def parse_seq(self):
result = []
while True:
token = self.next_noend()
tag = token.tag
if tag == "RawComma":
self.tokeniser.feeder.message("Syntax", "com")
result.append(Symbol("Null"))
self.consume()
elif tag in ("RawRightAssociation", "RawRightBrace",
"RawRightBracket"):
if result:
self.tokeniser.feeder.message("Syntax", "com")
result.append(Symbol("Null"))
break
else:
result.append(self.parse_exp(0))
token = self.next_noend()
tag = token.tag
if tag == "RawComma":
self.consume()
continue
elif tag in ("RawRightAssociation", "RawRightBrace",
"RawRightBracket"):
break
return result
def p_Pattern(self, token):
self.consume()
text = token.text
if "." in text:
name = text[:-2]
if name:
return Node(
"Optional",
Node("Pattern", Symbol(name, context=None), Node("Blank")),
)
else:
return Node("Optional", Node("Blank"))
pieces = text.split("_")
count = len(pieces) - 1
if count == 1:
name = "Blank"
elif count == 2:
name = "BlankSequence"
elif count == 3:
name = "BlankNullSequence"
if pieces[-1]:
blank = Node(name, Symbol(pieces[-1], context=None))
else:
blank = Node(name)
if pieces[0]:
return Node("Pattern", Symbol(pieces[0], context=None), blank)
else:
return blank
def p_PatternTest(self, token):
self.consume()
q = prefix_ops["Definition"]
child = self.parse_exp(q)
return Node(
"Information", child, Node("Rule", Symbol("LongForm"), Symbol("False"))
)
def parse_seq(self):
result = []
while True:
token = self.next_noend()
tag = token.tag
if tag == 'RawComma':
self.tokeniser.feeder.message('Syntax', 'com')
result.append(Symbol('Null'))
self.consume()
elif tag in ('RawRightAssociation', 'RawRightBrace',
'RawRightBracket'):
if result:
self.tokeniser.feeder.message('Syntax', 'com')
result.append(Symbol('Null'))
break
else:
result.append(self.parse_exp(0))
token = self.next_noend()
tag = token.tag
if tag == 'RawComma':
self.consume()
continue
elif tag in ('RawRightAssociation', 'RawRightBrace',
'RawRightBracket'):
break
return result
def p_Pattern(self, token):
self.consume()
text = token.text
if '.' in text:
name = text[:-2]
if name:
return Node(
'Optional',
Node('Pattern', Symbol(name, context=None), Node('Blank')))
else:
return Node('Optional', Node('Blank'))
pieces = text.split('_')
count = len(pieces) - 1
if count == 1:
name = 'Blank'
elif count == 2:
name = 'BlankSequence'
elif count == 3:
name = 'BlankNullSequence'
if pieces[-1]:
blank = Node(name, Symbol(pieces[-1], context=None))
else:
blank = Node(name)
if pieces[0]:
return Node('Pattern', Symbol(pieces[0], context=None), blank)
else:
return blank
def testFunction(self):
self.check('x &', Node('Function', Symbol('x')))
self.check('x \\[Function] y', 'Function[x, y]')
self.check('x \uf4a1 y', 'Function[x, y]')
self.incomplete_error('x \uf4a1')
self.check('x & y',
Node('Times', Node('Function', Symbol('x')), Symbol('y')))
def e_Span(self, expr1, token, p):
q = ternary_ops['Span']
if q < p:
return None
if expr1.get_head_name() == 'Span' and not expr1.parenthesised:
return None
self.consume()
# Span[expr1, expr2]
token = self.next()
if token.tag == 'Span':
expr2 = Symbol('All')
elif token.tag == 'END' and self.bracket_depth == 0:
# So that e.g. 'x = 1 ;;' doesn't wait for newline in the frontend
expr2 = Symbol('All')
return Node('Span', expr1, expr2)
