#!/usr/bin/env python
# coding: utf-8

# # Railroad Diagrams
# 
# The code in this notebook helps with drawing syntax-diagrams.  It is a (slightly customized) copy of the [excellent library from Tab Atkins jr.](https://github.com/tabatkins/railroad-diagrams), which unfortunately is not available as a Python package.

# **Prerequisites**
# 
# This notebook needs some understanding on advanced concepts in Python and Graphics, notably 
#     * classes
#     * the Python `with` statement
#     * Scalable Vector Graphics

# ## Excursion: Railroad diagrams implementation

# In[1]:


import bookutils.setup


# In[2]:


import re
import io


# In[3]:


class C:
    # Display constants
    DEBUG = False  # if true, writes some debug information into attributes
    VS = 8  # minimum vertical separation between things. For a 3px stroke, must be at least 4
    AR = 10  # radius of arcs
    DIAGRAM_CLASS = 'railroad-diagram'  # class to put on the root <svg>
    # is the stroke width an odd (1px, 3px, etc) pixel length?
    STROKE_ODD_PIXEL_LENGTH = True
    # how to align items when they have extra space. left/right/center
    INTERNAL_ALIGNMENT = 'center'
    # width of each monospace character. play until you find the right value
    # for your font
    CHAR_WIDTH = 8.5
    COMMENT_CHAR_WIDTH = 7  # comments are in smaller text by default

    DEFAULT_STYLE = '''\
    svg.railroad-diagram {
    }
    svg.railroad-diagram path {
        stroke-width:3;
        stroke:black;
        fill:white;
    }
    svg.railroad-diagram text {
        font:14px "Fira Mono", monospace;
        text-anchor:middle;
    }
    svg.railroad-diagram text.label{
        text-anchor:start;
    }
    svg.railroad-diagram text.comment{
        font:italic 12px "Fira Mono", monospace;
    }
    svg.railroad-diagram rect{
        stroke-width:2;
        stroke:black;
        fill:mistyrose;
    }
'''


# In[4]:


def e(text):
    text = re.sub(r"&", '&amp;', str(text))
    text = re.sub(r"<", '&lt;', str(text))
    text = re.sub(r">", '&gt;', str(text))
    return str(text)


# In[5]:


def determineGaps(outer, inner):
    diff = outer - inner
    if C.INTERNAL_ALIGNMENT == 'left':
        return 0, diff
    elif C.INTERNAL_ALIGNMENT == 'right':
        return diff, 0
    else:
        return diff / 2, diff / 2


# In[6]:


def doubleenumerate(seq):
    length = len(list(seq))
    for i, item in enumerate(seq):
        yield i, i - length, item


# In[7]:


def addDebug(el):
    if not C.DEBUG:
        return
    el.attrs['data-x'] = "{0} w:{1} h:{2}/{3}/{4}".format(
        type(el).__name__, el.width, el.up, el.height, el.down)


# In[8]:


class DiagramItem:
    def __init__(self, name, attrs=None, text=None):
        self.name = name
        # up = distance it projects above the entry line
        # height = distance between the entry/exit lines
        # down = distance it projects below the exit line
        self.height = 0
        self.attrs = attrs or {}
        self.children = [text] if text else []
        self.needsSpace = False

    def format(self, x, y, width):
        raise NotImplementedError  # Virtual

    def addTo(self, parent):
        parent.children.append(self)
        return self

    def writeSvg(self, write):
        write(u'<{0}'.format(self.name))
        for name, value in sorted(self.attrs.items()):
            write(u' {0}="{1}"'.format(name, e(value)))
        write(u'>')
        if self.name in ["g", "svg"]:
            write(u'\n')
        for child in self.children:
            if isinstance(child, DiagramItem):
                child.writeSvg(write)
            else:
                write(e(child))
        write(u'</{0}>'.format(self.name))

    def __eq__(self, other):
        return isinstance(self, type(
            other)) and self.__dict__ == other.__dict__

    def __ne__(self, other):
        return not (self == other)


# In[9]:


class Path(DiagramItem):
    def __init__(self, x, y):
        self.x = x
        self.y = y
        DiagramItem.__init__(self, 'path', {'d': 'M%s %s' % (x, y)})

    def m(self, x, y):
        self.attrs['d'] += 'm{0} {1}'.format(x, y)
        return self

    def ll(self, x, y):   # was l(), which violates PEP8 -- AZ
        self.attrs['d'] += 'l{0} {1}'.format(x, y)
        return self

    def h(self, val):
        self.attrs['d'] += 'h{0}'.format(val)
        return self

    def right(self, val):
        return self.h(max(0, val))

    def left(self, val):
        return self.h(-max(0, val))

    def v(self, val):
        self.attrs['d'] += 'v{0}'.format(val)
        return self

    def down(self, val):
        return self.v(max(0, val))

    def up(self, val):
        return self.v(-max(0, val))

