## 2018-10-16

### Scala-like match expression for JavaScript and TypeScript

The Scala language has a nice construct for branching based on the type of an object and at the same time extracting information from the the object. In Scala it's called a match expression.  ML and Haskell both have a similar construct, case expressions. Haxe has a similar switch expression.

Here is a Scala example straight from the Scala documentation site

First, we make a hierarchy of classes:

[If no code is showing above this line, try reloading the page using http instead of https.]

Now we can write a function like this using a match expression.

Can we do the same in TypeScript?

First we define the abstract base class:

The three methods are deconstuctors. The generic Option<a> type is defined in the collections module. It is an abstract class that has two concrete realizations. One is None<a>; objects of type None<a> have no fields and indicate an absence of a value of type a. The other is Some<a>; objects of type Some<a> have one field of type a; they indicate the presence of a value of type a. We use Option values to encode the success or failure of a pattern match.

In the concrete subclasses, we override the deconstructors so they succeed when applied to the appropriate type of recipient.

Next we define three convenience functions that take a function return a function.

That concludes the definition of the Notification, its subclasses, and associated functions.

Now we are ready to write some client code that uses pattern matching.

This code uses the match function defined in the collections module. The match function takes as arguments a value of any type and then a sequence of functions that return Option objects. It applies each of these functions in turn until one succeeds. The result of the call to match is the value that was wrapped in the Some object. If all the functions return None objects, then an error is thrown.

The code of the match function and a similar function optMatch that does not unwrap the result is given below:

We can supply a default action/value by supplying a function that will always succeed:

A function can fail even if its pattern match succeeds. To help with this the collections module exports a function guard:

With this we can write matches like this

## 2018-05-16

### How I use Git

Below are some thoughts on how I use Git and SourceTree.

## First some terminology

Repository:
A database containing a bunch of objects of the following kinds
• commits,
• blobs (each of which represents the contents of a file at some time),
• tree objects, and
• annotated tags.
Each of these object kinds are described below. Each repository also contains
• branches (also described),
• an index (described below
• information about how to contact other repositories.
Typically, for each project each developer has a repository on their local machine and there is also one repository that acts as a hub.  Typically the hub repository exists on a hosting service such as GitHub or Git Lab.  Each of the developers' repositories knows the hub repository as "origin".
Blob
A blob is just the contents of an ordinary file at some point in time.  In some cases the data is compressed in the database.; that's really not something you need to concern yourself with.  Blobs are immutable, so once created they always have the same contents. The interesting thing is how blobs are addressed.  Each blob is given an address that is a hash of its contents. Since Git uses a cyptographically secure hash function with 256 bits of output, the chances pretty good that any two blobs that have the same address. represent files with exactly the same content.
Tree
Just as a blob represents a snapshot of the contents of an ordinary file, a tree object represents a snapshot of the contents of a directory (aka folder).  Tree objects are immutable. A tree object can be thought of as a sequence of tuples, each of the form (t, p, n, a) where t gives the type of object (blob, tree, etc), p is a number representing file permissions, n is a file name, and a is the address of the file (i.e., its hash code).  Trees objects are also addressed by secure hash codes.
Commit:
A commit object consists of the address of a tree object (this represents the value of the commit's file tree) + the addresses of its parents + a message + a time stamp + the names of the author and the committer. Commits are immutable. The address of a commit is a secure hash of its value. Thus two commit objects in different repositories with the same address will (with near 100% probability) have the same value. Commits usually have one parent, but may have 0 or 2 or even more; commits form a rooted directed acyclic graph. When we talk about a commit we might be talking about an object (which exists in one repository) or a value (which might be represented by objects in different repositories). It often doesn't matter which we mean.
Branch:
A variable whose value is the address of a commit. Branches are mutable and are local to repositories; for example there might be a branch called master in my local repository and a branch called master in the hub repository; they are not the same and might, at some points in time, have different values. Each repository has two sets of branches: Local branches are intended for local work. Remote tracking branches represent local branches of other (remote) repositories; however the value of a remote tracking branch could be out of date with respect to the branch that it is tracking.
Currently checked out branch:
The branch that was most recently checked out. Making a new commit typically updates this branch.
Working copy:
A state of the file tree represented in a computer's file system. Each time you check out a branch, the working copy gets overwritten.
Index (also called the Staging Area).
A place in a repository where Git keeps changes that will become part of a commit in the future.
Merge:
A merge operation combines two commits to create another commit. If we merge two commits x and y that have a least common ancestor z, then the result commit w=merge(x,y) will contain all changes from z to x and also all the changes from z to y. Here is an example where we consider a file tree that contains only one file, so the state of the file tree is simply a sequence of characters.  Suppose z is a⏎b⏎c⏎d⏎e⏎f⏎ [The ⏎ represents the end of a line.] and x is a⏎c⏎d⏎e⏎f⏎ and y is a⏎b⏎c⏎d⏎e⏎f⏎g⏎. The changes from z to x is {delete the b between a and c}. The changes from y to z are {add a g after the f}. The union of the changes is {delete the b between a and c, add a g after the f}. So w is ac⏎d⏎e⏎f⏎g⏎. Sometimes it's not clear how to merge files, and in that case there is a "merge conflict". When y is the least common ancestor of x and y, then there is no need to create a new commit, so merge(x,y)=merge(y,x)=x. This is called merge by fast-forward.
Line of development:
A sequence of commits that may get added to over time. "Line of development" isn't really a Git concept, but I find it useful to think about lines of development. Often people use the term "branch" for this, but that's confusing because in Git a branch is a variable whose value is the address of a single commit; not a sequence of addresses of commits. Also, while each Git branch is associated with one repository, a line of development spans multiple repositories. I found Git much easier to use once I finally realized that branches and lines of development are different (but closely related) concepts. So next I'll try to explain with an example what I mean by a line of development.

