From 2d590459a177a55920d1bc9c6489fa2006613008 2014-11-01 23:41:07
From: MinRK <benjaminrk@gmail.com>
Date: 2014-11-01 23:41:07
Subject: [PATCH] remove heading cells in v4

---

diff --git a/IPython/html/nbconvert/tests/test_nbconvert_handlers.py b/IPython/html/nbconvert/tests/test_nbconvert_handlers.py
index 0e3cec7..87ce4ba 100644
--- a/IPython/html/nbconvert/tests/test_nbconvert_handlers.py
+++ b/IPython/html/nbconvert/tests/test_nbconvert_handlers.py
@@ -11,7 +11,7 @@ import requests
 from IPython.html.utils import url_path_join
 from IPython.html.tests.launchnotebook import NotebookTestBase, assert_http_error
 from IPython.nbformat.current import (new_notebook, write,
-                                      new_heading_cell, new_code_cell,
+                                      new_markdown_cell, new_code_cell,
                                       new_output)
 
 from IPython.testing.decorators import onlyif_cmds_exist
@@ -55,7 +55,7 @@ class APITest(NotebookTestBase):
         
         nb = new_notebook()
         
-        nb.cells.append(new_heading_cell(u'Created by test ³'))
+        nb.cells.append(new_markdown_cell(u'Created by test ³'))
         cc1 = new_code_cell(source=u'print(2*6)')
         cc1.outputs.append(new_output(output_type="stream", text=u'12'))
         cc1.outputs.append(new_output(output_type="execute_result",
diff --git a/IPython/html/services/contents/filemanager.py b/IPython/html/services/contents/filemanager.py
index 8077de1..14ed305 100644
--- a/IPython/html/services/contents/filemanager.py
+++ b/IPython/html/services/contents/filemanager.py
@@ -255,7 +255,7 @@ class FileContentsManager(ContentsManager):
                 try:
                     nb = current.read(f, u'json')
                 except Exception as e:
-                    raise web.HTTPError(400, u"Unreadable Notebook: %s %s" % (os_path, e))
+                    raise web.HTTPError(400, u"Unreadable Notebook: %s %r" % (os_path, e))
             self.mark_trusted_cells(nb, name, path)
             model['content'] = nb
             model['format'] = 'json'
diff --git a/IPython/html/services/contents/tests/test_contents_api.py b/IPython/html/services/contents/tests/test_contents_api.py
index bb5a175..0b704de 100644
--- a/IPython/html/services/contents/tests/test_contents_api.py
+++ b/IPython/html/services/contents/tests/test_contents_api.py
@@ -16,7 +16,7 @@ from IPython.html.utils import url_path_join, url_escape
 from IPython.html.tests.launchnotebook import NotebookTestBase, assert_http_error
 from IPython.nbformat import current
 from IPython.nbformat.current import (new_notebook, write, read,
-                                      new_heading_cell, to_notebook_json)
+                                      new_markdown_cell, to_notebook_json)
 from IPython.nbformat import v2
 from IPython.utils import py3compat
 from IPython.utils.data import uniq_stable
@@ -415,7 +415,7 @@ class APITest(NotebookTestBase):
         resp = self.api.read('a.ipynb', 'foo')
         nbcontent = json.loads(resp.text)['content']
         nb = to_notebook_json(nbcontent)
-        nb.cells.append(new_heading_cell(u'Created by test ³'))
+        nb.cells.append(new_markdown_cell(u'Created by test ³'))
 
         nbmodel= {'name': 'a.ipynb', 'path':'foo', 'content': nb, 'type': 'notebook'}
         resp = self.api.save('a.ipynb', path='foo', body=json.dumps(nbmodel))
@@ -452,7 +452,7 @@ class APITest(NotebookTestBase):
         # Modify it
         nbcontent = json.loads(resp.text)['content']
         nb = to_notebook_json(nbcontent)
-        hcell = new_heading_cell('Created by test')
+        hcell = new_markdown_cell('Created by test')
         nb.cells.append(hcell)
         # Save
         nbmodel= {'name': 'a.ipynb', 'path':'foo', 'content': nb, 'type': 'notebook'}
diff --git a/IPython/html/static/notebook/js/maintoolbar.js b/IPython/html/static/notebook/js/maintoolbar.js
index 6bb0f1b..becca07 100644
--- a/IPython/html/static/notebook/js/maintoolbar.js
+++ b/IPython/html/static/notebook/js/maintoolbar.js
@@ -139,12 +139,6 @@ define([
                 .append($('<option/>').attr('value','code').text('Code'))
                 .append($('<option/>').attr('value','markdown').text('Markdown'))
                 .append($('<option/>').attr('value','raw').text('Raw NBConvert'))
-                .append($('<option/>').attr('value','heading1').text('Heading 1'))
-                .append($('<option/>').attr('value','heading2').text('Heading 2'))
-                .append($('<option/>').attr('value','heading3').text('Heading 3'))
-                .append($('<option/>').attr('value','heading4').text('Heading 4'))
-                .append($('<option/>').attr('value','heading5').text('Heading 5'))
-                .append($('<option/>').attr('value','heading6').text('Heading 6'))
             );
     };
 
@@ -190,24 +184,18 @@ define([
         
         this.element.find('#cell_type').change(function () {
             var cell_type = $(this).val();
-            if (cell_type === 'code') {
+            switch (cell_type) {
+            case 'code':
                 that.notebook.to_code();
-            } else if (cell_type === 'markdown')  {
+                break;
+            case 'markdown':
                 that.notebook.to_markdown();
-            } else if (cell_type === 'raw')  {
+                break;
+            case 'raw':
                 that.notebook.to_raw();
-            } else if (cell_type === 'heading1')  {
-                that.notebook.to_heading(undefined, 1);
-            } else if (cell_type === 'heading2')  {
-                that.notebook.to_heading(undefined, 2);
-            } else if (cell_type === 'heading3')  {
-                that.notebook.to_heading(undefined, 3);
-            } else if (cell_type === 'heading4')  {
-                that.notebook.to_heading(undefined, 4);
-            } else if (cell_type === 'heading5')  {
-                that.notebook.to_heading(undefined, 5);
-            } else if (cell_type === 'heading6')  {
-                that.notebook.to_heading(undefined, 6);
+                break;
+            default:
+                console.log("unrecognized cell type:", cell_type);
             }
         });
         this.events.on('selected_cell_type_changed.Notebook', function (event, data) {
diff --git a/IPython/html/static/notebook/js/notebook.js b/IPython/html/static/notebook/js/notebook.js
index 98c6111..bc75dfc 100644
--- a/IPython/html/static/notebook/js/notebook.js
+++ b/IPython/html/static/notebook/js/notebook.js
@@ -824,7 +824,7 @@ define([
      * Index will be brought back into the accessible range [0,n]
      *
      * @method insert_cell_at_index
-     * @param [type] {string} in ['code','markdown','heading'], defaults to 'code'
+     * @param [type] {string} in ['code','markdown', 'raw'], defaults to 'code'
      * @param [index] {int} a valid index where to insert cell
      *
      * @return cell {cell|null} created cell or null
@@ -860,15 +860,19 @@ define([
                 notebook: this,
                 tooltip: this.tooltip,
             };
-            if (type === 'code') {
+            switch(type) {
+            case 'code':
                 cell = new codecell.CodeCell(this.kernel, cell_options);
                 cell.set_input_prompt();
-            } else if (type === 'markdown') {
+                break;
+            case 'markdown':
                 cell = new textcell.MarkdownCell(cell_options);
-            } else if (type === 'raw') {
+                break;
+            case 'raw':
                 cell = new textcell.RawCell(cell_options);
-            } else if (type === 'heading') {
-                cell = new textcell.HeadingCell(cell_options);
+                break;
+            default:
+                console.log("invalid cell type: ", type);
             }
 