    def arc_8(self, start, dir):
        # 1/8 of a circle
        arc = C.AR
        s2 = 1 / math.sqrt(2) * arc
        s2inv = (arc - s2)
        path = "a {0} {0} 0 0 {1} ".format(arc, "1" if dir == 'cw' else "0")
        sd = start + dir
        if sd == 'ncw':
            offset = [s2, s2inv]
        elif sd == 'necw':
            offset = [s2inv, s2]
        elif sd == 'ecw':
            offset = [-s2inv, s2]
        elif sd == 'secw':
            offset = [-s2, s2inv]
        elif sd == 'scw':
            offset = [-s2, -s2inv]
        elif sd == 'swcw':
            offset = [-s2inv, -s2]
        elif sd == 'wcw':
            offset = [s2inv, -s2]
        elif sd == 'nwcw':
            offset = [s2, -s2inv]
        elif sd == 'nccw':
            offset = [-s2, s2inv]
        elif sd == 'nwccw':
            offset = [-s2inv, s2]
        elif sd == 'wccw':
            offset = [s2inv, s2]
        elif sd == 'swccw':
            offset = [s2, s2inv]
        elif sd == 'sccw':
            offset = [s2, -s2inv]
        elif sd == 'seccw':
            offset = [s2inv, -s2]
        elif sd == 'eccw':
            offset = [-s2inv, -s2]
        elif sd == 'neccw':
            offset = [-s2, -s2inv]

        path += " ".join(str(x) for x in offset)
        self.attrs['d'] += path
        return self

    def arc(self, sweep):
        x = C.AR
        y = C.AR
        if sweep[0] == 'e' or sweep[1] == 'w':
            x *= -1
        if sweep[0] == 's' or sweep[1] == 'n':
            y *= -1
        cw = 1 if sweep == 'ne' or sweep == 'es' or sweep == 'sw' or sweep == 'wn' else 0
        self.attrs['d'] += 'a{0} {0} 0 0 {1} {2} {3}'.format(C.AR, cw, x, y)
        return self

    def format(self):
        self.attrs['d'] += 'h.5'
        return self

    def __repr__(self):
        return 'Path(%r, %r)' % (self.x, self.y)


# In[10]:


def wrapString(value):
    return value if isinstance(value, DiagramItem) else Terminal(value)


# In[11]:


class Style(DiagramItem):
    def __init__(self, css):
        self.name = 'style'
        self.css = css
        self.height = 0
        self.width = 0
        self.needsSpace = False

    def __repr__(self):
        return 'Style(%r)' % css

    def format(self, x, y, width):
        return self

    def writeSvg(self, write):
        # Write included stylesheet as CDATA. See
        # https:#developer.mozilla.org/en-US/docs/Web/SVG/Element/style
        cdata = u'/* <![CDATA[ */\n{css}\n/* ]]> */\n'.format(css=self.css)
        write(u'<style>{cdata}</style>'.format(cdata=cdata))


# In[12]:


class Diagram(DiagramItem):
    def __init__(self, *items, **kwargs):
        # Accepts a type=[simple|complex] kwarg
        DiagramItem.__init__(
            self, 'svg', {'class': C.DIAGRAM_CLASS, 'xmlns': "http://www.w3.org/2000/svg"})
        self.type = kwargs.get("type", "simple")
        self.items = [wrapString(item) for item in items]
        if items and not isinstance(items[0], Start):
            self.items.insert(0, Start(self.type))
        if items and not isinstance(items[-1], End):
            self.items.append(End(self.type))
        self.css = kwargs.get("css", C.DEFAULT_STYLE)
        if self.css:
            self.items.insert(0, Style(self.css))
        self.up = 0
        self.down = 0
        self.height = 0
        self.width = 0
        for item in self.items:
            if isinstance(item, Style):
                continue
            self.width += item.width + (20 if item.needsSpace else 0)
            self.up = max(self.up, item.up - self.height)
            self.height += item.height
            self.down = max(self.down - item.height, item.down)
        if self.items[0].needsSpace:
            self.width -= 10
        if self.items[-1].needsSpace:
            self.width -= 10
        self.formatted = False

    def __repr__(self):
        if self.css:
            items = ', '.join(map(repr, self.items[2:-1]))
        else:
            items = ', '.join(map(repr, self.items[1:-1]))
        pieces = [] if not items else [items]
        if self.css != C.DEFAULT_STYLE:
            pieces.append('css=%r' % self.css)
        if self.type != 'simple':
            pieces.append('type=%r' % self.type)
        return 'Diagram(%s)' % ', '.join(pieces)

    def format(self, paddingTop=20, paddingRight=None,
               paddingBottom=None, paddingLeft=None):
        if paddingRight is None:
            paddingRight = paddingTop
        if paddingBottom is None:
            paddingBottom = paddingTop
        if paddingLeft is None:
            paddingLeft = paddingRight
        x = paddingLeft
        y = paddingTop + self.up
        g = DiagramItem('g')
        if C.STROKE_ODD_PIXEL_LENGTH:
            g.attrs['transform'] = 'translate(.5 .5)'
        for item in self.items:
            if item.needsSpace:
                Path(x, y).h(10).addTo(g)
                x += 10
            item.format(x, y, item.width).addTo(g)
            x += item.width
            y += item.height
            if item.needsSpace:
                Path(x, y).h(10).addTo(g)
                x += 10
        self.attrs['width'] = self.width + paddingLeft + paddingRight
        self.attrs['height'] = self.up + self.height + \
            self.down + paddingTop + paddingBottom
        self.attrs['viewBox'] = "0 0 {width} {height}".format(**self.attrs)
        g.addTo(self)
        self.formatted = True
        return self