## More on "lines of development"

Consider this evolution of a system where commits are ordered in the order they are created (from left to right)
[Arrows go from children to their parents.] There are three lines of development here: the shared line, the x line and the y line. The x and y lines represent two different features and might be done by two different programmers. The shared line represents the amalgam of all completed features. Once a feature is completed, the last commit on its line is merged into the shared line. Once we have finished with a feature, we can delete the branches associated with it, but the lines of development remain. Commit x3 is particularly important. This represents the programmer catching up with all features completed since they started work on their feature -- in this case, just y. It's a good idea to make these catch-up merges each time we notice the shared line has been added to. (In the example the developer on the x line could have caught up earlier.) Running unit tests after these merges is important, since it can alert us to any conflicts that aren't flagged by Git. It's particularly important to make these catch-up merges (if needed) before merging back into the shared line. This ensures, that untested combinations of features never make it onto the shared line. (And, as we will see below, it also prevents merge conflicts from happening on GitHub.) A point not captured by the diagram above is that, if we allow fast-forward merges, not all the commits shown in the picture are different. We will have y1=shared1 and x4=shared2. SourceTree  might display the graph above like this
which is simpler, in that it has fewer nodes, but doesn't clearly show the lines of development. Like I said above, lines of development do not correspond to anything in Git. They are just a product how we think about software development.

## The five branches

Usually you only have to worry about two lines of development at a time: a shared line (typically called master) and a line that only you are working on. For illustration I'll call the shared line "shared" and the other line "feature". In implementation the lines of development are represented (sort of) by branches. But thanks to Git being distributed, line of development x is represented by actual branches in a number of places:
• There is GitHub's x branch, i.e. a copy of the branch that is on the hub. [I'm assuming here that the central repository is GitHub, but it could just as well by Git Lab or Bit Bucket or a private server.]
• There is a tracking branch in your repository; this is called origin/x.
• And there is your local copy of the branch, which is called x.
That's 3 branches for each line of development and they can all have different values. I'll call them "GitHub's x", "my origin/x", and "my x". Plus everyone else may have one or two copies in their own repositories. So if 10 people are working on 1 feature each, that's 11 lines (10 feature lines + the shared line) and there could be up to 21 branches for each line of development (1 on GitHub and then each local repository can have a local and a tracking branch). So there are up to 231 branches in total. Luckily you usually only have to worry 2 lines at a time and you only have to worry about the copies on GitHub and the copies on your own machine. And, of these, I don't ever use my origin/feature, so that's only 5 branches I have to worry about:
• GitHub's shared,
• my origin/shared,
• my shared,
• my feature,
• GitHub's feature.
plus the working copy and the index. We try to maintain the following relationships at all times between the commits that are the values of these 5 branches. (Here ≤ means "is equal to or an ancestor of".)
my shared ≤ my origin/shared ≤ GitHub's shared