             if(this._insert_element_at_index(cell.element,index)) {
@@ -1090,10 +1094,10 @@ define([
         if (this.is_valid_cell_index(i)) {
             var source_cell = this.get_cell(i);
             var target_cell = null;
-            if (source_cell instanceof textcell.HeadingCell) {
-                source_cell.set_level(level);
+            if (source_cell instanceof textcell.MarkdownCell) {
+                source_cell.set_heading_level(level);
             } else {
-                target_cell = this.insert_cell_below('heading',i);
+                target_cell = this.insert_cell_below('markdown',i);
                 var text = source_cell.get_text();
                 if (text === source_cell.placeholder) {
                     text = '';
@@ -1101,9 +1105,9 @@ define([
                 //metadata
                 target_cell.metadata = source_cell.metadata;
                 // We must show the editor before setting its contents
-                target_cell.set_level(level);
                 target_cell.unrender();
                 target_cell.set_text(text);
+                target_cell.set_heading_level(level);
                 // make this value the starting point, so that we can only undo
                 // to this state, instead of a blank cell
                 target_cell.code_mirror.clearHistory();
@@ -1117,7 +1121,7 @@ define([
             }
             this.set_dirty(true);
             this.events.trigger('selected_cell_type_changed.Notebook',
-                {'cell_type':'heading',level:level}
+                {'cell_type':'markdown',level:level}
             );
         }
     };
@@ -1526,8 +1530,8 @@ define([
         }
         this.codemirror_mode = newmode;
         codecell.CodeCell.options_default.cm_config.mode = newmode;
-        modename = newmode.mode || newmode.name || newmode
-
+        modename = newmode.mode || newmode.name || newmode;
+        
         that = this;
         utils.requireCodeMirrorMode(modename, function () {
             $.map(that.get_cells(), function(cell, i) {
@@ -1539,7 +1543,7 @@ define([
                     cell.cm_config.mode = newmode;
                 }
             });
-        })
+        });
     };
 
     // Session related things
@@ -2383,13 +2387,13 @@ define([
     Notebook.prototype.load_notebook_error = function (xhr, status, error) {
         this.events.trigger('notebook_load_failed.Notebook', [xhr, status, error]);
         utils.log_ajax_error(xhr, status, error);
-        var msg;
+        var msg = $("<div>");
         if (xhr.status === 400) {
-            msg = escape(utils.ajax_error_msg(xhr));
+            msg.text(utils.ajax_error_msg(xhr));
         } else if (xhr.status === 500) {
-            msg = "An unknown error occurred while loading this notebook. " +
+            msg.text("An unknown error occurred while loading this notebook. " +
             "This version can load notebook formats " +
-            "v" + this.nbformat + " or earlier. See the server log for details.";
+            "v" + this.nbformat + " or earlier. See the server log for details.");
         }
         dialog.modal({
             notebook: this,
diff --git a/IPython/html/static/notebook/js/textcell.js b/IPython/html/static/notebook/js/textcell.js
index f1fcf11..61db7af 100644
--- a/IPython/html/static/notebook/js/textcell.js
+++ b/IPython/html/static/notebook/js/textcell.js
@@ -222,6 +222,26 @@ define([
 
     MarkdownCell.prototype = Object.create(TextCell.prototype);
 
+    MarkdownCell.prototype.set_heading_level = function (level) {
+        // make a markdown cell a heading
+        level = level || 1;
+        var source = this.get_text();
+        // \s\S appears to be the js version of multi-line dot-all
+        var match = source.match(/(#*)\s*([\s\S]*)/);
+        // strip the leading `#` if it's already there
+        if (match) {
+            source = match[2];
+        }
+        // add `#` markdown heading prefix
+        var new_text = new Array(level + 1).join('#') + ' ' + source;
+
+        this.set_text(new_text);
+        this.refresh();
+        if (this.rendered) {
+            this.render();
+        }
+    };
+
     /**
      * @method render
      */
@@ -238,6 +258,19 @@ define([
             html = mathjaxutils.replace_math(html, math);
             html = security.sanitize_html(html);
             html = $($.parseHTML(html));
+            // add anchors to headings
+            // console.log(html);
+            html.find(":header").addBack(":header").each(function (i, h) {
+                h = $(h);
+                var hash = h.text().replace(/ /g, '-');
+                h.attr('id', hash);
+                h.append(
+                    $('<a/>')
+                        .addClass('anchor-link')
+                        .attr('href', '#' + hash)
+                        .text('¶')
+                );
+            })
             // links in markdown cells should open in new tabs
             html.find("a[href]").not('[href^="#"]').attr("target", "_blank");
             this.set_rendered(html);
@@ -305,121 +338,15 @@ define([
         return cont;
     };
 
-
-    var HeadingCell = function (options) {
-        // Constructor
-        //
-        // Parameters:
-        //  options: dictionary
-        //      Dictionary of keyword arguments.
-        //          events: $(Events) instance 
-        //          config: dictionary
-        //          keyboard_manager: KeyboardManager instance 
-        //          notebook: Notebook instance
-        options = options || {};
-        var config = utils.mergeopt(HeadingCell, options.config);
-        TextCell.apply(this, [$.extend({}, options, {config: config})]);
-
-        this.level = 1;
-        this.cell_type = 'heading';
-    };
-
-    HeadingCell.options_default = {
-        cm_config: {
-            theme: 'heading-1'
-        },
-        placeholder: "Type Heading Here"
-    };
-
-    HeadingCell.prototype = Object.create(TextCell.prototype);
-
-    /** @method fromJSON */
-    HeadingCell.prototype.fromJSON = function (data) {
-        if (data.level !== undefined){
-            this.level = data.level;
-        }
-        TextCell.prototype.fromJSON.apply(this, arguments);
-        this.code_mirror.setOption("theme", "heading-"+this.level);
-    };
-
-
-    /** @method toJSON */
-    HeadingCell.prototype.toJSON = function () {
-        var data = TextCell.prototype.toJSON.apply(this);
-        data.level = this.get_level();
-        return data;
-    };
-
-    /**
-     * Change heading level of cell, and re-render
-     * @method set_level
-     */
-    HeadingCell.prototype.set_level = function (level) {
-        this.level = level;
-        this.code_mirror.setOption("theme", "heading-"+level);
-
-        if (this.rendered) {
-            this.rendered = false;
-            this.render();
-        }
-    };
-
-    /** The depth of header cell, based on html (h1 to h6)
-     * @method get_level
-     * @return {integer} level - for 1 to 6
-     */
-    HeadingCell.prototype.get_level = function () {
-        return this.level;
-    };
-
-
-    HeadingCell.prototype.get_rendered = function () {
-        var r = this.element.find("div.text_cell_render");
-        return r.children().first().html();
-    };
-
-    HeadingCell.prototype.render = function () {
-        var cont = TextCell.prototype.render.apply(this);
-        if (cont) {
-            var text = this.get_text();
-            var math = null;
-            // Markdown headings must be a single line
-            text = text.replace(/\n/g, ' ');
-            if (text === "") { text = this.placeholder; }
-            text = new Array(this.level + 1).join("#") + " " + text;
-            var text_and_math = mathjaxutils.remove_math(text);
-            text = text_and_math[0];
-            math = text_and_math[1];
-            var html = marked.parser(marked.lexer(text));
-            html = mathjaxutils.replace_math(html, math);
-            html = security.sanitize_html(html);
-            var h = $($.parseHTML(html));
-            // add id and linkback anchor
-            var hash = h.text().trim().replace(/ /g, '-');
-            h.attr('id', hash);
-            h.append(
-                $('<a/>')
-                    .addClass('anchor-link')
-                    .attr('href', '#' + hash)
-                    .text('¶')
-            );
-            this.set_rendered(h);
-            this.typeset();
-        }
-        return cont;
-    };
-
     // Backwards compatability.
     IPython.TextCell = TextCell;
     IPython.MarkdownCell = MarkdownCell;
     IPython.RawCell = RawCell;
-    IPython.HeadingCell = HeadingCell;
 