    def writeSvg(self, write):
        if not self.formatted:
            self.format()
        return DiagramItem.writeSvg(self, write)

    def parseCSSGrammar(self, text):
        token_patterns = {
            'keyword': r"[\w-]+\(?",
            'type': r"<[\w-]+(\(\))?>",
            'char': r"[/,()]",
            'literal': r"'(.)'",
            'openbracket': r"\[",
            'closebracket': r"\]",
            'closebracketbang': r"\]!",
            'bar': r"\|",
            'doublebar': r"\|\|",
            'doubleand': r"&&",
            'multstar': r"\*",
            'multplus': r"\+",
            'multhash': r"#",
            'multnum1': r"{\s*(\d+)\s*}",
            'multnum2': r"{\s*(\d+)\s*,\s*(\d*)\s*}",
            'multhashnum1': r"#{\s*(\d+)\s*}",
            'multhashnum2': r"{\s*(\d+)\s*,\s*(\d*)\s*}"
        }


# In[13]:


class Sequence(DiagramItem):
    def __init__(self, *items):
        DiagramItem.__init__(self, 'g')
        self.items = [wrapString(item) for item in items]
        self.needsSpace = True
        self.up = 0
        self.down = 0
        self.height = 0
        self.width = 0
        for item in self.items:
            self.width += item.width + (20 if item.needsSpace else 0)
            self.up = max(self.up, item.up - self.height)
            self.height += item.height
            self.down = max(self.down - item.height, item.down)
        if self.items[0].needsSpace:
            self.width -= 10
        if self.items[-1].needsSpace:
            self.width -= 10
        addDebug(self)

    def __repr__(self):
        items = ', '.join(map(repr, self.items))
        return 'Sequence(%s)' % items

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y + self.height).h(rightGap).addTo(self)
        x += leftGap
        for i, item in enumerate(self.items):
            if item.needsSpace and i > 0:
                Path(x, y).h(10).addTo(self)
                x += 10
            item.format(x, y, item.width).addTo(self)
            x += item.width
            y += item.height
            if item.needsSpace and i < len(self.items) - 1:
                Path(x, y).h(10).addTo(self)
                x += 10
        return self


# In[14]:


class Stack(DiagramItem):
    def __init__(self, *items):
        DiagramItem.__init__(self, 'g')
        self.items = [wrapString(item) for item in items]
        self.needsSpace = True
        self.width = max(item.width + (20 if item.needsSpace else 0)
                         for item in self.items)
        # pretty sure that space calc is totes wrong
        if len(self.items) > 1:
            self.width += C.AR * 2
        self.up = self.items[0].up
        self.down = self.items[-1].down
        self.height = 0
        last = len(self.items) - 1
        for i, item in enumerate(self.items):
            self.height += item.height
            if i > 0:
                self.height += max(C.AR * 2, item.up + C.VS)
            if i < last:
                self.height += max(C.AR * 2, item.down + C.VS)
        addDebug(self)

    def __repr__(self):
        items = ', '.join(repr(item) for item in self.items)
        return 'Stack(%s)' % items

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)
        Path(x, y).h(leftGap).addTo(self)
        x += leftGap
        xInitial = x
        if len(self.items) > 1:
            Path(x, y).h(C.AR).addTo(self)
            x += C.AR
            innerWidth = self.width - C.AR * 2
        else:
            innerWidth = self.width
        for i, item in enumerate(self.items):
            item.format(x, y, innerWidth).addTo(self)
            x += innerWidth
            y += item.height
            if i != len(self.items) - 1:
                (Path(x, y)
                    .arc('ne').down(max(0, item.down + C.VS - C.AR * 2))
                    .arc('es').left(innerWidth)
                    .arc('nw').down(max(0, self.items[i + 1].up + C.VS - C.AR * 2))
                    .arc('ws').addTo(self))
                y += max(item.down + C.VS, C.AR * 2) + \
                    max(self.items[i + 1].up + C.VS, C.AR * 2)
                x = xInitial + C.AR
        if len(self.items) > 1:
            Path(x, y).h(C.AR).addTo(self)
            x += C.AR
        Path(x, y).h(rightGap).addTo(self)
        return self


# In[15]:


class OptionalSequence(DiagramItem):
    def __new__(cls, *items):
        if len(items) <= 1:
            return Sequence(*items)
        else:
            return super(OptionalSequence, cls).__new__(cls)

    def __init__(self, *items):
        DiagramItem.__init__(self, 'g')
        self.items = [wrapString(item) for item in items]
        self.needsSpace = False
        self.width = 0
        self.up = 0
        self.height = sum(item.height for item in self.items)
        self.down = self.items[0].down
        heightSoFar = 0
        for i, item in enumerate(self.items):
            self.up = max(self.up, max(C.AR * 2, item.up + C.VS) - heightSoFar)
            heightSoFar += item.height
            if i > 0:
                self.down = max(self.height + self.down, heightSoFar
                                + max(C.AR * 2, item.down + C.VS)) - self.height
            itemWidth = item.width + (20 if item.needsSpace else 0)
            if i == 0:
                self.width += C.AR + max(itemWidth, C.AR)
            else:
                self.width += C.AR * 2 + max(itemWidth, C.AR) + C.AR
        addDebug(self)

    def __repr__(self):
        items = ', '.join(repr(item) for item in self.items)
        return 'OptionalSequence(%s)' % items