and
GitHub's feature ≤ my feature

It's also a good idea to try to fold any changes made to the shared into our feature as soon as they show on GitHub's shared branch. So we try to keep
my shared = my origin/shared = GitHub's shared ≤ my feature

true as much as practical. (I.e., that my feature is descended from my shared, which is the same as the tracking branch which is up to date.) We do this with catch-up merges. This way, when we read, edit, and test our code, we are reading, editing, and testing it in the context of all completed features. Furthermore, when a pull-request is merged we want
my shared = my origin/shared = GitHub's shared ≤ GitHub's feature = my feature

That way merge-conflicts won't happen on GitHub's server.

## Information flow

The flow of information that I use is shown in the figure. I'll explain each part below.

## Basic operations

For the rest of the article I'll assume you are using SourceTree. Of course everything SourceTree does can also be done from the command line. Some of the basic operations of SourceTree work like this (somewhat simplified):
"Fetch" updates all your tracking branches. So Fetch means my origin/x := GitHub's x, for every x branch in GitHub's repository. Typically we use Fetch to bring changes made to GitHub's shared to my origin/shared.
"Pull" means update my current branch from GitHub's repository. So Pull means my origin/x := GitHub's x ; my x := merge( my x, my origin/x), where x is the currently checked-out branch. Typically this is a fast-forward merge. (Usually I do a Fetch first and then a Pull if x is behind origin/x. When x is behind origin/x the merge is done by "fast forward", i.e., we have my x := my origin/x). Typically we use Pull to bring changes made to GitHub's shared to my shared.
"Branch" means create a new branch.  It means y := x  where y is an existing branch and x is the currently checked-out branch. y becomes the currently checked-out branch. Typically we use Branch when we start working on a new feature.
"Merge" means my x := merge(my x, my y) where x is the currently checked-out branch and y is another branch. Usually we either merge my shared into my feature. In the flow I use, merges are always merging my shared with my feature to make a new value for my feature branch.
"Check out" updates the working copy to the value of a particular commit. In the flow this is used to check out my feature branch. Some operation in SourceTree only apply to the currently checked out branch, so there are times you will check out a branch just so you can do something else with it, such as a pull.
"Stage" Staging means moving changes that are in the working copy to the index. "Commit" Commit makes a new commit based on the changes in the index.  Of course it updates the currently checked-out branch.
"Push" means update GitHub's copy of the branch; it also updates the tracking branch. So Push means GitHub's x := my x; my origin/x := GitHub's x, where x is the currently checked-out branch. In the work flow, Push is used to push commits on my feature branch to GitHub's feature branch.
"Make and merge a pull request". A pull request is a request for someone else to review the changes on a branch and to merge one branch into another.  (Pull requests are called merge requests on Git Lab, which is a better name in my opinion.)  Pull requests are not a feature of Git, but rather of hosting services such as GitHub. SourceTree can help you create merge requests. The actual merging of the pull request is done using GitHub's web interface.

Here are some recipes for doing some common tasks with SourceTree.

### Catch up the shared branch

1. In source tree click on Fetch
2. If shared and origin/shared are the same, stop
3. Check out the shared branch by double clicking on "shared" under "Branches" on the left sidebar.
Click on Pull to get the local shared branch up to date with origin/shared
Here is an example. In this case someone has extended the shared line of development with a new commit, c. We first update origin/shared and then shared. HEAD indicates which branch is the checked out branch.

### Make a feature branch

1. Catch up the shared branch (see above)
2. Check out shared (if not already there).
3. Click on Branch.
4. Type "feature" as the New Branch. Click ok.
Here is an example. The branch operation does not create and new commits.