else:
messages = list(self.feeder.messages)
try:
expr2 = self.parse_exp(q + 1)
except TranslateError:
expr2 = Symbol('All')
self.backtrack(token.pos)
self.feeder.messages = messages
token = self.next()
if token.tag == 'Span':
self.consume()
messages = list(self.feeder.messages)
try:
expr3 = self.parse_exp(q + 1)
return Node('Span', expr1, expr2, expr3)
except TranslateError:
self.backtrack(token.pos)
self.feeder.messages = messages
return Node('Span', expr1, expr2)
def testFunction(self):
self.check("x &", Node("Function", Symbol("x")))
self.check("x \\[Function] y", "Function[x, y]")
self.check("x \uf4a1 y", "Function[x, y]")
self.incomplete_error("x \uf4a1")
self.check("x & y",
Node("Times", Node("Function", Symbol("x")), Symbol("y")))
def testBang(self):
self.check('5!', Node('Factorial', Number('5')))
self.check('5 !', Node('Factorial', Number('5')))
self.check('5 ! !', Node('Factorial', Node('Factorial', Number('5'))))
self.check('!1', Node('Not', Number('1')))
self.check('5 !!', Node('Factorial2', Number('5')))
self.check('x ! y', Node('Times', Node('Factorial', Symbol('x')), Symbol('y')))
def parse_inequality(self, expr1, token, p):
tag = token.tag
q = flat_binary_ops[tag]
if q < p:
return None
self.consume()
head = expr1.get_head_name()
expr2 = self.parse_exp(q + 1)
if head == 'Inequality' and not expr1.parenthesised:
expr1.children.append(Symbol(tag))
expr1.children.append(expr2)
elif head in inequality_ops and head != tag and not expr1.parenthesised:
children = []
first = True
for child in expr1.children:
if not first:
children.append(Symbol(head))
children.append(child)
first = False
children.append(Symbol(tag))
children.append(expr2)
expr1 = Node('Inequality', *children)
else:
expr1 = Node(tag, expr1, expr2).flatten()
return expr1
def p_Information(self, token):
self.consume()
q = prefix_ops["Information"]
child = self.parse_exp(q)
if child.__class__ is not Symbol:
raise InvalidSyntaxError()
return Node("Information", child,
Node("Rule", Symbol("LongForm"), Symbol("True")))
def testCompound(self):
self.check('a ; {b}', Node('CompoundExpression', Symbol('a'), Node('List', Symbol('b'))))
self.check('1 ;', Node('CompoundExpression', Number('1'), Symbol('Null')))
self.check('1 ; 5', Node('CompoundExpression', Number('1'), Number('5')))
self.check('4; 1 ; 5', Node('CompoundExpression', Number('4'), Number('1'), Number('5')))
self.check('4;1;', Node('CompoundExpression', Number('4'), Number('1'), Symbol('Null')))
self.check('(a;b);c', Node('CompoundExpression', Node('CompoundExpression', Symbol('a'), Symbol('b')), Symbol('c')))
self.check('f[a;]', 'f[CompoundExpression[a, Null]]')
def testBang(self):
self.check("5!", Node("Factorial", Number("5")))
self.check("5 !", Node("Factorial", Number("5")))
self.check("5 ! !", Node("Factorial", Node("Factorial", Number("5"))))
self.check("!1", Node("Not", Number("1")))
self.check("5 !!", Node("Factorial2", Number("5")))
self.check("x ! y",
Node("Times", Node("Factorial", Symbol("x")), Symbol("y")))
def testTimes(self):
self.check('1 2', Node('Times', Number('1'), Number('2')))
self.check('1*2', Node('Times', Number('1'), Number('2')))
self.check('1 2 3', Node('Times', Number('1'), Number('2'), Number('3')))