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)
        Path(x, y).right(leftGap).addTo(self)
        Path(x + leftGap + self.width, y
             + self.height).right(rightGap).addTo(self)
        x += leftGap
        upperLineY = y - self.up
        last = len(self.items) - 1
        for i, item in enumerate(self.items):
            itemSpace = 10 if item.needsSpace else 0
            itemWidth = item.width + itemSpace
            if i == 0:
                # Upper skip
                (Path(x, y)
                    .arc('se')
                    .up(y - upperLineY - C.AR * 2)
                    .arc('wn')
                    .right(itemWidth - C.AR)
                    .arc('ne')
                    .down(y + item.height - upperLineY - C.AR * 2)
                    .arc('ws')
                    .addTo(self))
                # Straight line
                (Path(x, y)
                    .right(itemSpace + C.AR)
                    .addTo(self))
                item.format(x + itemSpace + C.AR, y, item.width).addTo(self)
                x += itemWidth + C.AR
                y += item.height
            elif i < last:
                # Upper skip
                (Path(x, upperLineY)
                    .right(C.AR * 2 + max(itemWidth, C.AR) + C.AR)
                    .arc('ne')
                    .down(y - upperLineY + item.height - C.AR * 2)
                    .arc('ws')
                    .addTo(self))
                # Straight line
                (Path(x, y)
                    .right(C.AR * 2)
                    .addTo(self))
                item.format(x + C.AR * 2, y, item.width).addTo(self)
                (Path(x + item.width + C.AR * 2, y + item.height)
                    .right(itemSpace + C.AR)
                    .addTo(self))
                # Lower skip
                (Path(x, y)
                    .arc('ne')
                    .down(item.height + max(item.down + C.VS, C.AR * 2) - C.AR * 2)
                    .arc('ws')
                    .right(itemWidth - C.AR)
                    .arc('se')
                    .up(item.down + C.VS - C.AR * 2)
                    .arc('wn')
                    .addTo(self))
                x += C.AR * 2 + max(itemWidth, C.AR) + C.AR
                y += item.height
            else:
                # Straight line
                (Path(x, y)
                    .right(C.AR * 2)
                    .addTo(self))
                item.format(x + C.AR * 2, y, item.width).addTo(self)
                (Path(x + C.AR * 2 + item.width, y + item.height)
                    .right(itemSpace + C.AR)
                    .addTo(self))
                # Lower skip
                (Path(x, y)
                    .arc('ne')
                    .down(item.height + max(item.down + C.VS, C.AR * 2) - C.AR * 2)
                    .arc('ws')
                    .right(itemWidth - C.AR)
                    .arc('se')
                    .up(item.down + C.VS - C.AR * 2)
                    .arc('wn')
                    .addTo(self))
        return self


# In[16]:


class AlternatingSequence(DiagramItem):
    def __new__(cls, *items):
        if len(items) == 2:
            return super(AlternatingSequence, cls).__new__(cls)
        else:
            raise Exception(
                "AlternatingSequence takes exactly two arguments got " + len(items))

    def __init__(self, *items):
        DiagramItem.__init__(self, 'g')
        self.items = [wrapString(item) for item in items]
        self.needsSpace = False

        arc = C.AR
        vert = C.VS
        first = self.items[0]
        second = self.items[1]

        arcX = 1 / math.sqrt(2) * arc * 2
        arcY = (1 - 1 / math.sqrt(2)) * arc * 2
        crossY = max(arc, vert)
        crossX = (crossY - arcY) + arcX

        firstOut = max(arc + arc, crossY / 2 + arc + arc,
                       crossY / 2 + vert + first.down)
        self.up = firstOut + first.height + first.up

        secondIn = max(arc + arc, crossY / 2 + arc + arc,
                       crossY / 2 + vert + second.up)
        self.down = secondIn + second.height + second.down

        self.height = 0

        firstWidth = (20 if first.needsSpace else 0) + first.width
        secondWidth = (20 if second.needsSpace else 0) + second.width
        self.width = 2 * arc + max(firstWidth, crossX, secondWidth) + 2 * arc
        addDebug(self)

    def __repr__(self):
        items = ', '.join(repr(item) for item in self.items)
        return 'AlternatingSequence(%s)' % items

    def format(self, x, y, width):
        arc = C.AR
        gaps = determineGaps(width, self.width)
        Path(x, y).right(gaps[0]).addTo(self)
        x += gaps[0]
        Path(x + self.width, y).right(gaps[1]).addTo(self)
        # bounding box
        # Path(x+gaps[0], y).up(self.up).right(self.width).down(self.up+self.down).left(self.width).up(self.down).addTo(self)
        first = self.items[0]
        second = self.items[1]

        # top
        firstIn = self.up - first.up
        firstOut = self.up - first.up - first.height
        Path(x, y).arc('se').up(firstIn - 2 * arc).arc('wn').addTo(self)
        first.format(
            x
            + 2
            * arc,
            y
            - firstIn,
            self.width
            - 4
            * arc).addTo(self)
        Path(x + self.width - 2 * arc, y
             - firstOut).arc('ne').down(firstOut - 2 * arc).arc('ws').addTo(self)