1. Check out feature (if not already the checked out branch).
2. Make changes to the files. Run tests.  Etc.
3. Back in source tree, Cmd-R (Mac) or Cntl-R (Windows) or View >> Refresh
4. Select "Uncommitted changes"
5. Review all unstaged changes.
6. Stage all changes you want as part of the commit.
7. Click Commit. (This doesn't actually do the commit.)
8. Enter commit message
9. Click on "Commit" button at lower right. (This does the commit.)
10. Push the new commit to the origin, by clicking Push and OK.
11. If you've never pushed the branch before you may need to check a box in the previous step before clicking OK.
Pushing the new commit to the origin is optional, but it is good to do for a couple of reasons. One is that it saves your work remotely. The other is that it lets other people on your team see what you are doing. Here is an example: Here We've alreade one commit x on the feature line and make another y.

### Catch up the feature branch.

(Do this fairly frequently)



1. Catch up the shared branch (see above).
2. If shared is an ancestor of feature you are caught up. Stop.
3. Check out feature (if not already the checked out branch).
4. Click on merge.
5. Select shared.
6. Click OK.
7. Check for any merge conflicts. If there are merge conflicts they need to be resolved. That's a whole other story. (Maybe another blog post.)
8. Even absent merge conflicts, there may be silent problems that prevent compilation or introduce bugs. So carefully inspect all differences between the merged version and the previous version of feature. Also recompile and run unit tests.
9. Click on Push.
The final push is optional, but it saves your work.  Also you need to do it if you are going to make a pull request -- more on that below. Here is an example. In this case some one has added a new commit, c, to the shared line. We first update our local shared and then make a merge commit z to combine the changes from b to c with the changes from b to y. Finally the new commit is pushed.

### Merge your feature back to the shared branch.

(Do this when you think it's complete and ready for review.)

1. Catch up the feature branch. (See above.) Be sure to push the feature branch to the server.
2. If there are any problems, such as merge conflicts or failed tests, make sure they are all resolved before going on.
3. On GitHub, make a new "Pull Request", being careful that it is a request to pull feature into shared.
4. At this point, you might want to request someone else to review the pull request.
5. Wait for comments or for someone else to merge the pull request.
6. Or if no one else merges the pull request, merge it your self.
On some projects, there many be a requirement that someone else reviews each pull request. When there are comments that need to be addressed, you can modify your feature branch and push it again.  Pull requests are based on branches, not on commits. So when you push new commits on your branch they become part of the pull request.   If there are changes to the shared branch between the pull request being made and the the feature being merged, it's important to redo the process above so, for example all tests can be run on a caught up version of the commit. Example. Here we make a pull request. After suitable review it is merged by fast-forward.

Another example. In this case, the reviewer found some problems that I fixed with commit w. In the mean time some one else added to the shared branch (commit d). This new work didn't seem to require any further modifications from me. So I did another merge on my machine (commit m), tested, and pushed both commits w and m to the origin. Finally, the pull request is merged on Github. Beacause pull requests reference branches rather than commits, the meaning of the pull request changes as the shared and feature branches on origin change.

As always, merging a pull request should not create any merge commits; it is simply a fast forward. If I had not made commit m on my machine and merged the pull request with shared pointing to d and feature pointing to w, the same commit m would be created in the origin repository and shared would be set to point to m. But, that would mean the head of the shared branch would contain a version of the file tree that had not been seen by anyone or fully tested.

# Direct manipulation of abstract syntax trees part 1: Representing and manipulating trees

This is the second part of a two part post. Part 0 is here.

## Background

The PLAAY language is a visual language. The editor for PLAAY allows users to modify abstract syntax trees of PLAAY programs by direct manipulation.
An earlier post focussed on the user interface from the users' point of view. Here we look at the software design behind the GUI.

## Valid trees

Code in PLAAY is a tree made up of nodes of various kinds. Each kind of node has restrictions on what its children can be. For example many kinds of node aren't allowed to have any children at all.  A node representing a function call must only have children that are expressions. A node representing a while expression must have exactly 2 children and the first must be some kind of expression and the second must be an expression sequence. Expression sequence nodes can have any number of children, but each must be either some kind of expression or a variable declaration.  A valid tree obeys all these restrictions and the PLAAY editor is only capable of producing valid trees.
This idea of valid trees is essentially the same as XML's idea of valid documents.
The validity rules are PLAAY equivalent to the syntax rules of text based languages.  Since the editor can only produce valid trees, it is impossible, in PLAAY, to make a syntax error.
There is one loophole. Where the program is not finished, we allow a "placeholder" node to be placed. For example, as I mentioned, a while expression must have an expression as its first label. By default, this is an expression placeholder node, although as we will see later, we can create the expression first and then create the while node later, in which case we never need the placeholder.

