Predicates and functions in Python¶

Solvers can be extended with libraries of plain Python functions. Their arguments are converted from terms to Python values, and their results back:

• predicate makes a predicate out of a function returning a boolean (success or failure), or returning (or yielding) tuples of argument values, one per solution;
• function makes an arithmetic function, usable in is/2.

See also: Define predicates in Python.

In [1]:

from tuprolog.solve.function import function
from tuprolog.solve.library import library
from tuprolog.solve.primitive import predicate
from tuprolog.solve.prolog import prolog_solver


def is_prime(n):
    return n > 1 and all(n % d for d in range(2, int(n**0.5) + 1))


def divisors(n, _):
    # the second argument is the output: one solution per divisor
    for d in range(1, n + 1):
        if n % d == 0:
            yield n, d


lib = library(
    "number.theory",
    primitives={"prime/1": predicate(is_prime), "divisor/2": predicate(divisors)},
    functions={"sqrt/1": function(lambda x: x**0.5)},
)
solver = prolog_solver(libraries=lib)

from tuprolog.solve.function import function from tuprolog.solve.library import library from tuprolog.solve.primitive import predicate from tuprolog.solve.prolog import prolog_solver def is_prime(n): return n > 1 and all(n % d for d in range(2, int(n**0.5) + 1)) def divisors(n, _): # the second argument is the output: one solution per divisor for d in range(1, n + 1): if n % d == 0: yield n, d lib = library( "number.theory", primitives={"prime/1": predicate(is_prime), "divisor/2": predicate(divisors)}, functions={"sqrt/1": function(lambda x: x**0.5)}, ) solver = prolog_solver(libraries=lib)

In [2]:

list(solver.query("divisor(12, D)"))

list(solver.query("divisor(12, D)"))

Out[2]:

[{'D': 1}, {'D': 2}, {'D': 3}, {'D': 4}, {'D': 6}, {'D': 12}]

Python predicates mix freely with Prolog code and built-ins:

In [3]:

list(solver.query("findall(P, (member(P, [2, 3, 4, 5, 6, 7, 8, 9]), prime(P)), Primes)"))

list(solver.query("findall(P, (member(P, [2, 3, 4, 5, 6, 7, 8, 9]), prime(P)), Primes)"))

Out[3]:

[{'Primes': [2, 3, 5, 7]}]

In [4]:

list(solver.query("X is sqrt(16) + 1"))

list(solver.query("X is sqrt(16) + 1"))

Out[4]:

[{'X': 5.0}]

Errors¶

Python exceptions raised by these functions become logic errors (a system_error), which Prolog code can handle with catch/3:

In [5]:

from tuprolog.theory.parsing import parse_theory

risky = library("risky", functions={"inverse/1": function(lambda x: 1 / x)})
solver = prolog_solver(
    libraries=risky,
    static_kb=parse_theory("safe_inverse(X, Y) :- catch(Y is inverse(X), error(_, _), Y = none)."),
)
list(solver.query("safe_inverse(4, A), safe_inverse(0, B)"))

from tuprolog.theory.parsing import parse_theory risky = library("risky", functions={"inverse/1": function(lambda x: 1 / x)}) solver = prolog_solver( libraries=risky, static_kb=parse_theory("safe_inverse(X, Y) :- catch(Y is inverse(X), error(_, _), Y = none)."), ) list(solver.query("safe_inverse(4, A), safe_inverse(0, B)"))

Out[5]:

[{'A': 0.25, 'B': 'none'}]