     var textcell = {
-        'TextCell': TextCell,
-        'MarkdownCell': MarkdownCell,
-        'RawCell': RawCell,
-        'HeadingCell': HeadingCell,
+        TextCell: TextCell,
+        MarkdownCell: MarkdownCell,
+        RawCell: RawCell,
     };
     return textcell;
 });
diff --git a/IPython/html/templates/notebook.html b/IPython/html/templates/notebook.html
index 9fc7d97..958374e 100644
--- a/IPython/html/templates/notebook.html
+++ b/IPython/html/templates/notebook.html
@@ -189,12 +189,6 @@ class="notebook_app"
                               <li id="to_raw"
                                   title="Contents will pass through nbconvert unmodified">
                                   <a href="#">Raw NBConvert</a></li>
-                              <li id="to_heading1"><a href="#">Heading 1</a></li>
-                              <li id="to_heading2"><a href="#">Heading 2</a></li>
-                              <li id="to_heading3"><a href="#">Heading 3</a></li>
-                              <li id="to_heading4"><a href="#">Heading 4</a></li>
-                              <li id="to_heading5"><a href="#">Heading 5</a></li>
-                              <li id="to_heading6"><a href="#">Heading 6</a></li>
                             </ul>
                         </li>
                         <li class="divider"></li>
diff --git a/IPython/html/tests/notebook/dualmode_cellinsert.js b/IPython/html/tests/notebook/dualmode_cellinsert.js
index 039babe..0974690 100644
--- a/IPython/html/tests/notebook/dualmode_cellinsert.js
+++ b/IPython/html/tests/notebook/dualmode_cellinsert.js
@@ -52,12 +52,12 @@ casper.notebook_test(function () {
     
     this.then(function () {
         this.select_cell(2);
-        this.trigger_keydown('1'); // switch it to heading for the next test
-        this.test.assertEquals(this.get_cell(2).cell_type, 'heading', 'test cell is heading');
+        this.trigger_keydown('y'); // switch it to code for the next test
+        this.test.assertEquals(this.get_cell(2).cell_type, 'code', 'test cell is code');
         this.trigger_keydown('b'); // new cell below
-        this.test.assertEquals(this.get_cell(3).cell_type, 'heading', 'b; inserts a heading cell below heading cell');
+        this.test.assertEquals(this.get_cell(3).cell_type, 'code', 'b; inserts a code cell below code cell');
         this.trigger_keydown('a'); // new cell above
-        this.test.assertEquals(this.get_cell(3).cell_type, 'heading', 'a; inserts a heading cell below heading cell');
+        this.test.assertEquals(this.get_cell(3).cell_type, 'code', 'a; inserts a code cell below code cell');
     });
     
     this.thenEvaluate(function() {
diff --git a/IPython/html/tests/notebook/dualmode_cellmode.js b/IPython/html/tests/notebook/dualmode_cellmode.js
index d4bf5f0..3701792 100644
--- a/IPython/html/tests/notebook/dualmode_cellmode.js
+++ b/IPython/html/tests/notebook/dualmode_cellmode.js
@@ -4,25 +4,38 @@
 casper.notebook_test(function () {
     this.then(function () {
         // Cell mode change
-        this.select_cell(0);
+        var index = 0;
+        this.select_cell(index);
+        var a = 'hello\nmulti\nline';
+        this.set_cell_text(index, a);
         this.trigger_keydown('esc','r');
-        this.test.assertEquals(this.get_cell(0).cell_type, 'raw', 'r; cell is raw');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'raw', 'r; cell is raw');
         this.trigger_keydown('1');
-        this.test.assertEquals(this.get_cell(0).cell_type, 'heading', '1; cell is heading');
-        this.test.assertEquals(this.get_cell(0).level, 1, '1; cell is level 1 heading');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '1; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '# ' + a, '1; markdown heading');
         this.trigger_keydown('2');
-        this.test.assertEquals(this.get_cell(0).level, 2, '2; cell is level 2 heading');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '2; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '## ' + a, '2; markdown heading');
         this.trigger_keydown('3');
-        this.test.assertEquals(this.get_cell(0).level, 3, '3; cell is level 3 heading');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '3; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '### ' + a, '3; markdown heading');
         this.trigger_keydown('4');
-        this.test.assertEquals(this.get_cell(0).level, 4, '4; cell is level 4 heading');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '4; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '#### ' + a, '4; markdown heading');
         this.trigger_keydown('5');
-        this.test.assertEquals(this.get_cell(0).level, 5, '5; cell is level 5 heading');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '5; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '##### ' + a, '5; markdown heading');
         this.trigger_keydown('6');
-        this.test.assertEquals(this.get_cell(0).level, 6, '6; cell is level 6 heading');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '6; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '###### ' + a, '6; markdown heading');
         this.trigger_keydown('m');
-        this.test.assertEquals(this.get_cell(0).cell_type, 'markdown', 'm; cell is markdown');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', 'm; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '###### ' + a, 'm; still markdown heading');
         this.trigger_keydown('y');
-        this.test.assertEquals(this.get_cell(0).cell_type, 'code', 'y; cell is code');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'code', 'y; cell is code');
+        this.test.assertEquals(this.get_cell_text(index), '###### ' + a, 'y; still has hashes');
+        this.trigger_keydown('1');
+        this.test.assertEquals(this.get_cell(index).cell_type, 'markdown', '1; cell is markdown');
+        this.test.assertEquals(this.get_cell_text(index), '# ' + a, '1; markdown heading');
     });
 });
\ No newline at end of file
diff --git a/IPython/html/tests/notebook/markdown.js b/IPython/html/tests/notebook/markdown.js
index 5f28d31..4d7897f 100644
--- a/IPython/html/tests/notebook/markdown.js
+++ b/IPython/html/tests/notebook/markdown.js
@@ -10,38 +10,53 @@ casper.notebook_test(function () {
         cell.render();
         return cell.get_rendered();
     });
-    this.test.assertEquals(output.trim(), '<h1 id=\"foo\">Foo</h1>', 'Markdown JS API works.');
+    this.test.assertEquals(output.trim(), '<h1 id=\"Foo\">Foo<a class=\"anchor-link\" href=\"#Foo\">¶</a></h1>', 'Markdown JS API works.');
     
     // Test menubar entries.
     output = this.evaluate(function () {
         $('#to_code').mouseenter().click();
         $('#to_markdown').mouseenter().click();
         var cell = IPython.notebook.get_selected_cell();
-        cell.set_text('# Bar');
+        cell.set_text('**Bar**');
         $('#run_cell').mouseenter().click();
         return cell.get_rendered();
     });
-    this.test.assertEquals(output.trim(), '<h1 id=\"bar\">Bar</h1>', 'Markdown menubar items work.');
+    this.test.assertEquals(output.trim(), '<p><strong>Bar</strong></p>', 'Markdown menubar items work.');
     
     // Test toolbar buttons.
     output = this.evaluate(function () {
         $('#cell_type').val('code').change();
         $('#cell_type').val('markdown').change();
         var cell = IPython.notebook.get_selected_cell();
-        cell.set_text('# Baz');
+        cell.set_text('*Baz*');
         $('#run_b').click();
         return cell.get_rendered();
     });
-    this.test.assertEquals(output.trim(), '<h1 id=\"baz\">Baz</h1>', 'Markdown toolbar items work.');
+    this.test.assertEquals(output.trim(), '<p><em>Baz</em></p>', 'Markdown toolbar items work.');
     
-    // Test JavaScript models.
-    var output = this.evaluate(function () {
+    // Test markdown headings
 