self.check('(1 2) 3', Node('Times', Node('Times', Number('1'), Number('2')), Number('3')))
self.check('1*2*3', Node('Times', Number('1'), Number('2'), Number('3')))
self.check('x ^ 2 y', Node('Times', Node('Power', Symbol('x'), Number('2')), Symbol('y')))
def testExpression(self):
self.check('expr1[expr2]', Node('expr1', Symbol('expr2')))
self.check('expr1[expr2][expr3]', Node(Node('expr1', Symbol('expr2')), Symbol('expr3')))
self.check('expr1[[expr2]]', Node('Part', Symbol('expr1'), Symbol('expr2')))
self.check('expr1[[expr2, expr3]]', Node('Part', Symbol('expr1'), Symbol('expr2'), Symbol('expr3')))
self.check('expr1[[expr2]][[expr3]]', Node('Part', Node('Part', Symbol('expr1'), Symbol('expr2')), Symbol('expr3')))
self.check('expr1 ~ expr2 ~ expr3', Node('expr2', Symbol('expr1'), Symbol('expr3')))
self.check('x~f~y', 'f[x, y]')
def testPlus(self):
self.check("+1", Node("Plus", Number("1")))
self.check("1 + 2", Node("Plus", Number("1"), Number("2")))
self.check("1 + 2 + 3",
Node("Plus", Number("1"), Number("2"), Number("3")))
self.check("1 + 2 + 3 + 4", "Plus[1, 2, 3, 4]")
self.check("-a", Node("Times", Number("-1"), Symbol("a")))
self.check(
"a - b",
Node("Plus", Symbol("a"), Node("Times", Number("-1"),
Symbol("b"))))
self.check(
"a*b+c",
Node("Plus", Node("Times", Symbol("a"), Symbol("b")), Symbol("c")))
self.check(
"a*+b+c",
Node(
"Plus",
Node("Times", Symbol("a"), Node("Plus", Symbol("b"))),
Symbol("c"),
),
)
self.check("a+b*c", "a+(b*c)")
self.check("a*b+c", "(a*b) + c")
self.check("1-2", "1 - 2")
def testSpan(self):
self.check(";;", Node("Span", Number("1"), Symbol("All")))
self.check(
"a;;b;;",
Node(
"Times",
Node("Span", Symbol("a"), Symbol("b")),
Node("Span", Number("1"), Symbol("All")),
),
)
self.check("1;;2;;3",
Node("Span", Number("1"), Number("2"), Number("3")))
self.check("1;; ;;3",
Node("Span", Number("1"), Symbol("All"), Number("3")))
self.check("1;;;;3",
Node("Span", Number("1"), Symbol("All"), Number("3")))
self.check(
"1;;2;;",
Node(
"Times",
Node("Span", Number("1"), Number("2")),
Node("Span", Number("1"), Symbol("All")),
),
)
self.check(" ;;2;;3",
Node("Span", Number("1"), Number("2"), Number("3")))
self.check(" ;;2", Node("Span", Number("1"), Number("2")))
self.check("1;; ", Node("Span", Number("1"), Symbol("All")))
self.check(" ;; ", Node("Span", Number("1"), Symbol("All")))
self.check("1;;2;;3;;4;;5;;6",
"Times[Span[1, 2, 3], Span[1, 4, 5], Span[1, 6]]")
self.check("(a;;b);;c", "Span[Span[a, b], c]")
def b_FormBox(self, box1, token, p):
q = misc_ops['FormBox']
if q < p:
return None
if box1 is None:
box1 = Symbol('StandardForm') # RawForm
elif is_symbol_name(box1.value):
box1 = Symbol(box1.value, context=None)
else:
box1 = Node('Removed', String('$$Failure'))
self.consume()
box2 = self.parse_box(q)
return Node('FormBox', box2, box1)
def b_FormBox(self, box1, token, p):
q = misc_ops["FormBox"]
if q < p:
return None
if box1 is None:
box1 = Symbol("StandardForm") # RawForm
elif is_symbol_name(box1.value):
box1 = Symbol(box1.value, context=None)
else:
box1 = Node("Removed", String("$$Failure"))
self.consume()
box2 = self.parse_box(q)
return Node("FormBox", box2, box1)
def testCompound(self):
self.check(
"a ; {b}",
Node("CompoundExpression", Symbol("a"), Node("List", Symbol("b"))),
)
self.check("1 ;",