        # bottom
        secondIn = self.down - second.down - second.height
        secondOut = self.down - second.down
        Path(x, y).arc('ne').down(secondIn - 2 * arc).arc('ws').addTo(self)
        second.format(
            x
            + 2
            * arc,
            y
            + secondIn,
            self.width
            - 4
            * arc).addTo(self)
        Path(x + self.width - 2 * arc, y
             + secondOut).arc('se').up(secondOut - 2 * arc).arc('wn').addTo(self)

        # crossover
        arcX = 1 / Math.sqrt(2) * arc * 2
        arcY = (1 - 1 / Math.sqrt(2)) * arc * 2
        crossY = max(arc, C.VS)
        crossX = (crossY - arcY) + arcX
        crossBar = (self.width - 4 * arc - crossX) / 2
        (Path(x + arc, y - crossY / 2 - arc).arc('ws').right(crossBar)
            .arc_8('n', 'cw').ll(crossX - arcX, crossY - arcY).arc_8('sw', 'ccw')
            .right(crossBar).arc('ne').addTo(self))
        (Path(x + arc, y + crossY / 2 + arc).arc('wn').right(crossBar)
            .arc_8('s', 'ccw').ll(crossX - arcX, -(crossY - arcY)).arc_8('nw', 'cw')
            .right(crossBar).arc('se').addTo(self))

        return self


# In[17]:


class Choice(DiagramItem):
    def __init__(self, default, *items):
        DiagramItem.__init__(self, 'g')
        assert default < len(items)
        self.default = default
        self.items = [wrapString(item) for item in items]
        self.width = C.AR * 4 + max(item.width for item in self.items)
        self.up = self.items[0].up
        self.down = self.items[-1].down
        self.height = self.items[default].height
        for i, item in enumerate(self.items):
            if i in [default - 1, default + 1]:
                arcs = C.AR * 2
            else:
                arcs = C.AR
            if i < default:
                self.up += max(arcs, item.height + item.down
                               + C.VS + self.items[i + 1].up)
            elif i == default:
                continue
            else:
                self.down += max(arcs, item.up + C.VS
                                 + self.items[i - 1].down + self.items[i - 1].height)
        # already counted in self.height
        self.down -= self.items[default].height
        addDebug(self)

    def __repr__(self):
        items = ', '.join(repr(item) for item in self.items)
        return 'Choice(%r, %s)' % (self.default, items)

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)

        # Hook up the two sides if self is narrower than its stated width.
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y + self.height).h(rightGap).addTo(self)
        x += leftGap

        innerWidth = self.width - C.AR * 4
        default = self.items[self.default]

        # Do the elements that curve above
        above = self.items[:self.default][::-1]
        if above:
            distanceFromY = max(
                C.AR * 2,
                default.up
                + C.VS
                + above[0].down
                + above[0].height)
        for i, ni, item in doubleenumerate(above):
            Path(x, y).arc('se').up(distanceFromY
                                    - C.AR * 2).arc('wn').addTo(self)
            item.format(x + C.AR * 2, y - distanceFromY,
                        innerWidth).addTo(self)
            Path(x + C.AR * 2 + innerWidth, y - distanceFromY + item.height).arc('ne') \
                .down(distanceFromY - item.height + default.height - C.AR * 2).arc('ws').addTo(self)
            if ni < -1:
                distanceFromY += max(
                    C.AR,
                    item.up
                    + C.VS
                    + above[i + 1].down
                    + above[i + 1].height)

        # Do the straight-line path.
        Path(x, y).right(C.AR * 2).addTo(self)
        self.items[self.default].format(
            x + C.AR * 2, y, innerWidth).addTo(self)
        Path(x + C.AR * 2 + innerWidth, y
             + self.height).right(C.AR * 2).addTo(self)

        # Do the elements that curve below
        below = self.items[self.default + 1:]
        if below:
            distanceFromY = max(
                C.AR * 2,
                default.height
                + default.down
                + C.VS
                + below[0].up)
        for i, item in enumerate(below):
            Path(x, y).arc('ne').down(
                distanceFromY - C.AR * 2).arc('ws').addTo(self)
            item.format(x + C.AR * 2, y + distanceFromY,
                        innerWidth).addTo(self)
            Path(x + C.AR * 2 + innerWidth, y + distanceFromY + item.height).arc('se') \
                .up(distanceFromY - C.AR * 2 + item.height - default.height).arc('wn').addTo(self)
            distanceFromY += max(
                C.AR,
                item.height
                + item.down
                + C.VS
                + (below[i + 1].up if i + 1 < len(below) else 0))
        return self


# In[18]:


class MultipleChoice(DiagramItem):
    def __init__(self, default, type, *items):
        DiagramItem.__init__(self, 'g')
        assert 0 <= default < len(items)
        assert type in ["any", "all"]
        self.default = default
        self.type = type
        self.needsSpace = True
        self.items = [wrapString(item) for item in items]
        self.innerWidth = max(item.width for item in self.items)
        self.width = 30 + C.AR + self.innerWidth + C.AR + 20
        self.up = self.items[0].up
        self.down = self.items[-1].down
        self.height = self.items[default].height
        for i, item in enumerate(self.items):
            if i in [default - 1, default + 1]:
                minimum = 10 + C.AR
            else:
                minimum = C.AR
            if i < default:
                self.up += max(minimum, item.height
                               + item.down + C.VS + self.items[i + 1].up)
            elif i == default:
                continue
            else:
                self.down += max(minimum, item.up + C.VS
                                 + self.items[i - 1].down + self.items[i - 1].height)
        # already counted in self.height
        self.down -= self.items[default].height
        addDebug(self)

    def __repr__(self):
        items = ', '.join(map(repr, self.items))
        return 'MultipleChoice(%r, %r, %s)' % (self.default, self.type, items)