+    var text = 'multi\nline';
+
+    this.evaluate(function (text) {
         var cell = IPython.notebook.insert_cell_at_index('markdown', 0);
-        cell.set_text('# Qux');
-        cell.render();
-        return cell.get_rendered();
-    });
-    this.test.assertEquals(output.trim(), '<h1 id=\"qux\">Qux</h1>', 'Markdown JS API works.');
+        cell.set_text(text);
+    }, {text: text});
+
+    var set_level = function (level) {
+        return casper.evaluate(function (level) {
+            var cell = IPython.notebook.get_cell(0);
+            cell.set_heading_level(level);
+            return cell.get_text();
+        }, {level: level});
+    };
     
+    var level_text;
+    var levels = [ 1, 2, 3, 4, 5, 6, 2, 1 ];
+    for (var idx=0; idx < levels.length; idx++) {
+        var level = levels[idx];
+        level_text = set_level(level);
+        hashes = new Array(level + 1).join('#');
+        this.test.assertEquals(level_text, hashes + ' ' + text, 'markdown set_heading_level ' + level);
+    }
 });
diff --git a/IPython/nbconvert/exporters/tests/files/notebook2.ipynb b/IPython/nbconvert/exporters/tests/files/notebook2.ipynb
index aedf783..1c96833 100644
--- a/IPython/nbconvert/exporters/tests/files/notebook2.ipynb
+++ b/IPython/nbconvert/exporters/tests/files/notebook2.ipynb
@@ -1,11 +1,10 @@
 {
  "cells": [
   {
-   "cell_type": "heading",
-   "level": 1,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "NumPy and Matplotlib examples"
+    "# NumPy and Matplotlib examples"
    ]
   },
   {
diff --git a/IPython/nbconvert/exporters/tests/test_notebook.py b/IPython/nbconvert/exporters/tests/test_notebook.py
index 65e98e4..2af5491 100644
--- a/IPython/nbconvert/exporters/tests/test_notebook.py
+++ b/IPython/nbconvert/exporters/tests/test_notebook.py
@@ -8,6 +8,7 @@ import json
 from .base import ExportersTestsBase
 from ..notebook import NotebookExporter
 
+from IPython.nbformat.current import validate
 from IPython.testing.tools import assert_big_text_equal
 
 class TestNotebookExporter(ExportersTestsBase):
@@ -29,7 +30,7 @@ class TestNotebookExporter(ExportersTestsBase):
         exporter = self.exporter_class(nbformat_version=3)
         (output, resources) = exporter.from_filename(self._get_notebook())
         nb = json.loads(output)
-        self.assertEqual(nb['nbformat'], 3)
+        validate(nb)
 
     def test_downgrade_2(self):
         exporter = self.exporter_class(nbformat_version=2)
diff --git a/IPython/nbconvert/filters/markdown.py b/IPython/nbconvert/filters/markdown.py
index 10e57b0..b36f336 100755
--- a/IPython/nbconvert/filters/markdown.py
+++ b/IPython/nbconvert/filters/markdown.py
@@ -21,6 +21,7 @@ from pygments.formatters import HtmlFormatter
 from pygments.util import ClassNotFound
 
 # IPython imports
+from IPython.nbconvert.filters.strings import add_anchor
 from IPython.nbconvert.utils.pandoc import pandoc
 from IPython.nbconvert.utils.exceptions import ConversionException
 from IPython.utils.decorators import undoc
@@ -146,6 +147,10 @@ class IPythonRenderer(mistune.Renderer):
         formatter = HtmlFormatter()
         return highlight(code, lexer, formatter)
 
+    def header(self, text, level, raw=None):
+        html = super(IPythonRenderer, self).header(text, level, raw=raw)
+        return add_anchor(html)
+
     # Pass math through unaltered - mathjax does the rendering in the browser
     def block_math(self, text):
         return '$$%s$$' % text
diff --git a/IPython/nbconvert/filters/strings.py b/IPython/nbconvert/filters/strings.py
index 8b9a7bd..03c053a 100755
--- a/IPython/nbconvert/filters/strings.py
+++ b/IPython/nbconvert/filters/strings.py
@@ -4,17 +4,9 @@
 Contains a collection of useful string manipulation filters for use in Jinja
 templates.
 """
-#-----------------------------------------------------------------------------
-# Copyright (c) 2013, the IPython Development Team.
-#
-# Distributed under the terms of the Modified BSD License.
-#
-# The full license is in the file COPYING.txt, distributed with this software.
-#-----------------------------------------------------------------------------
 
-#-----------------------------------------------------------------------------
-# Imports
-#-----------------------------------------------------------------------------
+# Copyright (c) IPython Development Team.
+# Distributed under the terms of the Modified BSD License.
 
 import os
 import re
@@ -28,9 +20,6 @@ from xml.etree import ElementTree
 from IPython.core.interactiveshell import InteractiveShell
 from IPython.utils import py3compat
 
-#-----------------------------------------------------------------------------
-# Functions
-#-----------------------------------------------------------------------------
 
 __all__ = [
     'wrap_text',
@@ -88,9 +77,9 @@ def html2text(element):
 
 
 def add_anchor(html):
-    """Add an anchor-link to an html header tag
+    """Add an anchor-link to an html header
     
-    For use in heading cells
+    For use on markdown headings
     """
     try:
         h = ElementTree.fromstring(py3compat.cast_bytes_py2(html, encoding='utf-8'))
diff --git a/IPython/nbconvert/filters/tests/test_markdown.py b/IPython/nbconvert/filters/tests/test_markdown.py
index d2eb698..5da6259 100644
--- a/IPython/nbconvert/filters/tests/test_markdown.py
+++ b/IPython/nbconvert/filters/tests/test_markdown.py
@@ -1,3 +1,4 @@
+# coding: utf-8
 """Tests for conversions from markdown to other formats"""
 
 # Copyright (c) IPython Development Team.
@@ -26,7 +27,8 @@ class TestMarkdown(TestsBase):
         '#test',
         '##test',
         'test\n----',
-        'test [link](https://google.com/)']
+        'test [link](https://google.com/)',
+    ]
 
     tokens = [
         '*test',
@@ -39,7 +41,8 @@ class TestMarkdown(TestsBase):
         'test',
         'test',
         'test',
-        ('test', 'https://google.com/')]
+        ('test', 'https://google.com/'),
+    ]
 
 
     @dec.onlyif_cmds_exist('pandoc')
@@ -87,6 +90,17 @@ class TestMarkdown(TestsBase):
         for index, test in enumerate(self.tests):
             self._try_markdown(markdown2html, test, self.tokens[index])
 
+    def test_markdown2html_heading_anchors(self):
+        for md, tokens in [
+            ('# test',
+                ('<h1', '>test', 'id="test"', u'&#182;</a>', "anchor-link")
+            ),
+            ('###test head space',
+                ('<h3', '>test head space', 'id="test-head-space"', u'&#182;</a>', "anchor-link")
+            )
+        ]:
+            self._try_markdown(markdown2html, md, tokens)
+
     def test_markdown2html_math(self):
         # Mathematical expressions should be passed through unaltered
         cases = [("\\begin{equation*}\n"
diff --git a/IPython/nbconvert/templates/html/basic.tpl b/IPython/nbconvert/templates/html/basic.tpl
index ce467ac..40ba790 100644
--- a/IPython/nbconvert/templates/html/basic.tpl
+++ b/IPython/nbconvert/templates/html/basic.tpl
@@ -79,17 +79,6 @@ In&nbsp;[&nbsp;]:
 </div>
 {%- endblock markdowncell %}
 