## Program nodes and tree nodes

Each tree is represented by a program node (PNode) which has a label and a sequence of 0 or more children. PNodes are immutable and may be shared, so they form a directed acyclic graph. It's a precondition of the PNode constructor that it is valid and the precondition is checked at run time so the error of making an invalid tree is quickly found during testing.
Also we generally make trees through a method tryMake
tryMake(label:Label, children:Array<PNode>):Option<PNode>
The type Option<PNode> has values that are either None or Some(p) where p is a PNode. So the code that tries to make a PNode with this method has to deal with cases where the node would have been invalid. Option is a monad so we can use monad operations like bind and map to deal with the results of tryMake and similar functions.
Here is a tree.

The blue ellipses are expression nodes. The yellow square is an expression sequence node.
On the screen this tree is displayed as a set of nested boxes like this:

You can see that each expression node is displayed as a box. Expression sequences are not displayed, though their children are.
Since PNodes and labels are immutable, we can use the same PNode to represent multiple nodes in a tree.  The illustration below shows two equivalent representations of the same tree in terms of PNode objects (triangles), Label objects (squares), and arrays (rectangles). Other than the amount of space they take, these representation are treated as equivalent.

A node in the tree represented by a PNode p can be represented by p and a path from the p to the tree node. For example if p is the node labelled by * in either of the structures above, the 7 tree nodes in the tree represented by p are (p,[]), (p, [0]), (p, [0,0]), (p, [0,1]), (p,[1]), (p, [1,0]), and (p, [1,1]).
If a tree node has n children, then there are n+1 positions under it. Here is a tree and all the positions in it. The dotted lines simply show which tree node is associated with each position.

So a position consists of a tree node t --called the parent-- and an integer k such that 0 ≤ k ≤ n, where n is the number of children the tree node has. For example the second position under the node labelled + on the right is ((p, [1]), 1) where p is the PNode at the root.
There are no objects in the data structure representing positions. However when we render the tree into HTML, some positions are represented by HTML elements called drop zones. Drop zones are usually invisible, but light up when the mouse hovers over them. Also, as explained below, when the current selection corresponds to a position, the drop zone --if any-- for that position is shown in grey.

## Why immutability?

At this point you might wonder why I chose to use immutable objects to represent trees.
There are several reasons, but two stand out: correctness and simplicity.
Correctness: As mentioned above it is an invariant of PNodes that they are valid. In order to enforce this invariant we check that it is true on construction. Since nodes and labels are immutable the invariant can never become false. With a mutable structure we could enforce the invariant by checking that it is respected after every mutation. However what can we do when the assertion fails. At that point it is too late to recover. So for each mutator we need to write code that will predict whether the change will succeed or fail.  For example if I have a mutator that replaces children i to j of a node with a new set of children. I might write methods in PNode like this
    public canReplace( tn : TreeNode, i : int, j : int, nodes : Array<PNode>) : boolean {
... }
private replace( tn : TreeNode, i : int, j : int, nodes : Array<PNodes> ): void {

... }
public tryReplace( tn : TreeNode, i : int, j : int, nodes : Array<PNode>) : boolean {
if ( canReplace( tn, i, j, nodes ) ) {
replace( tn, i, j, nodes ) ;
return true ; }
else return false ; }
Now this style of coding can be made to work, but I have three problems with it. First, I know that when other people use this interface, some of them are going to ignore the result of tryReplace. The use of Option objects in the current design makes it more difficult to ignore the possibility of failure.  Second, the whole scheme rests on getting the implementation of the mutator and the predicate to be completely coherent, i.e. the can function should be true exactly if the mutator will succeed. This is easy simple cases but rapidly gets complex as the complexity of the mutations increases. Third these changes are not composable. Suppose I have an edit that consists of two changes in sequence. How can I know whether the second will succeed before doing the first?  And if I do the first, how can I get back to the original state if the second will not succeed. To answer the last two questions, we could use a command pattern based undo/facility with composable commands. However that is another level of complexity
A bonus from using immutable structures is that undo/redo is very easy and efficient. We simply keep two stacks of PNodes. Actually, we keep two stacks of Selections objects; Selection is another class of immutable objects and is discussed next.

