Add the first post in CS325 series
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@ -17,4 +17,3 @@ sorted(xs) = sorted(xs[0]) ++ [xs[1]] ++ sorted(xs[2]);
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search(xs, k) = |_search(xs, k)| != 0;
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insert(xs, k) = _insert(k, _search(xs, k));
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_insert(k, xs) = if |xs| == 0 then xs << [] << k << [] else xs
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@ -270,14 +270,13 @@ type Translator = Control.Monad.State.State (Map.Map String [String], Int)
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currentTemp :: Translator String
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currentTemp = do
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(_, t) <- get
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t <- gets snd
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return $ "temp" ++ show t
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incrementTemp :: Translator String
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incrementTemp = do
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(vs, t) <- get
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put (vs, t+1)
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return $ "temp" ++ show t
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modify (second (+1))
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currentTemp
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hasLambda :: Expr -> Bool
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hasLambda (ListLiteral es) = any hasLambda es
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@ -1,7 +1,6 @@
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---
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title: A Language for an Assignment - Homework 1
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date: 2019-12-27T23:27:09-08:00
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draft: true
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tags: ["Haskell", "Python", "Algorithms"]
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---
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@ -32,7 +31,7 @@ in our Programming Languages class. So the final goal ended up:
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It may not be worth it to create a whole
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{{< sidenote "right" "general-purpose-note" "general-purpose" >}}
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A general purpose language is one that's designed to be used in vairous
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A general purpose language is one that's designed to be used in various
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domains. For instance, C++ is a general-purpose language because it can
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be used for embedded systems, GUI programs, and pretty much anything else.
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This is in contrast to a domain-specific language, such as Game Maker Language,
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@ -41,7 +40,7 @@ which is aimed at a much narrower set of uses.
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but nowhere in the challenge did we say that it had to be general-purpose. In
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fact, some interesting design thinking can go into designing a domain-specific
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language for a particular assignment. So let's jump right into it, and make
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a language for the the first homework assignment.
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a language for the first homework assignment.
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### Homework 1
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There are two problems in Homework 1. Here they are, verbatim:
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@ -95,7 +94,7 @@ C++ optimizes the <a href="https://godbolt.org/z/3skK9j">Collatz Conjecture func
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Clang doesn't know whether or not the function will terminate (whether the Collatz Conjecture
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function terminates is an <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">unsolved problem</a>),
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but functions that don't terminate are undefined behavior. There's only one other way the function
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returns, and that's with "1". Thus, clang optimzes the entire function to a single "return 1" call.
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returns, and that's with "1". Thus, clang optimizes the entire function to a single "return 1" call.
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{{< /sidenote >}} in C++:
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we can do whatever we want. So, let's allow it to return `[]` in the `None` case.
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This makes this base case valid:
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@ -240,42 +239,271 @@ lazily evaluated, ordered expressions. The whole `qselect` becomes:
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We've now figured out all the language constructs. Let's start working on
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some implementation!
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#### Data Definitions
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Let's start with defining the AST and other data types for our language:
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#### Implementation
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It would be silly of me to explain every detail of creating a language in Haskell
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in this post; this is neither the purpose of the post, nor is it plausible
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to do this without covering monads, parser combinators, grammars, abstract syntax
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trees, and more. So, instead, I'll discuss the _interesting_ parts of the
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implementation.
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 14 52 >}}
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##### Temporary Variables
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Our language is expression-based, yes. A function is a single,
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arbitrarily complex expression (involving `if/else`, list
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selectors, and more). So it would make sense to translate
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a function to a single, arbitrarily complex Python expression.
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However, the way we've designed our language makes it
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not-so-suitable for converting to a single expression! For
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instance, consider `xs[rand]`. We need to compute the list,
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get its length, generate a random number, and then access
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the corresponding element in the list. We use the list
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here twice, and simply repeating the expression would not
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be very smart: we'd be evaluating twice. So instead,
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we'll use a variable, assign the list to that variable,
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and then access that variable multiple times.
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The `PossibleType` class will be used when we figure out if a function returns
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a list or not, for our base case insertion rule. The `Selector` type
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will hold a single line in the list selector we defined earlier, and
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the `SelectorMarker` will indicate if the user added the `!` "remove from list"
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marker at the end. To represent the various operators in our language, we create
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the `Op` data type. Note that unlike Python, `++` (list concatenation) and
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`+` (addition) are different operators in our language.
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To be extra safe, let's use a fresh temporary variable
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every time we need to store something. The simplest
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way is to simply maintain a counter of how many temporary
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variables we've already used, and generate a new variable
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by prepending the word "temp" to that number. We start
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with `temp0`, then `temp1`, and so on. To keep a counter,
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we can use a state monad:
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We then define valid expressions. Obviously, a variable (like `xs`), an
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integer literal (like `1`) and a list literal (like `[]`) are allowed.
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We also put in our selector, which consists of the expression on the
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left, the list of selector branches (`[Selector]`) and the expression
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of "what to actually do with the new variables". We also
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add `if`-expressions (like we discussed), and function calls. Lastly,
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we add binary operators like (`x+y`), the length operator (`|xs|`),
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and the list access operator (`xs[0]`). We also make `#0` a part
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of the expression syntax, even though it's only allowed inside
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a list access.
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 269 269 >}}
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Of course, we wouldn't want to write our language using
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Haskell. We want to actually write a text file, like `hw1.lang`,
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and then have our program translate that to Python. The first
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step to that is __parsing__: we need to turn our language text
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into the `Expr` structure we have.