-{% block headingcell scoped %}
-<div class="cell border-box-sizing text_cell rendered">
-{{ self.empty_in_prompt() }}
-<div class="inner_cell">
-<div class="text_cell_render border-box-sizing rendered_html">
-{{ ("#" * cell.level + cell.source) | replace('\n', ' ')  | markdown2html | strip_files_prefix | add_anchor }}
-</div>
-</div>
-</div>
-{% endblock headingcell %}
-
 {% block unknowncell scoped %}
 unknown type  {{ cell.type }}
 {% endblock unknowncell %}
diff --git a/IPython/nbconvert/templates/latex/base.tplx b/IPython/nbconvert/templates/latex/base.tplx
index 6e99ac3..24e0d09 100644
--- a/IPython/nbconvert/templates/latex/base.tplx
+++ b/IPython/nbconvert/templates/latex/base.tplx
@@ -185,27 +185,6 @@ This template does not define a docclass, the inheriting class must define this.
 ((*- endblock figure -*))
 ((*- endmacro *))
 
-% Draw heading cell.  Explicitly map different cell levels.
-((* block headingcell scoped *))
-
-    ((* if cell.level == 1 -*))
-        ((* block h1 -*))\section((* endblock h1 -*))
-    ((* elif cell.level == 2 -*))
-        ((* block h2 -*))\subsection((* endblock h2 -*))
-    ((* elif cell.level == 3 -*))
-        ((* block h3 -*))\subsubsection((* endblock h3 -*))
-    ((* elif cell.level == 4 -*))
-        ((* block h4 -*))\paragraph((* endblock h4 -*))
-    ((* elif cell.level == 5 -*))
-        ((* block h5 -*))\subparagraph((* endblock h5 -*))
-    ((* elif cell.level == 6 -*))
-        ((* block h6 -*))\\*\textit((* endblock h6 -*))
-    ((*- endif -*))
-    {((( cell.source | replace('\n', ' ') | citation2latex | strip_files_prefix | prevent_list_blocks | markdown2latex(markup='markdown_strict+tex_math_dollars') )))}
-    
-
-((* endblock headingcell *))
-
 % Redirect execute_result to display data priority.
 ((* block execute_result scoped *))
     ((* block data_priority scoped *))
diff --git a/IPython/nbconvert/templates/latex/skeleton/null.tplx b/IPython/nbconvert/templates/latex/skeleton/null.tplx
index 00e108e..b5197fa 100644
--- a/IPython/nbconvert/templates/latex/skeleton/null.tplx
+++ b/IPython/nbconvert/templates/latex/skeleton/null.tplx
@@ -75,9 +75,6 @@ consider calling super even if it is a leave block, we might insert more blocks 
         ((*- elif cell.cell_type in ['markdown'] -*))
             ((*- block markdowncell scoped-*))
             ((*- endblock markdowncell -*))
-        ((*- elif cell.cell_type in ['heading'] -*))
-            ((*- block headingcell scoped-*))
-            ((*- endblock headingcell -*))
         ((*- elif cell.cell_type in ['raw'] -*))
             ((*- block rawcell scoped -*))
             ((* if cell.metadata.get('raw_mimetype', '').lower() in resources.get('raw_mimetypes', ['']) *))
diff --git a/IPython/nbconvert/templates/markdown.tpl b/IPython/nbconvert/templates/markdown.tpl
index ab4e20c..a6b9d35 100644
--- a/IPython/nbconvert/templates/markdown.tpl
+++ b/IPython/nbconvert/templates/markdown.tpl
@@ -58,11 +58,6 @@
 {{ cell.source }}
 {% endblock markdowncell %}
 