## Selections

A selection is a pair of positions. We restrict these positions to having the same parent, so it might be better to say that a selection is a tree node t and two integers a and f such that 0 ≤ a,f ≤ n where n is the number of children t has. The numbers a and f are called the anchor and focus. The minimum of a and f is called the first and the maximum the last. When a=f, a selection just indicates a position. When a ≠ f, there is a nonempty set of tree nodes that are called the selected nodes. The number of selected nodes is the last minus the first.
Selections can be represented by triples consisting of a tree node, the anchor, and the focus.
For example, here is a selection with 0 selected nodes ((p, [0]), 2, 2)

A selection with one selected node ((p,[]), 0, 1)

And a selection with two selected nodes ((p, []), 2, 0)

When we display selections to the user, the selected nodes are shown with a grey background. If there are no selected nodes, we usually display the position by colouring a small rectangle called a drop zone grey. (The other drop zones are transparent.) Here are the three selections above as displayed in the editor.

The editor does not create a drop zone for every position in the tree, only those where it makes sense to insert a tree. There is a drop zone in the example above because addition nodes can have three children. While they are technically valid, we avoid creating selections corresponding to positions that don't have drop zones; such selections aren't needed and are would be confusing to the user.
In the code, we represent selections with a class Selection, which is immutable and such that all the restrictions are checked at construction time.  Selections are guaranteed to be valid.

## Edits on selections

Another key concept is that of an edit. An object of type Edit<Selection> is an object that represents a function from Selection to Option<Selection>. (In general, for any type A, an Edit<A> object is an object that represents a function from A to Option<A>. We're only interested in the case where A is Selection.) There are two operations on edits, applyEdit takes a selection and returns an Option<Selection>, and canApply is a function that takes a selection and returns true if applyEdit would succeed. I.e.
!e.canApply(s) iff e.applyEdit(s).isEmpty()
The only advantage of canApply is that it might be quicker to call canApply than to call applyEdit and see if it succeeded.
The nice thing about edits is that we can compose them in various interesting ways. For example
• Applying compose(e, f) applies e and then applies f to the result. Of course, if either application fails, the application of the whole edit fails.
• Applying alt( [e, f, g] ) applies the first edit in the list that succeeds.
Edits are a special case of what functional programmers call "arrows". I won't go into that now, since you don't need to know the theory of arrows to understand edits any more than you need to know group theory in order to understand addition.

## Some example edits

### Replace-children edits

A replace-children edit attempts to replace the selected nodes with a fixed list of trees. If there are no selected nodes, it simply attempts to insert the list of nodes at the given position. For example if the list of trees is

and we apply the resulting replace edit to the selection

the resulting selection is

The replace-children edit fails (i.e. returns None) if the resulting tree would be invalid. For example if the same edit were applied to the selection

it would fail, because assignment nodes with 3 children are invalid.

### Engulf edits

Engulf edits are built out of selections called templates. Suppose we start with a template

and we built an engulf edit out of it; the engulf edit applied to a selection

results in a selection

In general engulfing is a three step process:
• First replace the selected nodes of the template selection with the selected nodes of the target selection to make a temporary selection.
• Second replace the selected nodes of the target selection with the root of the temporary selection.
• Third, the path, anchor and focus are adjusted so that the selection corresponds to the position after the last node inserted into the temporary tree.

### Engulf or replace

A number of GUI actions are associated with edits that choose between an engulf or a replace based on a particular template. For example the ':' key is associated with an edit that either engulfs with the template

or replaces the current selection with the tree from the same template.  In either case, there is an optional movement edit --movement edit are discussed below-- after the replace or engulf.
Similarly the +, *, -, =, <, and > keys are associated edits that engulf or replace using calls to the appropriate function. The ?, @, and \ keys engulf or replace with templates for, respectively, an if expression, a looping expression, and a lambda expression.
The choice between replace and engulf is made as follows. If every selected node is a place holder (including the cases where there are no selected nodes), then replace is preferred. Otherwise engulf is preferred. Of course, if the preferred edit does not succeed, the other edit is tried.
In fact a choice of templates can be tried. The first template to succeed is applied. For example, there are two alternative templates for while loop expressions.

