def define_nat_double(prelude):
"""Defines a function that doubles a nat. Adds a field called
'double' to the prelude, giving the GlobalVar pointing to
the function.
"""
prelude.double = GlobalVar("double")
x = Var("x", prelude.nat())
y = Var("y")
z_case = Clause(PatternConstructor(prelude.z), prelude.z())
s_case = Clause(PatternConstructor(prelude.s, [PatternVar(y)]),
prelude.s(prelude.s(prelude.double(y))))
prelude.mod[prelude.double] = Function([x], Match(x, [z_case, s_case]))
def define_nat_add(prelude):
"""Defines a function that adds two nats and adds a field to the
prelude 'add' giving the GlobalVar pointing to that function.
"""
prelude.add = GlobalVar("add")
x = Var("x", prelude.nat())
y = Var("y", prelude.nat())
a = Var("a")
z_case = Clause(PatternConstructor(prelude.z), y)
s_case = Clause(PatternConstructor(prelude.s, [PatternVar(a)]),
prelude.s(prelude.add(a, y)))
prelude.mod[prelude.add] = Function([x, y], Match(x, [z_case, s_case]))
def define_nat_nth(prelude):
"""Defines a function to get the nth eleemnt of a list using
a nat to index into the list.
nat_nth(l, n): fun<a>(list[a], nat) -> a
"""
prelude.nat_nth = GlobalVar("nat_nth")
a = TypeVar("a")
x = Var("x", prelude.l(a))
n = Var("n", prelude.nat())
y = Var("y")
z_case = Clause(PatternConstructor(prelude.z), prelude.hd(x))
s_case = Clause(PatternConstructor(prelude.s, [PatternVar(y)]),
prelude.nat_nth(prelude.tl(x), y))
prelude.mod[prelude.nat_nth] = Function([x, n], Match(n, [z_case, s_case]),
a, [a])
def define_nat_iterate(prelude):
"""Defines a function that takes a number n and a function f;
returns a closure that takes an argument and applies f
n times to its argument.
Signature: fn<a>(fn(a) -> a, nat) -> fn(a) -> a
"""
prelude.nat_iterate = GlobalVar("nat_iterate")
a = TypeVar("a")
f = Var("f", FuncType([a], a))
x = Var("x", prelude.nat())
y = Var("y", prelude.nat())
z_case = Clause(PatternConstructor(prelude.z), prelude.id)
s_case = Clause(PatternConstructor(prelude.s, [PatternVar(y)]),
prelude.compose(f, prelude.nat_iterate(f, y)))
prelude.mod[prelude.nat_iterate] = Function([f, x],
Match(x, [z_case, s_case]),
FuncType([a], a), [a])
def define_nat_update(prelude):
"""Defines a function to update the nth element of a list and return the updated list.
nat_update(l, i, v) : fun<a>(list[a], nat, a) -> list[a]
"""
prelude.nat_update = GlobalVar("nat_update")
a = TypeVar("a")
# pylint: disable=invalid-name
l = Var("l", prelude.l(a))
n = Var("n", prelude.nat())
v = Var("v", a)
y = Var("y")
z_case = Clause(PatternConstructor(prelude.z),
prelude.cons(v, prelude.tl(l)))
s_case = Clause(
PatternConstructor(prelude.s, [PatternVar(y)]),
prelude.cons(prelude.hd(l), prelude.nat_update(prelude.tl(l), y, v)))
prelude.mod[prelude.nat_update] = Function([l, n, v],
Match(n, [z_case, s_case]),
prelude.l(a), [a])