-
-{% block headingcell scoped %}
-{{ '#' * cell.level }} {{ cell.source | replace('\n', ' ') }}
-{% endblock headingcell %}
-
 {% block unknowncell scoped %}
 unknown type  {{ cell.type }}
 {% endblock unknowncell %}
\ No newline at end of file
diff --git a/IPython/nbconvert/templates/python.tpl b/IPython/nbconvert/templates/python.tpl
index 706ba6e..3918e25 100644
--- a/IPython/nbconvert/templates/python.tpl
+++ b/IPython/nbconvert/templates/python.tpl
@@ -15,7 +15,3 @@
 {% block markdowncell scoped %}
 {{ cell.source | comment_lines }}
 {% endblock markdowncell %}
-
-{% block headingcell scoped %}
-{{ '#' * cell.level }}{{ cell.source | replace('\n', ' ') | comment_lines }}
-{% endblock headingcell %}
diff --git a/IPython/nbconvert/templates/skeleton/null.tpl b/IPython/nbconvert/templates/skeleton/null.tpl
index 4ed4976..ae22cd7 100644
--- a/IPython/nbconvert/templates/skeleton/null.tpl
+++ b/IPython/nbconvert/templates/skeleton/null.tpl
@@ -71,9 +71,6 @@ consider calling super even if it is a leave block, we might insert more blocks 
         {%- elif cell.cell_type in ['markdown'] -%}
             {%- block markdowncell scoped-%}
             {%- endblock markdowncell -%}
-        {%- elif cell.cell_type in ['heading'] -%}
-            {%- block headingcell scoped-%}
-            {%- endblock headingcell -%}
         {%- elif cell.cell_type in ['raw'] -%}
             {%- block rawcell scoped -%}
             {% if cell.metadata.get('raw_mimetype', '').lower() in resources.get('raw_mimetypes', ['']) %}
diff --git a/IPython/nbconvert/tests/files/notebook1.ipynb b/IPython/nbconvert/tests/files/notebook1.ipynb
index 759184e..9ffa91d 100644
--- a/IPython/nbconvert/tests/files/notebook1.ipynb
+++ b/IPython/nbconvert/tests/files/notebook1.ipynb
@@ -1,11 +1,10 @@
 {
  "cells": [
   {
-   "cell_type": "heading",
-   "level": 1,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A simple SymPy example"
+    "# A simple SymPy example"
    ]
   },
   {
diff --git a/IPython/nbconvert/tests/files/notebook2.ipynb b/IPython/nbconvert/tests/files/notebook2.ipynb
index 866f45c..dd5786e 100644
--- a/IPython/nbconvert/tests/files/notebook2.ipynb
+++ b/IPython/nbconvert/tests/files/notebook2.ipynb
@@ -1,11 +1,10 @@
 {
  "cells": [
   {
-   "cell_type": "heading",
-   "level": 1,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "NumPy and Matplotlib examples"
+    "# NumPy and Matplotlib examples"
    ]
   },
   {
@@ -157,11 +156,10 @@
    ]
   },
   {
-   "cell_type": "heading",
-   "level": 2,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here is a very long heading that pandoc will wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap"
+    "## Here is a very long heading that pandoc will wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap"
    ]
   },
   {
diff --git a/IPython/nbformat/tests/invalid.ipynb b/IPython/nbformat/tests/invalid.ipynb
index e7c3032..23fc399 100644
--- a/IPython/nbformat/tests/invalid.ipynb
+++ b/IPython/nbformat/tests/invalid.ipynb
@@ -1,145 +1,306 @@
 {
- "metadata": {
-  "name": 0
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
+ "cells": [
   {
-   "cells": [
-    {
-     "cell_type": "heading",
-     "level": 1,
-     "source": [
-      "nbconvert latex test"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "**Lorem ipsum** dolor sit amet, consectetur adipiscing elit. Nunc luctus bibendum felis dictum sodales. Ut suscipit, orci ut interdum imperdiet, purus ligula mollis *justo*, non malesuada nisl augue eget lorem. Donec bibendum, erat sit amet porttitor aliquam, urna lorem ornare libero, in vehicula diam diam ut ante. Nam non urna rhoncus, accumsan elit sit amet, mollis tellus. Vestibulum nec tellus metus. Vestibulum tempor, ligula et vehicula rhoncus, sapien turpis faucibus lorem, id dapibus turpis mauris ac orci. Sed volutpat vestibulum venenatis."
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "Printed Using Python"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "print(\"hello\")"
-     ],
-     "language": "python",
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "hello\n"
-       ]
-      }
-     ],
-     "prompt_number": 1
-    },
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Lorem ipsum** dolor sit amet, consectetur adipiscing elit. Nunc luctus bibendum felis dictum sodales. Ut suscipit, orci ut interdum imperdiet, purus ligula mollis *justo*, non malesuada nisl augue eget lorem. Donec bibendum, erat sit amet porttitor aliquam, urna lorem ornare libero, in vehicula diam diam ut ante. Nam non urna rhoncus, accumsan elit sit amet, mollis tellus. Vestibulum nec tellus metus. Vestibulum tempor, ligula et vehicula rhoncus, sapien turpis faucibus lorem, id dapibus turpis mauris ac orci. Sed volutpat vestibulum venenatis."
+   ]
+  },
+  {
+   "cell_type": "heading",
+   "level": 2,
+   "metadata": {},
+   "source": [
+    "Printed Using Python"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "heading",
-     "level": 1000,
-     "metadata": {},
-     "source": [
-      "Pyout"
+     "name": "stdout",
+     "output_type": "bad stream",
+     "text": [
+      "hello\n"
      ]
-    },
+    }
+   ],
+   "source": [
+    "print(\"hello\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Pyout"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from IPython.display import HTML\n",
-      "HTML(\"\"\"\n",
-      "<script>\n",
-      "console.log(\"hello\");\n",
-      "</script>\n",
-      "<b>HTML</b>\n",
-      "\"\"\")"
-     ],
-     "language": "python",
+     "data": {
+      "text/html": [
+       "\n",
+       "<script>\n",
+       "console.log(\"hello\");\n",
+       "</script>\n",
+       "<b>HTML</b>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML at 0x1112757d0>"
+      ]
+     },
+     "execution_count": 3,
      "metadata": {},
-     "outputs": [
-      {
-       "html": [
-        "\n",
-        "<script>\n",
-        "console.log(\"hello\");\n",
-        "</script>\n",
-        "<b>HTML</b>\n"
-       ],
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 3,
-       "text": [
-        "<IPython.core.display.HTML at 0x1112757d0>"
-       ]
-      }
-     ],
-     "prompt_number": 3
-    },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from IPython.display import HTML\n",
+    "HTML(\"\"\"\n",
+    "<script>\n",
+    "console.log(\"hello\");\n",
+    "</script>\n",
+    "<b>HTML</b>\n",
+    "\"\"\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "%%javascript\n",
-      "console.log(\"hi\");"
-     ],
-     "language": "python",
+     "data": {
+      "application/javascript": [
+       "console.log(\"hi\");"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Javascript at 0x1112b4b50>"
+      ]
+     },
      "metadata": {},
-     "outputs": [
-      {
-       "javascript": [
-        "console.log(\"hi\");"
-       ],
-       "metadata": {},
-       "output_type": "display_data",
-       "text": [
-        "<IPython.core.display.Javascript at 0x1112b4b50>"
-       ]
-      }
-     ],
-     "prompt_number": 7
-    },
-    {
-     "cell_type": "heading",
-     "level": 3,
-     "metadata": {}
-    },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%%javascript\n",
+    "console.log(\"hi\");"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Image"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from IPython.display import Image\n",
-      "Image(\"http://ipython.org/_static/IPy_header.png\")"
-     ],
-     "language": "python",
+     "data": {
+      "image/png": [
+       "iVBORw0KGgoAAAANSUhEUgAAAggAAABDCAYAAAD5/P3lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
+       "AAAH3AAAB9wBYvxo6AAAABl0RVh0U29mdHdhcmUAd3d3Lmlua3NjYXBlLm9yZ5vuPBoAACAASURB\n",
+       "VHic7Z15uBxF1bjfugkJhCWBsCSAJGACNg4QCI3RT1lEAVE+UEBNOmwCDcjHT1wQgU+WD3dFxA1o\n",
+       "CAikAZFFVlnCjizpsCUjHQjBIAkQlpCFJGS79fvjdGf69vTsc2fuza33eeaZmeqq6jM9vZw6dc4p\n",
+       "BUwC+tE+fqW1fqmRDpRSHjCggS40sBxYDCxKvL8KzNBaL21EPoPB0DPIWVY/4NlE0ffzYfhgu+Qx\n",
+       "GHoy/YFjaK+CcB3QkIIAHAWs3wRZsuhUSs0CXgQeBm7UWi/spn0Z+jA5yxpEfYruqnwYllRic5a1\n",
+       "MaWv8U5gaT4M19Sx396IAnZLfB/SLkEMhp5O/3YL0AvoAHaKXl8HLlZK3QZcpbWe0lbJDOsaHuDU\n",
+       "0e4u4JAy2wPk/C1JzrKWArOQ0fUtwH35MOysQxaDwbCO0NFuAXoh6wPjgQeUUvcqpUa0WyCDoQls\n",
+       "CIwBjgfuAV7KWdY+7RWpmJxlXZezrEdylvXxdstiMKzrGAtCYxwI/EspdZbW+g/tFsbQ67kQuBHY\n",
+       "FNgseh9FV6vCbUAeWBC9PgBeq2EfS6J2MQOBrRDTe5KdgAdzlvW1fBjeUUP/3UbOsoYBE6OvG7VT\n",
+       "FoOhL9Af+BUwFLkZpV+DaY6V4UPkRpb1+ncT+m8nGwK/V0oN01qf025hDL2XfBi+DLycLMtZVo6u\n",
+       "CsKfGnSq8/NheEpqHwOBEcDBwJnAsGhTP2ByzrJG5cPwnQb22Sy+0G4BDIa+RH+t9dmlNiqlFKIk\n",
+       "JJWGi+jq5JPmq8BbJJQArfXqpkncczlbKbVQa/3rdgtiMNRCPgxXAK8Ar+Qs63LgXmDvaPPGwPeA\n",
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+       "TdZ9K52xrhTl7knnUVB6SqVeTsr4apQU6lDEbG4hCsFbROsRBE1ebjrwnNB2/XGIGf5gRBkYhPyv\n",
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+       "9Cpe28gaJgORqEEAbNffDLlvHIQoAndR8NEYilwjExD/nwuUiTQ0GAwGw7qC7fqjEUvKqsBzmhWd\n",
+       "t05gu/5pyNoifw48J9N5PForxQeeNFMMBoPBYDD0DWL/llvK1In9jt4zCoLBYDAYDH2DePo5MwrJ\n",
+       "dv0hFPwTnjBRDAaDwWAw9A3+hPgOHRPl25iK+FhsiuR4OARx0Lwf+J1REAwGg8Fg6AMEnvNklL78\n",
+       "HMRRca/E5hVINNIVwI2B56z6/3ExLRI31pXNAAAAAElFTkSuQmCC\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image at 0x111275490>"
+      ]
+     },
+     "execution_count": 6,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "png": 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/pIqv1FrXnVNh7AmTR3V0qIwwRH1E4E28pd5+De0hZ1m/Bb4bfX0+H4Z7dMM+hgGjkDwC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\nHMRRca/E5hVINNIVwI2B56z6/3ExLRI31pXNAAAAAElFTkSuQmCC\n",
-       "prompt_number": 6,
-       "text": [
-        "<IPython.core.display.Image at 0x111275490>"
-       ]
-      }
-     ],
-     "prompt_number": 6
+     "output_type": "execute_result"
     }
    ],
-   "metadata": {}
+   "source": [
+    "from IPython.display import Image\n",
+    "Image(\"http://ipython.org/_static/IPy_header.png\")"
+   ]
   }
- ]
-}
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/IPython/nbformat/tests/test4.ipynb b/IPython/nbformat/tests/test4.ipynb
index 0562011..fa14dd2 100644
--- a/IPython/nbformat/tests/test4.ipynb
+++ b/IPython/nbformat/tests/test4.ipynb
@@ -1,11 +1,10 @@
 {
  "cells": [
   {
-   "cell_type": "heading",
-   "level": 1,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "nbconvert latex test"
+    "# nbconvert latex test"
    ]
   },
   {
@@ -16,11 +15,10 @@
    ]
   },
   {
-   "cell_type": "heading",
-   "level": 2,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Printed Using Python"
+    "## Printed Using Python"
    ]
   },
   {
@@ -43,11 +41,10 @@
    ]
   },
   {
-   "cell_type": "heading",
-   "level": 2,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Pyout"
+    "## Pyout"
    ]
   },
   {
@@ -111,11 +108,10 @@
    ]
   },
   {
-   "cell_type": "heading",
-   "level": 3,
+   "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Image"
+    "### Image"
    ]
   },
   {
diff --git a/IPython/nbformat/tests/test_validator.py b/IPython/nbformat/tests/test_validator.py
index eb91953..c0e2402 100644
--- a/IPython/nbformat/tests/test_validator.py
+++ b/IPython/nbformat/tests/test_validator.py
@@ -28,7 +28,7 @@ class TestValidator(TestsBase):
         self.assertEqual(isvalid(nb), True)
 