Node("CompoundExpression", Number("1"), Symbol("Null")))
self.check("1 ; 5", Node("CompoundExpression", Number("1"),
Number("5")))
self.check(
"4; 1 ; 5",
Node("CompoundExpression", Number("4"), Number("1"), Number("5")),
)
self.check(
"4;1;",
Node("CompoundExpression", Number("4"), Number("1"),
Symbol("Null")))
self.check(
"(a;b);c",
Node(
"CompoundExpression",
Node("CompoundExpression", Symbol("a"), Symbol("b")),
Symbol("c"),
),
)
self.check("f[a;]", "f[CompoundExpression[a, Null]]")
def testTimes(self):
self.check("1 2", Node("Times", Number("1"), Number("2")))
self.check("1*2", Node("Times", Number("1"), Number("2")))
self.check("1 2 3", Node("Times", Number("1"), Number("2"),
Number("3")))
self.check(
"(1 2) 3",
Node("Times", Node("Times", Number("1"), Number("2")),
Number("3")),
)
self.check("1*2*3", Node("Times", Number("1"), Number("2"),
Number("3")))
self.check(
"x ^ 2 y",
Node("Times", Node("Power", Symbol("x"), Number("2")),
Symbol("y")),
)
def testBlank(self):
self.check('f_', Node('Pattern', Symbol('f'), Node('Blank')))
self.check('f__', Node('Pattern', Symbol('f'), Node('BlankSequence')))
self.check('f___', Node('Pattern', Symbol('f'), Node('BlankNullSequence')))
self.check('_', 'Blank[]')
self.check('_expr', 'Blank[expr]')
self.check('__', 'BlankSequence[]')
self.check('__expr', 'BlankSequence[expr]')
self.check('___', 'BlankNullSequence[]')
self.check('___expr', 'BlankNullSequence[expr]')
self.check('_.', 'Optional[Blank[]]')
self.check('symb_', 'Pattern[symb, Blank[]]')
self.check('symb_expr', 'Pattern[symb, Blank[expr]]')
self.check('symb__', 'Pattern[symb, BlankSequence[]]')
self.check('symb__expr', 'Pattern[symb, BlankSequence[expr]]')
self.check('symb___', 'Pattern[symb, BlankNullSequence[]]')
self.check('symb___expr', 'Pattern[symb, BlankNullSequence[expr]]')
self.check('symb_.', 'Optional[Pattern[symb, Blank[]]]')
def testPlus(self):
self.check('+1', Node('Plus', Number('1')))
self.check('1 + 2', Node('Plus', Number('1'), Number('2')))
self.check('1 + 2 + 3', Node('Plus', Number('1'), Number('2'), Number('3')))
self.check('1 + 2 + 3 + 4', 'Plus[1, 2, 3, 4]')
self.check('-a', Node('Times', Number('-1'), Symbol('a')))
self.check('a - b', Node('Plus', Symbol('a'), Node('Times', Number('-1'), Symbol('b'))))
self.check('a*b+c', Node('Plus', Node('Times', Symbol('a'), Symbol('b')), Symbol('c')))
self.check('a*+b+c', Node('Plus', Node('Times', Symbol('a'), Node('Plus', Symbol('b'))), Symbol('c')))
self.check('a+b*c', 'a+(b*c)')
self.check('a*b+c', '(a*b) + c')
self.check('1-2', '1 - 2')
def testBlank(self):
self.check("f_", Node("Pattern", Symbol("f"), Node("Blank")))
self.check("f__", Node("Pattern", Symbol("f"), Node("BlankSequence")))
self.check("f___",
Node("Pattern", Symbol("f"), Node("BlankNullSequence")))
self.check("_", "Blank[]")
self.check("_expr", "Blank[expr]")
self.check("__", "BlankSequence[]")
self.check("__expr", "BlankSequence[expr]")
self.check("___", "BlankNullSequence[]")
self.check("___expr", "BlankNullSequence[expr]")
self.check("_.", "Optional[Blank[]]")
self.check("symb_", "Pattern[symb, Blank[]]")
self.check("symb_expr", "Pattern[symb, Blank[expr]]")
self.check("symb__", "Pattern[symb, BlankSequence[]]")
self.check("symb__expr", "Pattern[symb, BlankSequence[expr]]")