If one expression x (which is not a placeholder) is selected, pressing @ will engulf that x with the first (left) template so that x becomes the guard. However, if two more more expressions are selected, the tree from engulfing with the first template would be invalid (it would result in a tree with 3 or more children under a while loop node, which is invalid). Instead the two expressions are engulfed with the second template so that they become the body of the while loop.  This sort of thing is easy to do using the alt function.  For example the code that creates an edit to try engulfing with each of an array of templates looks like this
    const editList : Array<Edit<Selection>>
= templates.map( (template) =>
new EngulfEdit( template ) ) ;
return alt( editList )  ;

### Movement edits

There are several classes of edits that only affect the path, focus, and anchor. These are used in the PLAAY editor to implement, among other things, the response to pressing the arrow keys. For example, if the selection is a shown on at the left, pressing the right arrow key four times will move through the sequence shown here. The right arrow edit only stops when the position corresponds to a drop zone. In the example, that explains why it skips the positions under the 3 and the x node.

The space bar is used to select the parent. For example the edit associated with the space bar will take the selection on the left below to the selection on the right:

The tab key is associated with an edit that attempts to move the selection to the right until a suitable place for insertion is identified. Suitable places for insertion are either positions where there is a drop zone or selections where there is one selected node and it is some sort of placeholder node. An exception is that drop zones that occur just before or after placeholders are skipped. Some tab edits are shown below

### Open and closed labels

Several classes of labels are associated with a string and these labels are capable of being in two states, open and closed. Open nodes are rendered by the GIU as text fields. Typing a letter, say 'a', attempts to insert an open identifier node with a string value of "a".  Subsequent characters typed go to the text field and, when the text field is closed, the label is updated and closed.  Numbers are entered in a similar way. Function calls are entered in almost the same way; typing a '' creates a new function call, but the name of the function is empty.

The text field can be closed by typing an enter or a tab key. If an enter key closes an open node, then that node (now closed) will the selected node. If a tab key closes an open node, a tab edit is added on, so there will be a search for the next suitable place for an insertion. The figure below shows the distinction between an open node (green) being closed with an enter versus a tab.

This distinction turns out to be very useful for entering expressions in either infix or prefix order.

### Other useful edits

Some other useful edits include moves and swaps.  Both of these make substitutions at two points in the same tree. We need moves and swaps since breaking these edits down into constituents may cause the tree to become invalid temporally and that is not allowed. For example we can swap child 1 with child 2 of an if-node. (Equivalently we can move the child 1 to position 3.) These are both legal edits. But achieving the same result by a sequence of simpler edits will usually not work. For example duplicating the child 1 to make a fourth child and then deleting the child 1 would mean that the if has 4 children at one point in time and this is an invalid tree.
Another category of useful edits expands the selection in some way. In the editor, these are attached to pressing arrows while the shift key is held down.

# Direct manipulation of abstract syntax trees part 0. Infix and prefix tree entry

This is the first of a two part post. Part 1 is here.

## Mental friction

All this lexing, parsing, unparsing, and unlexing creates friction in the programming process. One of the goals of the PLAAY visual programming language is to eliminate much of this mental busy work by presenting the abstract syntax tree in a more direct form and to get away from the distractions of lexing and parsing.
However eliminating friction on the reading and comprehension end is not helpful if we create the same or more friction on the production and manipulation end. Furthermore, for experienced programmers, there is the additional hurdle that they are used to producing and editing code using text and some text editor or IDE be it Vim, Sublime, Eclipse, ... .
So we need a low friction way to enter and manipulate abstract syntax trees.
The rest of this post shows that, using the PLAAY editor, entering trees is easy and flexible.
It's easy in that it takes about as many keystrokes as entering the equivalent expression in a text-based language.
It's flexible in that it allows trees to be created either top-down (prefix entry) or left-to-right (infix entry).
A later post will look at how the required transformations on trees are implemented.

