def make_map():
"""
in scheme
(define (map proc lis)
(cond ((null? lis)
'())
((pair? lis)
(cons (proc (car lis))
(map proc (cdr lis))))))
nil ≔ (nil)
map ≔ λ:
F, (cons X, Y) ↦ (cons μ(F, X), μ(map, F, Y))
_, nil ↦ nil
"""
f = Variable("F")
x = Variable("X")
y = Variable("Y")
_ = Variable("_")
_2 = Variable("_")
m = lamb()
m._name = "map"
m._rules = rules([([p(f), p(cons("cons", x, y))],
e(cons("cons", mu(f, [x]), mu(m, [f, y])))),
([p(_), p(nil())], e(nil()))])
return m
def make_pred():
x = Variable("x")
l = lamb()
l._rules = rules([
([_p(_zero())], e(_zero())),
([pp(x) ], e(x))])
l._name = "pred"
return l
def make_append():
x1 = Variable("x")
x2 = Variable("x")
h = Variable("head")
t = Variable("tail")
l = lamb()
l._name = "append"
l._rules = rules([([p(nil()), p(x1)], e(x1)),
([p(cons("cons", h, t)),
p(x2)], e(cons("cons", h, mu(l, [t, x2]))))])
return l
def make_plus():
x1 = Variable("x")
x2 = Variable("x")
x3 = Variable("x")
y = Variable("y")
l = lamb()
l._rules = rules([
([pp(_zero()), pp(_zero())], e(_zero())),
([pp(x1) , pp(_zero())], e(x1)),
([pp(_zero()), pp(x2) ], e(x2)),
([pp(x3) , _p(y) ], e(p_(mu(l, [x3, y]))))])
l._name = "plus"
return l
def make_mult():
_1 = Variable("_")
_2 = Variable("_")
x = Variable("x")
y = Variable("y")
l = lamb()
l._rules = rules([
([pp(_1) , pp(_zero()) ], e(_zero())),
([pp(_zero()), pp(_2) ], e(_zero())),
# ([pp(x) , _p(y) ], e(mu(_plus(),[]), mu(l, [x, y])), x)))
([pp(x) , _p(y) ], e(mu(_plus(),[x, mu(l, [x, y])])))
])
l._name = "mult"
return l
def make_reverse():
a1 = Variable("acc")
a2 = Variable("acc")
h = Variable("head")
t = Variable("tail")
reverse_acc = lamb()
reverse_acc._name = "r_acc"
reverse_acc._rules = rules([([p(nil()), p(a1)], e(a1)),
([p(cons("cons", h, t)),
p(a2)],
e(mu(reverse_acc,
[t, cons("cons", h, a2)])))])
l = Variable("list")
reverse = lamb()
reverse._rules = rules([([p(l)], mu(reverse_acc, [l, nil()]))])
reverse._name = "reverse"
return reverse
def test_lambda_solo(self, parser):
t = parser.parse("""λ. ↦ 1""")
# lambdas cannot compare equal meaningfully
assert t[0]._rules == [
expression.Rule(patterns=[], expression=model.w_integer(1))
]
t = parser.parse("""λ. x ↦ x""")
# lambdas cannot compare equal meaningfully
x = Variable("x")
assert t[0]._rules == [
expression.Rule(patterns=[p(x)], expression=e(x))
]
assert t[0]._rules[0]._patterns[0].variable is \
t[0]._rules[0]._expression.variable
def test_lambda_simple_pattern(self, parser):
t = parser.parse("""λ. 1. 1 ↦ 5""")
# lambdas cannot compare equal meaningfully
assert t[0]._rules == [
expression.Rule(patterns=[p(model.w_integer(1))],
expression=e(model.w_integer(5)))
]
# should work, but meaningless
t = parser.parse("""λ.
1. 1 ↦ 4
2. 2 ↦ 12345
""")
assert t[0]._rules == [
expression.Rule(patterns=[p(model.w_integer(1))],
expression=e(model.w_integer(4))),
expression.Rule(patterns=[p(model.w_integer(2))],
expression=e(model.w_integer(12345)))
]
t = parser.parse("""λ. 1. x ↦ x""")
# lambdas cannot compare equal meaningfully
x = Variable("x")
assert t[0]._rules == [
expression.Rule(patterns=[p(x)], expression=e(x))
]
assert t[0]._rules[0]._patterns[0].variable is \
t[0]._rules[0]._expression.variable
# should work, but meaningless
t = parser.parse("""λ.