self.check("symb___", "Pattern[symb, BlankNullSequence[]]")
self.check("symb___expr", "Pattern[symb, BlankNullSequence[expr]]")
self.check("symb_.", "Optional[Pattern[symb, Blank[]]]")
def testOptional(self):
self.check('x:expr', Node('Pattern', Symbol('x'), Symbol('expr')))
self.check(
'x_:expr',
Node('Optional', Node('Pattern', Symbol('x'), Node('Blank')),
Symbol('expr')))
self.check(
'f:a|b',
Node('Pattern', Symbol('f'),
Node('Alternatives', Symbol('a'), Symbol('b'))))
self.check('rev:(True|False):False',
'Optional[Pattern[rev, Alternatives[True, False]], False]')
def testSpan(self):
self.check(';;', Node('Span', Number('1'), Symbol('All')))
self.check('a;;b;;', Node('Times', Node('Span', Symbol('a'), Symbol('b')), Node('Span', Number('1'), Symbol('All'))))
self.check('1;;2;;3', Node('Span', Number('1'), Number('2'), Number('3')))
self.check('1;; ;;3', Node('Span', Number('1'), Symbol('All'), Number('3')))
self.check('1;;;;3', Node('Span', Number('1'), Symbol('All'), Number('3')))
self.check('1;;2;;', Node('Times', Node('Span', Number('1'), Number('2')), Node('Span', Number('1'), Symbol('All'))))
self.check(' ;;2;;3', Node('Span', Number('1'), Number('2'), Number('3')))
self.check(' ;;2', Node('Span', Number('1'), Number('2')))
self.check('1;; ', Node('Span', Number('1'), Symbol('All')))
self.check(' ;; ', Node('Span', Number('1'), Symbol('All')))
self.check('1;;2;;3;;4;;5;;6', 'Times[Span[1, 2, 3], Span[1, 4, 5], Span[1, 6]]')
self.check('(a;;b);;c', 'Span[Span[a, b], c]')
def e_Semicolon(self, expr1, token, p):
q = flat_binary_ops['CompoundExpression']
if q < p:
return None
self.consume()
# XXX this has to come before call to self.next()
pos = self.tokeniser.pos
messages = list(self.feeder.messages)
# So that e.g. 'x = 1;' doesn't wait for newline in the frontend
tag = self.next().tag
if tag == 'END' and self.bracket_depth == 0:
expr2 = Symbol('Null')
return Node('CompoundExpression', expr1, expr2).flatten()
# XXX look for next expr otherwise backtrack
try:
expr2 = self.parse_exp(q + 1)
except TranslateError:
self.backtrack(pos)
self.feeder.messages = messages
expr2 = Symbol('Null')
return Node('CompoundExpression', expr1, expr2).flatten()
def testOptional(self):
self.check("x:expr", Node("Pattern", Symbol("x"), Symbol("expr")))
self.check(
"x_:expr",
Node("Optional", Node("Pattern", Symbol("x"), Node("Blank")),
Symbol("expr")),
)
self.check(
"f:a|b",
Node("Pattern", Symbol("f"),
Node("Alternatives", Symbol("a"), Symbol("b"))),
)
self.check(
"rev:(True|False):False",
"Optional[Pattern[rev, Alternatives[True, False]], False]",
)
def testSymbol(self):
self.check("xX", Symbol("xX"))
self.check("context`name", Symbol("context`name"))
self.check("`name", Symbol("`name"))
self.check("`context`name", Symbol("`context`name"))
def testNonAscii(self):
self.check("z \\[Conjugate]", Node("Conjugate", Symbol("z")))
self.check("z \\[Transpose]", Node("Transpose", Symbol("z")))
self.check("z \\[ConjugateTranspose]",
Node("ConjugateTranspose", Symbol("z")))
self.check("z \uf3c7 ", Node("Transpose", Symbol("z")))
self.check("z \uf3c8 ", Node("Conjugate", Symbol("z")))
self.check("z \uf3c9 ", Node("ConjugateTranspose", Symbol("z")))
self.check(
"\\[Integral] x \\[DifferentialD] x",