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)

        # Hook up the two sides if self is narrower than its stated width.
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y + self.height).h(rightGap).addTo(self)
        x += leftGap

        default = self.items[self.default]

        # Do the elements that curve above
        above = self.items[:self.default][::-1]
        if above:
            distanceFromY = max(
                10 + C.AR,
                default.up
                + C.VS
                + above[0].down
                + above[0].height)
        for i, ni, item in doubleenumerate(above):
            (Path(x + 30, y)
                .up(distanceFromY - C.AR)
                .arc('wn')
                .addTo(self))
            item.format(x + 30 + C.AR, y - distanceFromY,
                        self.innerWidth).addTo(self)
            (Path(x + 30 + C.AR + self.innerWidth, y - distanceFromY + item.height)
                .arc('ne')
                .down(distanceFromY - item.height + default.height - C.AR - 10)
                .addTo(self))
            if ni < -1:
                distanceFromY += max(
                    C.AR,
                    item.up
                    + C.VS
                    + above[i + 1].down
                    + above[i + 1].height)

        # Do the straight-line path.
        Path(x + 30, y).right(C.AR).addTo(self)
        self.items[self.default].format(
            x + 30 + C.AR, y, self.innerWidth).addTo(self)
        Path(x + 30 + C.AR + self.innerWidth, y
             + self.height).right(C.AR).addTo(self)

        # Do the elements that curve below
        below = self.items[self.default + 1:]
        if below:
            distanceFromY = max(
                10 + C.AR,
                default.height
                + default.down
                + C.VS
                + below[0].up)
        for i, item in enumerate(below):
            (Path(x + 30, y)
                .down(distanceFromY - C.AR)
                .arc('ws')
                .addTo(self))
            item.format(x + 30 + C.AR, y + distanceFromY,
                        self.innerWidth).addTo(self)
            (Path(x + 30 + C.AR + self.innerWidth, y + distanceFromY + item.height)
                .arc('se')
                .up(distanceFromY - C.AR + item.height - default.height - 10)
                .addTo(self))
            distanceFromY += max(
                C.AR,
                item.height
                + item.down
                + C.VS
                + (below[i + 1].up if i + 1 < len(below) else 0))
        text = DiagramItem('g', attrs={"class": "diagram-text"}).addTo(self)
        DiagramItem('title', text="take one or more branches, once each, in any order" if self.type
                    == "any" else "take all branches, once each, in any order").addTo(text)
        DiagramItem('path', attrs={
            "d": "M {x} {y} h -26 a 4 4 0 0 0 -4 4 v 12 a 4 4 0 0 0 4 4 h 26 z".format(x=x + 30, y=y - 10),
            "class": "diagram-text"
        }).addTo(text)
        DiagramItem('text', text="1+" if self.type == "any" else "all", attrs={
            "x": x + 15,
            "y": y + 4,
            "class": "diagram-text"
        }).addTo(text)
        DiagramItem('path', attrs={
            "d": "M {x} {y} h 16 a 4 4 0 0 1 4 4 v 12 a 4 4 0 0 1 -4 4 h -16 z".format(x=x + self.width - 20, y=y - 10),
            "class": "diagram-text"
        }).addTo(text)
        DiagramItem('text', text=u"↺", attrs={
            "x": x + self.width - 10,
            "y": y + 4,
            "class": "diagram-arrow"
        }).addTo(text)
        return self


# In[19]:


class HorizontalChoice(DiagramItem):
    def __new__(cls, *items):
        if len(items) <= 1:
            return Sequence(*items)
        else:
            return super(HorizontalChoice, cls).__new__(cls)

    def __init__(self, *items):
        DiagramItem.__init__(self, 'g')
        self.items = [wrapString(item) for item in items]
        allButLast = self.items[:-1]
        middles = self.items[1:-1]
        first = self.items[0]
        last = self.items[-1]
        self.needsSpace = False

        self.width = (C.AR  # starting track
                      + C.AR * 2 * (len(self.items) - 1)  # inbetween tracks
                      + sum(x.width + (20 if x.needsSpace else 0)
                            for x in self.items)  # items
                      # needs space to curve up
                      + (C.AR if last.height > 0 else 0)
                      + C.AR)  # ending track

        # Always exits at entrance height
        self.height = 0

        # All but the last have a track running above them
        self._upperTrack = max(
            C.AR * 2,
            C.VS,
            max(x.up for x in allButLast) + C.VS
        )
        self.up = max(self._upperTrack, last.up)