## Entering a simple expression in PLAAY

I had two pleasant surprises when I developed the PLAAY editor.
• First, I was surprised that we could accommodate entering expressions in either prefix or infix order without having to make any concessions.  That is we could both methods easy without having to make either less easy than we would have if making both easy wasn't a goal.
• Second, the total amount of effort on the part of the user is about the same as for a textual language. Of course "effort" is subjective, but, if we measure effort by counting keystrokes, this claim can be proved objectively.
The video below illustrates entering expressions using either prefix or infix order.

### Prefix entry

I'll start with entering expressions in using prefix order, i.e. entering operations before their operands.

We can enter it with the following keystrokes
• '+' creates an addition operation with two placeholders as operands, giving
• '*' replaces the selected place holder with an multiplication operation, giving
• 'a' creates an identifier and displays a text field, giving
• tab closes the text field and selects the next place holder, giving
• 'x' creates an identifier and displays a text field, giving
• A tab closes the text field and selects the next place an expression can be added, giving
• (Note that the multiplication operator can have more than 2 operands. That's why an area left of the second operand is selected. This gives us a chance to enter a third operand.) Another tab selects the next place holder, giving
• '*', 'b', tab, 'y', tab give
That's 12 keystrokes versus 7 to type a*x+b*y.

### Infix entry

We can also enter the same expression in using more traditional infix notation. We have:
• 'a' creates an identifier and displays a text field.
• An enter closes the text field and selects the identifier.
• '*' engulfs the identifier with a multiplication operation; it then selects a placeholder.
• 'x' creates an identifier and displays a text field.
• An enter replaces the place holder with an identifier and displays a text field.
• A space selects the parent of the current selection.
• '+' engulfs the identifier with an addition operation.
• 'b', enter, '*', 'y', tab give
This took 12 keystrokes, the same as prefix entry.
One reason that it takes more keystrokes in PLAAY than in Java, C++ etc. is that in PLAAY identifiers can include characters like *,+ and spaces. If we imagine modifying the language so that this is not the case, we could arrange that typing an operator into a text field is equivalent to typing enter followed by the operator or space.  That accounts for 4 characters. A second reason is that PLAAY has no operator precedence. This means that a space is needed to expand the selection. It should be noted that the expression corresponding to (a+x)*(b+y) also takes 12 keystrokes to enter in PLAAY: no increase; whereas in C there are 4 additional keystrokes.

### No keyboard

If a keyboard is not available (e.g., on an iPad or similar tablet) or the user prefers not to use it, there are alternative user actions that can construct the trees.

## A larger example

### Prefix entry a larger example

Although we've seen prefix and infix entry of trees before, it might be good to look at another example and think about the edit applied in response to each keystroke.
Suppose we want the tree

We can enter this in prefix form with following key strokes
• ? < a tab b tab tab
• : x tab * a tab  s i n tab t h e t a tab down-arrow down-arrow
• : x tab * b tab  c o s tab t h e t a tab
That's 43 key strokes. (The back tick character  is used to create a function call. The down-arrow moves the selection right until a drop zone is found under an expression sequence node some other node that is formatted vertically.)

Comparing to C or Java we have
    if(a < b)
x = b*sin(theta);
else
x = b*cos(theta);

which takes 53 key strokes with most editors

### Infix entry of a larger example

The same tree can be entered in infix.
• a enter < b enter space ?
• x enter : a enter * t h e t a enter  s i n enter down-arrow down-arrow
• x enter : b enter * t h e t a enter  c o s enter
That's 43 keystrokes, same as prefix entry.

### Postfix

In the last example, you'll notice that the function calls to sin and cos are done in postfix order. I.e., the argument, theta, first and then the function name: t h e t a enter ` s i n enter. Postfix works fine for operators with one operand. We can also use postfix for operators with multiple operands, but the UI is not optimized for this case.

## Other manipulations

Entering code in the first place is probably where a visual language such as PLAAY has the biggest disadvantages. Once a tree is entered, it is much easier to manipulate in PLAAY's editor than with a text editor that is mostly oblivious to the structure of the program. The PLAAY editor makes it easy to select, move, delete, or duplicate entire subtrees representing units of meaning such as variables, expressions, commands, declarations, and types. The price is that some manipulations are harder. In particular any edit that would produce a syntactically incorrect program is forbidden.

PART 1 explores the coding behind the editor.