     def test_nb4(self):
-        """Test that a v3 notebook passes validation"""
+        """Test that a v4 notebook passes validation"""
         with self.fopen(u'test4.ipynb', u'r') as f:
             nb = read(f, u'json')
         validate(nb)
@@ -37,9 +37,9 @@ class TestValidator(TestsBase):
     def test_invalid(self):
         """Test than an invalid notebook does not pass validation"""
         # this notebook has a few different errors:
-        # - the name is an integer, rather than a string
         # - one cell is missing its source
-        # - one cell has an invalid level
+        # - invalid cell type
+        # - invalid output_type
         with self.fopen(u'invalid.ipynb', u'r') as f:
             nb = read(f, u'json')
         with self.assertRaises(ValidationError):
diff --git a/IPython/nbformat/v4/__init__.py b/IPython/nbformat/v4/__init__.py
index e753218..73b53a3 100644
--- a/IPython/nbformat/v4/__init__.py
+++ b/IPython/nbformat/v4/__init__.py
@@ -6,7 +6,7 @@
 from .nbbase import (
     NotebookNode, from_dict,
     nbformat, nbformat_minor, nbformat_schema,
-    new_code_cell, new_heading_cell, new_markdown_cell, new_notebook,
+    new_code_cell, new_markdown_cell, new_notebook,
     new_output, output_from_msg,
 )
 
diff --git a/IPython/nbformat/v4/convert.py b/IPython/nbformat/v4/convert.py
index 417c2a1..6770d80 100644
--- a/IPython/nbformat/v4/convert.py
+++ b/IPython/nbformat/v4/convert.py
@@ -4,6 +4,7 @@
 # Distributed under the terms of the Modified BSD License.
 
 import json
+import re
 
 from .nbbase import (
     nbformat, nbformat_minor,
@@ -72,6 +73,7 @@ def upgrade(nb, from_version=3, from_minor=0):
 def upgrade_cell(cell):
     """upgrade a cell from v3 to v4
 
+    heading cell -> markdown heading
     code cell:
         - remove language metadata
         - cell.input -> cell.source
@@ -82,9 +84,16 @@ def upgrade_cell(cell):
     if cell.cell_type == 'code':
         cell.pop('language', '')
         cell.metadata.collapsed = cell.pop('collapsed')
-        cell.source = cell.pop('input')
+        cell.source = cell.pop('input', '')
         cell.execution_count = cell.pop('prompt_number', None)
         cell.outputs = upgrade_outputs(cell.outputs)
+    elif cell.cell_type == 'heading':
+        cell.cell_type = 'markdown'
+        level = cell.pop('level', 1)
+        cell.source = '{hashes} {single_line}'.format(
+            hashes='#' * level,
+            single_line = ' '.join(cell.get('source', '').splitlines()),
+        )
     elif cell.cell_type == 'html':
         # Technically, this exists. It will never happen in practice.
         cell.cell_type = 'markdown'
@@ -98,6 +107,8 @@ def downgrade_cell(cell):
         - cell.input <- cell.source
         - cell.prompt_number <- cell.execution_count
         - update outputs
+    markdown cell:
+        - single-line heading -> heading cell
     """
     if cell.cell_type == 'code':
         cell.language = 'python'
@@ -105,6 +116,13 @@ def downgrade_cell(cell):
         cell.prompt_number = cell.pop('execution_count', None)
         cell.collapsed = cell.metadata.pop('collapsed', False)
         cell.outputs = downgrade_outputs(cell.outputs)
+    elif cell.cell_type == 'markdown':
+        source = cell.get('source', '')
+        if '\n' not in source and source.startswith('#'):
+            prefix, text = re.match(r'(#+)\s*(.*)', source).groups()
+            cell.cell_type = 'heading'
+            cell.source = text
+            cell.level = len(prefix)
     return cell
 
 _mime_map = {
diff --git a/IPython/nbformat/v4/nbbase.py b/IPython/nbformat/v4/nbbase.py
index adb223c..f45ca0f 100644
--- a/IPython/nbformat/v4/nbbase.py
+++ b/IPython/nbformat/v4/nbbase.py
@@ -121,16 +121,6 @@ def new_markdown_cell(source='', **kwargs):
     validate(cell, 'markdown_cell')
     return cell
 
-def new_heading_cell(source='', **kwargs):
-    """Create a new heading cell"""
-    cell = NotebookNode(cell_type='heading', source=source)
-    cell.update(from_dict(kwargs))
-    cell.setdefault('metadata', NotebookNode())
-    cell.setdefault('level', 1)
-
-    validate(cell, 'heading_cell')
-    return cell
-
 def new_raw_cell(source='', **kwargs):
     """Create a new raw cell"""
     cell = NotebookNode(cell_type='raw', source=source)
diff --git a/IPython/nbformat/v4/nbformat.v4.schema.json b/IPython/nbformat/v4/nbformat.v4.schema.json
index 9a3f190..988b6ac 100644
--- a/IPython/nbformat/v4/nbformat.v4.schema.json
+++ b/IPython/nbformat/v4/nbformat.v4.schema.json
@@ -59,7 +59,6 @@
                 "oneOf": [
                     {"$ref": "#/definitions/raw_cell"},
                     {"$ref": "#/definitions/markdown_cell"},
-                    {"$ref": "#/definitions/heading_cell"},
                     {"$ref": "#/definitions/code_cell"}
                 ]
             }
@@ -118,34 +117,6 @@
             }
         },
 
-        "heading_cell": {
-            "description": "Notebook heading cell.",
-            "type": "object",
-            "additionalProperties": false,
-            "required": ["cell_type", "metadata", "source", "level"],
-            "properties": {
-                "cell_type": {
-                    "description": "String identifying the type of cell.",
-                    "enum": ["heading"]
-                },
-                "metadata": {
-                    "description": "Cell-level metadata.",
-                    "type": "object",
-                    "properties": {
-                        "name": {"$ref": "#/definitions/misc/metadata_name"},
-                        "tags": {"$ref": "#/definitions/misc/metadata_tags"}
-                    },
-                    "additionalProperties": true
-                },
-                "source": {"$ref": "#/definitions/misc/source"},
-                "level": {
-                    "description": "Level of heading cells.",
-                    "type": "integer",
-                    "minimum": 1
-                }
-            }
-        },
-
         "code_cell": {
             "description": "Notebook code cell.",
             "type": "object",
diff --git a/IPython/nbformat/v4/rwbase.py b/IPython/nbformat/v4/rwbase.py
index 7acf407..6d33f8f 100644
--- a/IPython/nbformat/v4/rwbase.py
+++ b/IPython/nbformat/v4/rwbase.py
@@ -44,14 +44,15 @@ def rejoin_lines(nb):
     for cell in nb.cells:
         if 'source' in cell and isinstance(cell.source, list):
             cell.source = _join_lines(cell.source)
-        if cell.cell_type == 'code':
-            for output in cell.outputs:
-                if output.output_type in {'execute_result', 'display_data'}:
-                    for key, value in output.data.items():
+        if cell.get('cell_type', None) == 'code':
+            for output in cell.get('outputs', []):
+                output_type = output.get('output_type', '')
+                if output_type in {'execute_result', 'display_data'}:
+                    for key, value in output.get('data', {}).items():
                         if key != 'application/json' and isinstance(value, list):
                             output.data[key] = _join_lines(value)
-                elif output.output_type == 'stream':
-                    if isinstance(output.text, list):
+                elif output_type:
+                    if isinstance(output.get('text', ''), list):
                         output.text = _join_lines(output.text)
     return nb
 