        # All but the first have a track running below them
        # Last either straight-lines or curves up, so has different calculation
        self._lowerTrack = max(
            C.VS,
            max(x.height + max(x.down + C.VS, C.AR * 2)
                for x in middles) if middles else 0,
            last.height + last.down + C.VS
        )
        if first.height < self._lowerTrack:
            # Make sure there's at least 2*C.AR room between first exit and
            # lower track
            self._lowerTrack = max(self._lowerTrack, first.height + C.AR * 2)
        self.down = max(self._lowerTrack, first.height + first.down)

        addDebug(self)

    def format(self, x, y, width):
        # Hook up the two sides if self is narrower than its stated width.
        leftGap, rightGap = determineGaps(width, self.width)
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y + self.height).h(rightGap).addTo(self)
        x += leftGap

        first = self.items[0]
        last = self.items[-1]

        # upper track
        upperSpan = (sum(x.width + (20 if x.needsSpace else 0) for x in self.items[:-1])
                     + (len(self.items) - 2) * C.AR * 2
                     - C.AR)
        (Path(x, y)
            .arc('se')
            .up(self._upperTrack - C.AR * 2)
            .arc('wn')
            .h(upperSpan)
            .addTo(self))

        # lower track
        lowerSpan = (sum(x.width + (20 if x.needsSpace else 0) for x in self.items[1:])
                     + (len(self.items) - 2) * C.AR * 2
                     + (C.AR if last.height > 0 else 0)
                     - C.AR)
        lowerStart = x + C.AR + first.width + \
            (20 if first.needsSpace else 0) + C.AR * 2
        (Path(lowerStart, y + self._lowerTrack)
            .h(lowerSpan)
            .arc('se')
            .up(self._lowerTrack - C.AR * 2)
            .arc('wn')
            .addTo(self))

        # Items
        for [i, item] in enumerate(self.items):
            # input track
            if i == 0:
                (Path(x, y)
                    .h(C.AR)
                    .addTo(self))
                x += C.AR
            else:
                (Path(x, y - self._upperTrack)
                    .arc('ne')
                    .v(self._upperTrack - C.AR * 2)
                    .arc('ws')
                    .addTo(self))
                x += C.AR * 2

            # item
            itemWidth = item.width + (20 if item.needsSpace else 0)
            item.format(x, y, itemWidth).addTo(self)
            x += itemWidth

            # output track
            if i == len(self.items) - 1:
                if item.height == 0:
                    (Path(x, y)
                        .h(C.AR)
                        .addTo(self))
                else:
                    (Path(x, y + item.height)
                        .arc('se')
                        .addTo(self))
            elif i == 0 and item.height > self._lowerTrack:
                # Needs to arc up to meet the lower track, not down.
                if item.height - self._lowerTrack >= C.AR * 2:
                    (Path(x, y + item.height)
                        .arc('se')
                        .v(self._lowerTrack - item.height + C.AR * 2)
                        .arc('wn')
                        .addTo(self))
                else:
                    # Not enough space to fit two arcs
                    # so just bail and draw a straight line for now.
                    (Path(x, y + item.height)
                        .ll(C.AR * 2, self._lowerTrack - item.height)
                        .addTo(self))
            else:
                (Path(x, y + item.height)
                    .arc('ne')
                    .v(self._lowerTrack - item.height - C.AR * 2)
                    .arc('ws')
                    .addTo(self))
        return self


# In[20]:


def Optional(item, skip=False):
    return Choice(0 if skip else 1, Skip(), item)


# In[21]:


class OneOrMore(DiagramItem):
    def __init__(self, item, repeat=None):
        DiagramItem.__init__(self, 'g')
        repeat = repeat or Skip()
        self.item = wrapString(item)
        self.rep = wrapString(repeat)
        self.width = max(self.item.width, self.rep.width) + C.AR * 2
        self.height = self.item.height
        self.up = self.item.up
        self.down = max(
            C.AR * 2,
            self.item.down + C.VS + self.rep.up + self.rep.height + self.rep.down)
        self.needsSpace = True
        addDebug(self)

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)

        # Hook up the two sides if self is narrower than its stated width.
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y + self.height).h(rightGap).addTo(self)
        x += leftGap

        # Draw item
        Path(x, y).right(C.AR).addTo(self)
        self.item.format(x + C.AR, y, self.width - C.AR * 2).addTo(self)
        Path(x + self.width - C.AR, y + self.height).right(C.AR).addTo(self)

        # Draw repeat arc
        distanceFromY = max(C.AR * 2, self.item.height
                            + self.item.down + C.VS + self.rep.up)
        Path(x + C.AR, y).arc('nw').down(distanceFromY - C.AR * 2) \
            .arc('ws').addTo(self)
        self.rep.format(x + C.AR, y + distanceFromY,
                        self.width - C.AR * 2).addTo(self)
        Path(x + self.width - C.AR, y + distanceFromY + self.rep.height).arc('se') \
            .up(distanceFromY - C.AR * 2 + self.rep.height - self.item.height).arc('en').addTo(self)

        return self

    def __repr__(self):
        return 'OneOrMore(%r, repeat=%r)' % (self.item, self.rep)


# In[22]:


def ZeroOrMore(item, repeat=None, skip=False):
    result = Optional(OneOrMore(item, repeat), skip)
    return result


