Just fixing some typos

ipynb/pal3.ipynb

@@ -257,7 +257,7 @@
    "metadata": {},
    "source": [
     "The main point of the `Panama` class is to allow the `.search()` method to search for a long palindrome. The [overall strategy](http://norvig.com/pal-alg.html#v3) is explained elsewhere. The search\n",
-    "adds a lett1er at a time to both left and right side, backtracking when necessary. The state of the search is represented by the four fields `.left, .L, .R, .right`, for example:\n",
+    "adds a letter at a time to both left and right side, backtracking when necessary. The state of the search is represented by the four fields `.left, .L, .R, .right`, for example:\n",
     " \n",
     "    A man, a plan, a cam, a yak, a yam, a canal, Panama\n",
     "    \n",
@@ -272,7 +272,7 @@
     "\n",
     "    cat(left + [L]) == cat([R] + right)[::-1]\n",
     "    \n",
-    "The `search` method would be more straightforward if we could write it is a recursive function. But Python does not perform well when recursing to 100 thousand levels deep. So instead I manually manage a *stack* of *commands* that tell the search what to do and to undo. A command can be a `DoCommand`, which consists of a list of letters describing all the possible actions we could take at this point. Actions include letters that could be added (only the letters that make a legitimate prefix of a known phrase in `.L` and a legitimate suffix of a known phrase in `.R`). Actions can also include the character `','`, which is used to dignal that `.L` is a complete word and should be moved ontot he `.left` list, or `';'` to signal the same for `.R/.right`. A command can also be a `UndoCommand`, which consists of a single character; one that was previously chosen to be done. So the list of characters in a `DoCommand` constitutes a choice point; we first choose one, and continue deeper from there, but we put on the command stack an `UndoCommand` to reverse the effects of the action, and put back the remaining characters to try instead, if the first character doesn't work out. Note that we pop characters off the end of a `DoCommand`, so the last character is the first one tried.\n",
+    "The `search` method would be more straightforward if we could write it is a recursive function. But Python does not perform well when recursing to 100 thousand levels deep. So instead I manually manage a *stack* of *commands* that tell the search what to do and to undo. A command can be a `DoCommand`, which consists of a list of letters describing all the possible actions we could take at this point. Actions include letters that could be added (only the letters that make a legitimate prefix of a known phrase in `.L` and a legitimate suffix of a known phrase in `.R`). Actions can also include the character `','`, which is used to signal that `.L` is a complete word and should be moved onto the `.left` list, or `';'` to signal the same for `.R/.right`. A command can also be a `UndoCommand`, which consists of a single character; one that was previously chosen to be done. So the list of characters in a `DoCommand` constitutes a choice point; we first choose one, and continue deeper from there, but we put on the command stack an `UndoCommand` to reverse the effects of the action, and put back the remaining characters to try instead, if the first character doesn't work out. Note that we pop characters off the end of a `DoCommand`, so the last character is the first one tried.\n",
     "\n",
     "Let's see how it works:"
    ]
@@ -452,7 +452,7 @@
     "- I'm not sure when to end a word and when to try to continue to a longer word; experimentation here would be useful.\n",
     "- The program is deterministic, and thus always finds the same plaindrome. that's boring; can some randomness be introduced?\n",
     "- Can we make more interesting phrases? Include determiners other than \"a\" and \"an\"; include adjectives, etc.\n",
-    "- The counts of prefixes and suffixes include all the phrases in the dictionary. But we are not allowed to repeat a phrase, so can we modify the code to subtract one from the counts every time a phrase is used (and add onr back in when we backtrack over the phrase)?\n",
+    "- The counts of prefixes and suffixes include all the phrases in the dictionary. But we are not allowed to repeat a phrase, so can we modify the code to subtract one from the counts every time a phrase is used (and add one back in when we backtrack over the phrase)?\n",
     "\n",
     "Perhaps you can find other areas to explore.\n",
     "\n",