-like embedded DSL for Python ≥ 3.13.

Hornet lets you write logic programs directly in Python. Instead of parsing Prolog strings, it hijacks Python's operator overloading and __call__ syntax to build expression trees, which a resolution engine then solves via unification and backtracking.

Installation

pip install hornet

Requires Python 3.13+. Dependencies: toolz, immutables.

Core Concepts

Terms

Hornet's term algebra mirrors Prolog's:

Import symbols dynamically from hornet.symbols. Names starting with uppercase become Variables; lowercase become Atoms; _ is the anonymous wildcard.

from hornet.symbols import X, Y, parent, mortal, human

Facts and Rules

Facts and rules are built with .when():

db.tell(
    parent('socrates', 'sophroniscus'),   # fact
    human('socrates'),                     # fact
    mortal(X).when(human(X)),             # rule: mortal(X) :- human(X).
)

Queries

from hornet import database
from hornet.symbols import X, mortal

db = database()
db.tell(human('socrates'))
db.tell(mortal(X).when(human(X)))

for subst in db.ask(mortal(X)):
    print(subst[X])   # → socrates

db.ask() returns an iterable of substitutions. Each substitution maps variables to their bound values.

Built-in Predicates

Hornet ships a standard library of predicates pre-loaded in every database:

Arithmetic

Arithmetic expressions are built using Python's operators on symbolic terms and evaluated lazily by let:

from hornet.symbols import X, Y, R, let, arithmetic_equal

# R is X * Y + 1
db.ask(let(R, X * Y + 1))

# supported: + - * / // % ** ~ & | ^ << >>

Definite Clause Grammars (DCGs)

Hornet supports DCG notation via DCG() and DCGs():

from hornet import DCGs, database
from hornet.symbols import S, NP, VP, noun, verb, det, phrase

db = database()
db.tell(*DCGs(
    S.when(NP, VP),
    NP.when(det, noun),
    VP.when(verb),
    det.when(['the']),
    noun.when(['cat']),
    verb.when(['sleeps']),
))

for subst in db.ask(phrase(S, ['the', 'cat', 'sleeps'])):
    print('parsed!')

DCG rules are automatically expanded to difference lists. The inline(goal) escape hatch lets you embed regular Prolog goals inside a DCG body.

Extending with Python

Register native Python predicates using the @predicate decorator. This is how ifelse/3 is implemented internally:

from hornet import database, predicate
from hornet.clauses import Database, Subst
from hornet.combinators import Step, if_then_else
from hornet.clauses import resolve
from hornet.symbols import T, Y, N

db = database()

@db.tell
@predicate(ifelse(T, Y, N))
def _(db: Database, subst: Subst) -> Step[Database]:
    return if_then_else(
        resolve(subst[T]),
        resolve(subst[Y]),
        resolve(subst[N]),
    )(db, subst.map)

Architecture

Hornet is built on two main layers:

Term algebra (hornet.terms): Python expressions construct expression trees rather than computing values. Operator overloading (+, *, |, **, …) and __call__ produce nested Symbolic structures — Functor, Atom, Variable, Cons, Operator subclasses — which represent both data and goals. promote() lifts Python primitives (integers, strings, lists) into this algebra transparently.

Resolution engine (hornet.combinators): A triple-barrelled continuation monad drives search. Every goal is a function (ctx, subst) → Step, where a Step takes three continuations — success (emit a substitution and continue), failure (backtrack), and prune (implement cut). The combinators then, choice, prunable, neg, and if_then_else compose goals; trampoline() drives the whole thing iteratively to avoid stack overflow.

Examples

The examples/ directory includes:

• append.py — list splitting via backtracking
• queens.py — N-queens constraint solver
• fizzbuzz.py — FizzBuzz via DCGs
• symdiff.py — symbolic differentiation and simplification
• parsing.py — natural language parsing with a German grammar
• turing.py — a Turing machine interpreter
• hanoi.py — Towers of Hanoi with Turtle graphics

License

MIT. See LICENSE.md.