clausal

A Prolog-style logic programming DSL embedded in Python. write relational logic programs in .clausal source files that load via Python's standard import system, with full constraint solving, tabling, DCGs, and a rich standard library.

Features

• .clausal source files — import logic modules with Python's standard import system
• Prolog-style predicates — Horn clauses, unification, backtracking search
• Constraint solving — CLP(FD) for integers, CLP(B) for booleans, dif/2 disequality
• SLG tabling — memoised subgoal calls for termination on cyclic structures
• DCGs — Definite Clause Grammars with >> syntax and Phrase/2,3
• Well-Founded Semantics — negation-as-failure for tabled predicates
• Module system — -import_from/2, -import_module/1, qualified calls
• Meta-predicates — findall/3, bagof/3, setof/3, forall/2, Call/N
• Higher-order — maplist/2,3, foldl/4, include/3, exclude/3
• Python interop — ++expr escape, lambda goal closures, f-string support in terms
• SciPy integration — wrappers for scipy.special, scipy.linalg, scipy.optimize, scipy.interpolate, scipy.signal
• Regex — match/2,3, search/2,3, replace/4, split/3 with auto-binding goal expansion
• Term expansion — macro system for source-level term rewriting
• C extensions — fast logic variables, trail-based backtracking, trampoline (no WAM)

Installation

pip install clausal

Requires Python ≥ 3.13 and a C compiler (used automatically by pip when building from source).

Quick start

.clausal source files

Facts use a trailing comma. Rules use <- with a parenthesised, comma-separated body. Predicate names are lowercase (snake_case by convention); variables are ALL_CAPS.

# family.clausal
parent(tom, bob),
parent(tom, liz),
parent(bob, ann),
parent(bob, pat),

grandparent(X, Z) <- (parent(X, Y), parent(Y, Z))

import family   # .clausal files load via the import hook

from clausal import call, deref, Var

GRANDCHILD = Var()
results = [deref(GRANDCHILD) for _ in call("Grandparent", "tom", GRANDCHILD, module=family)]
# → ['ann', 'pat']

Arithmetic

# fib.clausal
Fib(0, 0),
Fib(1, 1),
Fib(N, RESULT) <- (
    N > 1,
    N1 := N - 1,
    N2 := N - 2,
    Fib(N1, A),
    Fib(N2, B),
    RESULT := A + B
)

Tabling (memoisation for cyclic graphs)

-table(Path/2)

Edge(1, 2),
Edge(2, 3),
Edge(3, 1),

Path(X, Y) <- Edge(X, Y)
Path(X, Y) <- (Edge(X, Z), Path(Z, Y))

DCGs

Sentence >> (NounPhrase, VerbPhrase)
NounPhrase >> (["the", "dog"] or ["the", "cat"])
VerbPhrase >> (["runs"] or ["barks"])

from clausal import once
result = once(call("Phrase", "Sentence", ["the", "cat", "runs"], module=grammar))

CLP(FD) — constraint logic programming over integers

Sendmoney(S, E, N, D, M, O, R, Y) <- (
    in_domain([S, E, N, D, M, O, R, Y], 0, 9),
    all_different([S, E, N, D, M, O, R, Y]),
    S != 0,
    M != 0,
    label([S, E, N, D, M, O, R, Y]),
    SEND  := S * 1000 + E * 100 + N * 10 + D,
    MORE  := M * 1000 + O * 100 + R * 10 + E,
    MONEY := M * 10000 + O * 1000 + N * 100 + E * 10 + Y,
    SEND + MORE == MONEY
)

Meta-predicates

Squares(Ns, Squares) <- (
    findall(
        Sq,
        (in_(X, Ns), Sq := X * X),
        Squares
    )
)

Testing

.clausal files can include inline tests as Test/1 clauses:

Test("fib(5) = 5") <- Fib(5, 5)
Test("tom's grandchildren") <- (
    Grandparent(tom, ann),
    Grandparent(tom, pat)
)

Standalone runner:

python -m clausal.testing clausal/examples/           # all .clausal files
python -m clausal.testing clausal/examples/hanoi.clausal  # single file
python -m clausal.testing -v clausal/examples/        # verbose

Via pytest (.clausal tests collected automatically):

python -m pytest tests/ clausal/examples/ -q

Logic variables and backtracking

The C extension clausal.logic.variables provides Prolog-style logic variables and trail-based backtracking without a Warren Abstract Machine.

from clausal.logic.variables import Var, Trail, unify, is_var

trail = Trail()
X = Var()
Y = Var()

unify(X, 42, trail)
assert X.value == 42

mark = trail.mark()
unify(Y, "temporary", trail)
trail.undo(mark)
assert is_var(Y)   # Y is unbound again

Constraints

from clausal.logic.variables import Var, Trail, unify
from clausal.logic.constraints import dif

trail = Trail()
X, Y = Var(), Var()

dif(X, Y, trail)      # post: X ≠ Y
unify(X, 1, trail)    # ok — still satisfiable
unify(Y, 2, trail)    # ok — satisfied (1 ≠ 2)

Requirements

• Python ≥ 3.13
• greenlet
• pyyaml ≥ 6.0
• C compiler (for building from source)

License

MIT