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rl/Lib/site-packages/sympy/strategies/branch/__init__.py

@@ -0,0 +1,14 @@
+from . import traverse
+from .core import (
+    condition, debug, multiplex, exhaust, notempty,
+    chain, onaction, sfilter, yieldify, do_one, identity)
+from .tools import canon
+
+__all__ = [
+    'traverse',
+
+    'condition', 'debug', 'multiplex', 'exhaust', 'notempty', 'chain',
+    'onaction', 'sfilter', 'yieldify', 'do_one', 'identity',
+
+    'canon',
+]

rl/Lib/site-packages/sympy/strategies/branch/core.py

@@ -0,0 +1,116 @@
+""" Generic SymPy-Independent Strategies """
+
+
+def identity(x):
+    yield x
+
+
+def exhaust(brule):
+    """ Apply a branching rule repeatedly until it has no effect """
+    def exhaust_brl(expr):
+        seen = {expr}
+        for nexpr in brule(expr):
+            if nexpr not in seen:
+                seen.add(nexpr)
+                yield from exhaust_brl(nexpr)
+        if seen == {expr}:
+            yield expr
+    return exhaust_brl
+
+
+def onaction(brule, fn):
+    def onaction_brl(expr):
+        for result in brule(expr):
+            if result != expr:
+                fn(brule, expr, result)
+            yield result
+    return onaction_brl
+
+
+def debug(brule, file=None):
+    """ Print the input and output expressions at each rule application """
+    if not file:
+        from sys import stdout
+        file = stdout
+
+    def write(brl, expr, result):
+        file.write("Rule: %s\n" % brl.__name__)
+        file.write("In: %s\nOut: %s\n\n" % (expr, result))
+
+    return onaction(brule, write)
+
+
+def multiplex(*brules):
+    """ Multiplex many branching rules into one """
+    def multiplex_brl(expr):
+        seen = set()
+        for brl in brules:
+            for nexpr in brl(expr):
+                if nexpr not in seen:
+                    seen.add(nexpr)
+                    yield nexpr
+    return multiplex_brl
+
+
+def condition(cond, brule):
+    """ Only apply branching rule if condition is true """
+    def conditioned_brl(expr):
+        if cond(expr):
+            yield from brule(expr)
+        else:
+            pass
+    return conditioned_brl
+
+
+def sfilter(pred, brule):
+    """ Yield only those results which satisfy the predicate """
+    def filtered_brl(expr):
+        yield from filter(pred, brule(expr))
+    return filtered_brl
+
+
+def notempty(brule):
+    def notempty_brl(expr):
+        yielded = False
+        for nexpr in brule(expr):
+            yielded = True
+            yield nexpr
+        if not yielded:
+            yield expr
+    return notempty_brl
+
+
+def do_one(*brules):
+    """ Execute one of the branching rules """
+    def do_one_brl(expr):
+        yielded = False
+        for brl in brules:
+            for nexpr in brl(expr):
+                yielded = True
+                yield nexpr
+            if yielded:
+                return
+    return do_one_brl
+
+
+def chain(*brules):
+    """
+    Compose a sequence of brules so that they apply to the expr sequentially
+    """
+    def chain_brl(expr):
+        if not brules:
+            yield expr
+            return
+
+        head, tail = brules[0], brules[1:]
+        for nexpr in head(expr):
+            yield from chain(*tail)(nexpr)
+
+    return chain_brl
+
+
+def yieldify(rl):
+    """ Turn a rule into a branching rule """
+    def brl(expr):
+        yield rl(expr)
+    return brl

rl/Lib/site-packages/sympy/strategies/branch/tests/test_core.py

@@ -0,0 +1,117 @@
+from sympy.strategies.branch.core import (
+    exhaust, debug, multiplex, condition, notempty, chain, onaction, sfilter,
+    yieldify, do_one, identity)
+
+
+def posdec(x):
+    if x > 0:
+        yield x - 1
+    else:
+        yield x
+
+
+def branch5(x):
+    if 0 < x < 5:
+        yield x - 1
+    elif 5 < x < 10:
+        yield x + 1
+    elif x == 5:
+        yield x + 1
+        yield x - 1
+    else:
+        yield x
+
+
+def even(x):
+    return x % 2 == 0
+
+
+def inc(x):
+    yield x + 1
+
+
+def one_to_n(n):
+    yield from range(n)
+
+
+def test_exhaust():
+    brl = exhaust(branch5)
+    assert set(brl(3)) == {0}
+    assert set(brl(7)) == {10}
+    assert set(brl(5)) == {0, 10}
+
+
+def test_debug():
+    from io import StringIO
+    file = StringIO()
+    rl = debug(posdec, file)
+    list(rl(5))
+    log = file.getvalue()
+    file.close()
+
+    assert posdec.__name__ in log
+    assert '5' in log
+    assert '4' in log
+
+
+def test_multiplex():
+    brl = multiplex(posdec, branch5)
+    assert set(brl(3)) == {2}
+    assert set(brl(7)) == {6, 8}
+    assert set(brl(5)) == {4, 6}
+
+
+def test_condition():
+    brl = condition(even, branch5)
+    assert set(brl(4)) == set(branch5(4))
+    assert set(brl(5)) == set()
+
+
+def test_sfilter():
+    brl = sfilter(even, one_to_n)
+    assert set(brl(10)) == {0, 2, 4, 6, 8}
+
+
+def test_notempty():
+    def ident_if_even(x):
+        if even(x):
+            yield x
+
+    brl = notempty(ident_if_even)
+    assert set(brl(4)) == {4}
+    assert set(brl(5)) == {5}
+
+
+def test_chain():
+    assert list(chain()(2)) == [2]  # identity
+    assert list(chain(inc, inc)(2)) == [4]
+    assert list(chain(branch5, inc)(4)) == [4]
+    assert set(chain(branch5, inc)(5)) == {5, 7}
+    assert list(chain(inc, branch5)(5)) == [7]
+
+
+def test_onaction():
+    L = []
+
+    def record(fn, input, output):
+        L.append((input, output))
+
+    list(onaction(inc, record)(2))
+    assert L == [(2, 3)]
+
+    list(onaction(identity, record)(2))
+    assert L == [(2, 3)]
+
+
+def test_yieldify():
+    yinc = yieldify(lambda x: x + 1)
+    assert list(yinc(3)) == [4]
+
+
+def test_do_one():
+    def bad(expr):
+        raise ValueError
+
+    assert list(do_one(inc)(3)) == [4]
+    assert list(do_one(inc, bad)(3)) == [4]
+    assert list(do_one(inc, posdec)(3)) == [4]