diff --git a/IPython/nbformat/v4/tests/nbexamples.py b/IPython/nbformat/v4/tests/nbexamples.py
index da9eb3f..b55a0c4 100644
--- a/IPython/nbformat/v4/tests/nbexamples.py
+++ b/IPython/nbformat/v4/tests/nbexamples.py
@@ -4,7 +4,7 @@ import os
 from base64 import encodestring
 
 from ..nbbase import (
-    new_code_cell, new_heading_cell, new_markdown_cell, new_notebook,
+    new_code_cell, new_markdown_cell, new_notebook,
     new_output, new_raw_cell
 )
 
@@ -31,9 +31,8 @@ cells.append(new_raw_cell(
     source='A random array',
 ))
 
-cells.append(new_heading_cell(
-    source=u'My Heading',
-    level=2,
+cells.append(new_markdown_cell(
+    source=u'## My Heading',
 ))
 
 cells.append(new_code_cell(
diff --git a/IPython/nbformat/v4/tests/test_convert.py b/IPython/nbformat/v4/tests/test_convert.py
index 06f59e1..3cfe8da 100644
--- a/IPython/nbformat/v4/tests/test_convert.py
+++ b/IPython/nbformat/v4/tests/test_convert.py
@@ -1,10 +1,13 @@
 import copy
 
+import nose.tools as nt
+
 from IPython.nbformat.current import validate
 from .. import convert
 
 from . import nbexamples
 from IPython.nbformat.v3.tests import nbexamples as v3examples
+from IPython.nbformat import v3, v4
 
 def test_upgrade_notebook():
     nb03 = copy.deepcopy(v3examples.nb0)
@@ -17,3 +20,48 @@ def test_downgrade_notebook():
     validate(nb04)
     nb03 = convert.downgrade(nb04)
     validate(nb03)
+
+def test_upgrade_heading():
+    v3h = v3.new_heading_cell
+    v4m = v4.new_markdown_cell
+    for v3cell, expected in [
+        (
+            v3h(source='foo', level=1),
+            v4m(source='# foo'),
+        ),
+        (
+            v3h(source='foo\nbar\nmulti-line\n', level=4),
+            v4m(source='#### foo bar multi-line'),
+        ),
+    ]:
+        upgraded = convert.upgrade_cell(v3cell)
+        nt.assert_equal(upgraded, expected)
+
+def test_downgrade_heading():
+    v3h = v3.new_heading_cell
+    v4m = v4.new_markdown_cell
+    v3m = lambda source: v3.new_text_cell('markdown', source)
+    for v4cell, expected in [
+        (
+            v4m(source='# foo'),
+            v3h(source='foo', level=1),
+        ),
+        (
+            v4m(source='#foo'),
+            v3h(source='foo', level=1),
+        ),
+        (
+            v4m(source='#\tfoo'),
+            v3h(source='foo', level=1),
+        ),
+        (
+            v4m(source='# \t  foo'),
+            v3h(source='foo', level=1),
+        ),
+        (
+            v4m(source='# foo\nbar'),
+            v3m(source='# foo\nbar'),
+        ),
+    ]:
+        downgraded = convert.downgrade_cell(v4cell)
+        nt.assert_equal(downgraded, expected)
diff --git a/IPython/nbformat/v4/tests/test_nbbase.py b/IPython/nbformat/v4/tests/test_nbbase.py
index 4d6c5e8..6172657 100644
--- a/IPython/nbformat/v4/tests/test_nbbase.py
+++ b/IPython/nbformat/v4/tests/test_nbbase.py
@@ -6,7 +6,7 @@ import nose.tools as nt
 from IPython.nbformat.validator import isvalid, validate, ValidationError
 from ..nbbase import (
     NotebookNode, nbformat,
-    new_code_cell, new_heading_cell, new_markdown_cell, new_notebook,
+    new_code_cell, new_markdown_cell, new_notebook,
     new_output, new_raw_cell,
 )
 
@@ -34,17 +34,6 @@ def test_raw_cell():
     cell = new_raw_cell('hi')
     nt.assert_equal(cell.source, u'hi')
 
-def test_empty_heading_cell():
-    cell = new_heading_cell()
-    nt.assert_equal(cell.cell_type, u'heading')
-    nt.assert_equal(cell.source, '')
-    nt.assert_equal(cell.level, 1)
-
-def test_heading_cell():
-    cell = new_heading_cell(u'hi', level=2)
-    nt.assert_equal(cell.source, u'hi')
-    nt.assert_equal(cell.level, 2)
-
 def test_empty_code_cell():
     cell = new_code_cell('hi')
     nt.assert_equal(cell.cell_type, 'code')
diff --git a/IPython/nbformat/v4/tests/test_validate.py b/IPython/nbformat/v4/tests/test_validate.py
index 9caf5f0..dbef2cb 100644
--- a/IPython/nbformat/v4/tests/test_validate.py
+++ b/IPython/nbformat/v4/tests/test_validate.py
@@ -12,7 +12,7 @@ from IPython.nbformat.validator import validate, ValidationError
 from ..nbjson import reads
 from ..nbbase import (
     nbformat,
-    new_code_cell, new_heading_cell, new_markdown_cell, new_notebook,
+    new_code_cell, new_markdown_cell, new_notebook,
     new_output, new_raw_cell,
 )
 
@@ -73,31 +73,6 @@ def test_invalid_markdown_cell():
     with nt.assert_raises(ValidationError):
         validate4(cell, 'markdown_cell')
 
-def test_invalid_heading_cell():
-    cell = new_heading_cell()
-
-    cell['source'] = 5
-    with nt.assert_raises(ValidationError):
-        validate4(cell, 'heading_cell')
-
-    cell = new_heading_cell()
-    del cell['metadata']
-
-    with nt.assert_raises(ValidationError):
-        validate4(cell, 'heading_cell')
-
-    cell = new_heading_cell()
-    del cell['source']
-
-    with nt.assert_raises(ValidationError):
-        validate4(cell, 'heading_cell')
-
-    cell = new_heading_cell()
-    del cell['cell_type']
-
-    with nt.assert_raises(ValidationError):
-        validate4(cell, 'heading_cell')
-
 def test_invalid_raw_cell():
     cell = new_raw_cell()
 
diff --git a/docs/source/notebook/nbformat.rst b/docs/source/notebook/nbformat.rst
index beb3d4c..57988b3 100644
--- a/docs/source/notebook/nbformat.rst
+++ b/docs/source/notebook/nbformat.rst
@@ -82,24 +82,9 @@ as defined in `GitHub-flavored markdown`_, and implemented in marked_.
       "source" : ["some *markdown*"],
     }
 
+.. versionchanged:: 4.0
 
-Heading cells
--------------
-
-Heading cells are single lines describing a section header (mapping onto h1-h6 tags in HTML).
-These cells indicate structure of the document,
-and are used for things like outline-views and automatically generating HTML anchors
-within the page for quick navigation.
-They have a ``level`` field, with an integer value from 1-6 (inclusive).
-
-.. sourcecode:: python
-
-    {
-      "cell_type" : "markdown",
-      "metadata" : {},
-      "level" : 1, # An integer on [1-6]
-      "source" : ["A simple heading"],
-    }
+    Heading cells have been removed, in favor of simple headings in markdown.
 
 
 Code cells