Node("Integrate", Symbol("x"), Symbol("x")),
)
self.check("\\[Del] x", Node("Del", Symbol("x")))
self.check("\\[Square] x", Node("Square", Symbol("x")))
self.check("1 \\[SmallCircle] 2",
Node("SmallCircle", Number("1"), Number("2")))
self.check(
"1 \\[SmallCircle] 2 \\[SmallCircle] 3",
Node("SmallCircle", Number("1"), Number("2"), Number("3")),
)
self.check("1 \u2218 2", Node("SmallCircle", Number("1"), Number("2")))
self.check("1 \\[CircleDot] 2",
Node("CircleDot", Number("1"), Number("2")))
self.check("1 \u2299 2", Node("CircleDot", Number("1"), Number("2")))
self.check("1 \\[Diamond] 2", Node("Diamond", Number("1"),
Number("2")))
self.check("1 \\[Wedge] 2", Node("Wedge", Number("1"), Number("2")))
self.check("1 \\[Vee] 2", Node("Vee", Number("1"), Number("2")))
self.check("1 \\[CircleTimes] 2",
Node("CircleTimes", Number("1"), Number("2")))
self.check("1 \\[CenterDot] 2",
Node("CenterDot", Number("1"), Number("2")))
self.check("1 \\[Star] 2", Node("Star", Number("1"), Number("2")))
self.check("a \\[Cap] b", "Cap[a,b]")
self.check("a \\[Cup] b \\[Cup] c", "Cup[a,b,c]")
self.check("a \u2322 b \u2322 c", "Cap[a,b,c]")
self.check("a \u2323 b", "Cup[a, b]")
self.check("1 \u22C4 2", Node("Diamond", Number("1"), Number("2")))
self.check("1 \u22C0 2", Node("Wedge", Number("1"), Number("2")))
self.check("1 \u22c1 2", Node("Vee", Number("1"), Number("2")))
self.check("1 \u2297 2", Node("CircleTimes", Number("1"), Number("2")))
self.check("1 \u00B7 2", Node("CenterDot", Number("1"), Number("2")))
self.check("1 \u22C6 2", Node("Star", Number("1"), Number("2")))
self.check(
"expr1 ** expr2",
Node("NonCommutativeMultiply", Symbol("expr1"), Symbol("expr2")),
)
self.check(
"expr1 ** expr2 ** expr3",
Node(
"NonCommutativeMultiply",
Symbol("expr1"),
Symbol("expr2"),
Symbol("expr3"),
),
)
self.check("1 \\[Cross] 2", Node("Cross", Number("1"), Number("2")))
self.check("1 \uf4a0 2", Node("Cross", Number("1"), Number("2")))
self.check(
"3\\[Divide]2",
Node("Times", Number("3"), Node("Power", Number("2"),
Number("-1"))),
)
self.check("3 \u00f7 2", "Times[3, Power[2, -1]]")
self.scan_error("3\\2")
self.check("1 \\[Times] 2", Node("Times", Number("1"), Number("2")))
self.check("1 \u00d7 2", Node("Times", Number("1"), Number("2")))
self.check("1 \\[PlusMinus] 2",
Node("PlusMinus", Number("1"), Number("2")))
self.check("1 \\[MinusPlus] 2",
Node("MinusPlus", Number("1"), Number("2")))
self.check("\\[PlusMinus] 1", Node("PlusMinus", Number("1")))
self.check("\\[MinusPlus] 1", Node("MinusPlus", Number("1")))
self.check("\u00b1 1", Node("PlusMinus", Number("1")))
self.check("\u2213 1", Node("MinusPlus", Number("1")))
self.check("1 \\[And] 2", Node("And", Number("1"), Number("2")))
self.check("1 \u2227 2", Node("And", Number("1"), Number("2")))
self.check("1 \\[Or] 2", Node("Or", Number("1"), Number("2")))
self.check("1 \u2228 2", Node("Or", Number("1"), Number("2")))
self.check("a \\[Colon] b", Node("Colon", Symbol("a"), Symbol("b")))
self.check("a \u2236 b", Node("Colon", Symbol("a"), Symbol("b")))
self.check("x1 \\[RightTee] x2", "RightTee[x1, x2]")
self.check("x1 \\[DoubleRightTee] x2", "DoubleRightTee[x1, x2]")
self.check("x1 \\[LeftTee] x2", "LeftTee[x1, x2]")
self.check("x1 \\[DoubleLeftTee] x2", "DoubleLeftTee[x1, x2]")