1. x ↦ x
2. x ↦ 4
""")
x1 = Variable("x")
x2 = Variable("x")
assert t[0]._rules == [
expression.Rule(patterns=[p(x1)], expression=e(x1)),
expression.Rule(patterns=[p(x2)], expression=e(model.w_integer(4)))
]
assert t[0]._rules[0]._patterns[0].variable.name == \
t[0]._rules[1]._patterns[0].variable.name
assert t[0]._rules[0]._patterns[0].variable is not \
t[0]._rules[1]._patterns[0].variable
def make_mult_acc():
_f1 = Variable("_")
_f2 = Variable("_")
a1 = Variable("accumulator")
a2 = Variable("accumulator")
a3 = Variable("accumulator")
a4 = Variable("accumulator")
f1 = Variable("factor1")
f2 = Variable("factor2")
l_acc = lamb()
l_acc._rules = rules([
([pp(_zero()), pp(_zero()), pp(a1)], e(a1)),
([pp(_f1) , pp(_zero()), pp(a2)], e(a2)),
([pp(_zero()), pp(_f2) , pp(a3)], e(a3)),
([pp(f1) , _p(f2) , pp(a4)],
e(mu(l_acc, [f1, f2, mu(_plus_acc(), [a4, f1])])))
])
l_acc._name = "mult/a"
_1 = Variable("_")
_2 = Variable("_")
x = Variable("x")
y = Variable("y")
l = lamb()
l._rules = rules([
([pp(_1) , pp(_zero())], e(_zero())),
([pp(_zero()), pp(_2) ], e(_zero())),
([pp(x) , pp(y) ], e(mu(l_acc, [x, y, _zero()]))),
# ([pp(x) , _p(y) ], e(mu(_plus(),[]), mu(l, [x, y])), x)))
# ([pp(x) , _p(y) ], e(mu(_plus(),[]), x, mu(l, [x, y])))))
])
l._name = "mult"
return l
def make_plus_acc():
x1 = Variable("x")
x2 = Variable("x")
x3 = Variable("x")
y = Variable("y")
a1 = Variable("accumulator")
a2 = Variable("accumulator")
o1 = Variable("op")
l_acc = lamb()
l_acc._rules = rules([
([pp(a1), pp(_zero())], e(a1)),
([pp(a2), _p(o1) ], e(mu(l_acc, [p_(a2), o1])))])
l_acc._name = "plus/a"
l = lamb()
l._rules = rules([
([pp(_zero()), pp(_zero()) ], e(_zero())),
([pp(x1) , pp(_zero()) ], e(x1)),
([pp(_zero()), pp(x2) ], e(x2)),
([pp(x3) , pp(y) ], e(mu(l_acc, [x3, y])))])
l._name = "plus"
return l
def make_succ():
x = Variable("x")
l = lamb()
l._rules= rules( [([pp(x)], e(p_(x)) )] )
l._name = "succ"
return l
def p_(x):
from theseus.model import w_constructor
return w_constructor(tag("p", 1), [e(x)])
def make_gc_bench():
w_tStart_v0 = Variable("tStart")
w_tStart_v1 = Variable("tStart")
w_tStart_v2 = Variable("tStart")
w_tFinish_v0 = Variable("tFinish")
w_root_v0 = Variable("root")
w_root_v1 = Variable("root")
w_kStretchTreeDepth_v0 = Variable("kStretchTreeDepth")
w_iDepth_v0 = Variable("iDepth")
w_Make_Tree = lamb()
w_Make_Tree._name = "MakeTree"
w_Make_Tree._rules = rules([
([p(integer(0))], e(cons("Node", nil(), nil()))),
([p(w_iDepth_v0)],
e(
cons("Node",
mu(w_Make_Tree,
[mu(_minus(), [w_iDepth_v0, integer(1)])]),
mu(w_Make_Tree,
[mu(_minus(), [w_iDepth_v0, integer(1)])]))))
])
w_gc_bench_cont1 = lamb()
w_gc_bench_cont1._name = "gc_bench$cont0"
w_gc_bench_cont1._rules = rules([(
[p(w_tStart_v2), p(w_tFinish_v0),
p(w_root_v1)], # we 'un-reference'
e(mu(_print_int(), [mu(_minus(), [w_tFinish_v0, w_tStart_v2])])))])
w_gc_bench_cont0 = lamb()
w_gc_bench_cont0._name = "gc_bench$cont0"
w_gc_bench_cont0._rules = rules([([p(w_tStart_v1),
p(w_root_v0)],
e(
mu(w_gc_bench_cont1, [
w_tStart_v1,
mu(_currentmilliseconds(), []),
w_root_v0,
])))])
w_gc_bench_let0 = lamb()
w_gc_bench_let0._name = "gc_bench$let0"
w_gc_bench_let0._rules = rules([
([p(w_kStretchTreeDepth_v0), p(w_tStart_v0)],
e(
mu(w_gc_bench_cont0,
[w_tStart_v0,
mu(w_Make_Tree, [w_kStretchTreeDepth_v0])])))
])
w_gc_bench = lamb()
w_gc_bench._name = "gc_bench"
w_gc_bench._rules = rules([(
[],
e(
mu(
w_gc_bench_let0,
[
integer(18), # kStretchTreeDepth
mu(_currentmilliseconds(), []), # tStart
])))])
return w_gc_bench