rl/Lib/site-packages/sympy/strategies/branch/tests/test_tools.py

@@ -0,0 +1,42 @@
+from sympy.strategies.branch.tools import canon
+from sympy.core.basic import Basic
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+
+
+def posdec(x):
+    if isinstance(x, Integer) and x > 0:
+        yield x - 1
+    else:
+        yield x
+
+
+def branch5(x):
+    if isinstance(x, Integer):
+        if 0 < x < 5:
+            yield x - 1
+        elif 5 < x < 10:
+            yield x + 1
+        elif x == 5:
+            yield x + 1
+            yield x - 1
+        else:
+            yield x
+
+
+def test_zero_ints():
+    expr = Basic(S(2), Basic(S(5), S(3)), S(8))
+    expected = {Basic(S(0), Basic(S(0), S(0)), S(0))}
+
+    brl = canon(posdec)
+    assert set(brl(expr)) == expected
+
+
+def test_split5():
+    expr = Basic(S(2), Basic(S(5), S(3)), S(8))
+    expected = {
+        Basic(S(0), Basic(S(0), S(0)), S(10)),
+        Basic(S(0), Basic(S(10), S(0)), S(10))}
+
+    brl = canon(branch5)
+    assert set(brl(expr)) == expected

rl/Lib/site-packages/sympy/strategies/branch/tests/test_traverse.py

@@ -0,0 +1,53 @@
+from sympy.core.basic import Basic
+from sympy.core.numbers import Integer
+from sympy.core.singleton import S
+from sympy.strategies.branch.traverse import top_down, sall
+from sympy.strategies.branch.core import do_one, identity
+
+
+def inc(x):
+    if isinstance(x, Integer):
+        yield x + 1
+
+
+def test_top_down_easy():
+    expr = Basic(S(1), S(2))
+    expected = Basic(S(2), S(3))
+    brl = top_down(inc)
+
+    assert set(brl(expr)) == {expected}
+
+
+def test_top_down_big_tree():
+    expr = Basic(S(1), Basic(S(2)), Basic(S(3), Basic(S(4)), S(5)))
+    expected = Basic(S(2), Basic(S(3)), Basic(S(4), Basic(S(5)), S(6)))
+    brl = top_down(inc)
+
+    assert set(brl(expr)) == {expected}
+
+
+def test_top_down_harder_function():
+    def split5(x):
+        if x == 5:
+            yield x - 1
+            yield x + 1
+
+    expr = Basic(Basic(S(5), S(6)), S(1))
+    expected = {Basic(Basic(S(4), S(6)), S(1)), Basic(Basic(S(6), S(6)), S(1))}
+    brl = top_down(split5)
+
+    assert set(brl(expr)) == expected
+
+
+def test_sall():
+    expr = Basic(S(1), S(2))
+    expected = Basic(S(2), S(3))
+    brl = sall(inc)
+
+    assert list(brl(expr)) == [expected]
+
+    expr = Basic(S(1), S(2), Basic(S(3), S(4)))
+    expected = Basic(S(2), S(3), Basic(S(3), S(4)))
+    brl = sall(do_one(inc, identity))
+
+    assert list(brl(expr)) == [expected]

rl/Lib/site-packages/sympy/strategies/branch/tools.py

@@ -0,0 +1,12 @@
+from .core import exhaust, multiplex
+from .traverse import top_down
+
+
+def canon(*rules):
+    """ Strategy for canonicalization
+
+    Apply each branching rule in a top-down fashion through the tree.
+    Multiplex through all branching rule traversals
+    Keep doing this until there is no change.
+    """
+    return exhaust(multiplex(*map(top_down, rules)))

rl/Lib/site-packages/sympy/strategies/branch/traverse.py

@@ -0,0 +1,25 @@
+""" Branching Strategies to Traverse a Tree """
+from itertools import product
+from sympy.strategies.util import basic_fns
+from .core import chain, identity, do_one
+
+
+def top_down(brule, fns=basic_fns):
+    """ Apply a rule down a tree running it on the top nodes first """
+    return chain(do_one(brule, identity),
+                 lambda expr: sall(top_down(brule, fns), fns)(expr))
+
+
+def sall(brule, fns=basic_fns):
+    """ Strategic all - apply rule to args """
+    op, new, children, leaf = map(fns.get, ('op', 'new', 'children', 'leaf'))
+
+    def all_rl(expr):
+        if leaf(expr):
+            yield expr
+        else:
+            myop = op(expr)
+            argss = product(*map(brule, children(expr)))
+            for args in argss:
+                yield new(myop, *args)
+    return all_rl