# In[23]:


class Start(DiagramItem):
    def __init__(self, type="simple", label=None):
        DiagramItem.__init__(self, 'g')
        if label:
            self.width = max(20, len(label) * C.CHAR_WIDTH + 10)
        else:
            self.width = 20
        self.up = 10
        self.down = 10
        self.type = type
        self.label = label
        addDebug(self)

    def format(self, x, y, _width):
        path = Path(x, y - 10)
        if self.type == "complex":
            path.down(20).m(0, -10).right(self.width).addTo(self)
        else:
            path.down(20).m(10, -20).down(20).m(-10,
                                                - 10).right(self.width).addTo(self)
        if self.label:
            DiagramItem('text', attrs={
                        "x": x, "y": y - 15, "style": "text-anchor:start"}, text=self.label).addTo(self)
        return self

    def __repr__(self):
        return 'Start(type=%r, label=%r)' % (self.type, self.label)


# In[24]:


class End(DiagramItem):
    def __init__(self, type="simple"):
        DiagramItem.__init__(self, 'path')
        self.width = 20
        self.up = 10
        self.down = 10
        self.type = type
        addDebug(self)

    def format(self, x, y, _width):
        if self.type == "simple":
            self.attrs['d'] = 'M {0} {1} h 20 m -10 -10 v 20 m 10 -20 v 20'.format(
                x, y)
        elif self.type == "complex":
            self.attrs['d'] = 'M {0} {1} h 20 m 0 -10 v 20'
        return self

    def __repr__(self):
        return 'End(type=%r)' % self.type


# In[25]:


class Terminal(DiagramItem):
    def __init__(self, text, href=None, title=None):
        DiagramItem.__init__(self, 'g', {'class': 'terminal'})
        self.text = text
        self.href = href
        self.title = title
        self.width = len(text) * C.CHAR_WIDTH + 20
        self.up = 11
        self.down = 11
        self.needsSpace = True
        addDebug(self)

    def __repr__(self):
        return 'Terminal(%r, href=%r, title=%r)' % (
            self.text, self.href, self.title)

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)

        # Hook up the two sides if self is narrower than its stated width.
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y).h(rightGap).addTo(self)

        DiagramItem('rect', {'x': x + leftGap, 'y': y - 11, 'width': self.width,
                             'height': self.up + self.down, 'rx': 10, 'ry': 10}).addTo(self)
        text = DiagramItem('text', {'x': x + width / 2, 'y': y + 4}, self.text)
        if self.href is not None:
            a = DiagramItem('a', {'xlink:href': self.href}, text).addTo(self)
            text.addTo(a)
        else:
            text.addTo(self)
        if self.title is not None:
            DiagramItem('title', {}, self.title).addTo(self)
        return self


# In[26]:


class NonTerminal(DiagramItem):
    def __init__(self, text, href=None, title=None):
        DiagramItem.__init__(self, 'g', {'class': 'non-terminal'})
        self.text = text
        self.href = href
        self.title = title
        self.width = len(text) * C.CHAR_WIDTH + 20
        self.up = 11
        self.down = 11
        self.needsSpace = True
        addDebug(self)

    def __repr__(self):
        return 'NonTerminal(%r, href=%r, title=%r)' % (
            self.text, self.href, self.title)

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)

        # Hook up the two sides if self is narrower than its stated width.
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y).h(rightGap).addTo(self)

        DiagramItem('rect', {'x': x + leftGap, 'y': y - 11, 'width': self.width,
                             'height': self.up + self.down}).addTo(self)
        text = DiagramItem('text', {'x': x + width / 2, 'y': y + 4}, self.text)
        if self.href is not None:
            a = DiagramItem('a', {'xlink:href': self.href}, text).addTo(self)
            text.addTo(a)
        else:
            text.addTo(self)
        if self.title is not None:
            DiagramItem('title', {}, self.title).addTo(self)
        return self


# In[27]:


class Comment(DiagramItem):
    def __init__(self, text, href=None, title=None):
        DiagramItem.__init__(self, 'g')
        self.text = text
        self.href = href
        self.title = title
        self.width = len(text) * C.COMMENT_CHAR_WIDTH + 10
        self.up = 11
        self.down = 11
        self.needsSpace = True
        addDebug(self)

    def __repr__(self):
        return 'Comment(%r, href=%r, title=%r)' % (
            self.text, self.href, self.title)

    def format(self, x, y, width):
        leftGap, rightGap = determineGaps(width, self.width)

        # Hook up the two sides if self is narrower than its stated width.
        Path(x, y).h(leftGap).addTo(self)
        Path(x + leftGap + self.width, y).h(rightGap).addTo(self)

        text = DiagramItem(
            'text', {'x': x + width / 2, 'y': y + 5, 'class': 'comment'}, self.text)
        if self.href is not None:
            a = DiagramItem('a', {'xlink:href': self.href}, text).addTo(self)
            text.addTo(a)
        else:
            text.addTo(self)
        if self.title is not None:
            DiagramItem('title', {}, self.title).addTo(self)
        return self


# In[28]:


class Skip(DiagramItem):
    def __init__(self):
        DiagramItem.__init__(self, 'g')
        self.width = 0
        self.up = 0
        self.down = 0
        addDebug(self)

    def format(self, x, y, width):
        Path(x, y).right(width).addTo(self)
        return self

    def __repr__(self):
        return 'Skip()'


# In[29]:


def show_diagram(graph, log=False):
    with io.StringIO() as f:
        d = Diagram(graph)
        if log:
            print(d)
        d.writeSvg(f.write)
        mysvg = f.getvalue()
        return mysvg


# ## End of Excursion