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Don't worry about the `Map.Map String [String]`, we'll get to that in a bit.
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For now, all we have to worry about is the second element of the tuple,
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the integer counting how many temporary variables we've used. We can
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get the current temporary variable as follows:
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#### Parsing
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We'll be using `Parsec` for parsing. `Parsec` is a parsing library
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based on
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{{< sidenote "right" "monad-note" "monadic" >}}
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Haskell is a language with more monad tutorials than
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programmers. For this reason, I will resist the temptation
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to explain what monads are. If you <em>don't</em> know
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what they are, don't worry, there are plenty of other resources.
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{{< /sidenote >}} parser combinators.
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 271 274 >}}
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We can also get a fresh temporary variable like this:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 276 279 >}}
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Now, the
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{{< sidenote "left" "" "code" >}}
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Since we are translating an expression, we must have the result of
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the translation yield an Python expression we can use in generating
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larger Python expressions. However, as we've seen, we occasionally
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have to use statements. Thus, the <code>translateExpr</code> function
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returns a <code>Translator ([Py.PyStmt], Py.PyExpr)</code>.
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{{< /sidenote >}}for generating a random list access looks like
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{{< sidenote "right" "ast-note" "this:" >}}
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The <code>Py.*</code> constructors are a part of a Python AST module I quickly
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threw together. I won't showcase it here, but you can always look at the
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source code for the blog (which includes this project)
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<a href="https://dev.danilafe.com/Web-Projects/blog-static">here</a>.
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{{< /sidenote >}}
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 364 369 >}}
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##### Implementing "lazy evaluation"
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Lazy evaluation in functional programs usually arises from
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{{< sidenote "right" "graph-note" "graph reduction" >}}
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Graph reduction, more specifically the <em>Spineless,
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Tagless G-machine</em> is at the core of the Glasgow Haskell
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Compiler (GHC). Simon Peyton Jones' earlier book,
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<em>Implementing Functional Languages: a tutorial</em>
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details an earlier version of the G-machine.
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{{< /sidenote >}}. However, Python is neither
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functional nor graph-based, and we only lazily
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evaluate list selectors. Thus, we'll have to do
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some work to get our lazy evaluation to work as we desire.
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Here's what I came up with:
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1. It's difficult to insert Python statements where they are
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needed: we'd have to figure out in which scope each variable
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has already been declared, and in which scope it's yet
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to be assigned.
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2. Instead, we can use a Python dictionary, called `cache`,
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and store computed versions of each variable in the cache.
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3. It's pretty difficult to check if a variable
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is in the cache, compute it if not, and then return the
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result of the computation, in one expression. This is
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true, unless that single expression is a function call, and we have a dedicated
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function that takes no arguments, computes the expression if needed,
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and uses the cache otherwise. We choose this route.
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4. We have already promised that we'd evaluate all the selected
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variables above a given variable before evaluating the variable
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itself. So, each function will first call (and therefore
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{{< sidenote "right" "force-note" "force" >}}
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{{< todo >}}Explain forcing{{< /todo >}}
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{{< /sidenote >}}) the functions
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generated for variables declared above the function's own variable.
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5. To keep track of all of this, we use the already-existing state monad
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as a reader monad (that is, we clear the changes we make to the monad
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after we're done translating the list selector). This is where the `Map.Map String [String]`
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comes from.
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The `Map.Map String [String]` keeps track of variables that will be lazily computed,
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and also of the dependencies of each variable (the variables that need
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to be access before the variable itself). We compute such a map for
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each selector as follows:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 337 337 >}}
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We update the existing map using `Map.union`:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 338 338 >}}
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And, after we're done generating expressions in the body of this selector,
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we clear it to its previous value `vs`:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 341 341 >}}
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We generate a single selector as follows:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 307 320 >}}
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This generates a function definition statement, which we will examine in
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generated Python code later on.
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Solving the problem this way also introduces another gotcha: sometimes,
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a variable is produced by a function call, and other times the variable
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is just a Python variable. We write this as follows:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 322 327 >}}
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##### Special Case Insertion
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This is a silly language for a single homework assignment. I'm not
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planning to implement Hindley-Milner type inference, or anything
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of that sort. For the purpose of this language, things will be
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either a list, or not a list. And as long as a function __can__ return
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a list, it can also return the list from its base case. Thus,
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that's all we will try to figure out. The checking code is so
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short that we can include the whole snippet at once:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 258 266 >}}
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`mergePossibleType`
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{{< sidenote "right" "bool-identity-note" "figures out" >}}
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An observant reader will note that this is just a logical
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OR function. It's not, however, good practice to use
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booleans for types that have two constructors with no arguments.
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Check out this <a href="https://programming-elm.com/blog/2019-05-20-solving-the-boolean-identity-crisis-part-1/">
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Elm-based article</a> about this, which the author calls the
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Boolean Identity Crisis.
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{{< /sidenote >}}, given two possible types for an
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expression, the final type for the expression.
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There's only one real trick to this. Sometimes, like in
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`_search`, the only time we return something _known_ to be a list, that
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something is `xs`. Since we're making a list manipulation language,
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let's __assume the first argument to the function is a list__, and
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__use this information to determine expression types__. We guess
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types in a very basic manner otherwise: If you use the concatenation
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operator, or a list literal, then obviously we're working on a list.
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If you're returning the first argument of the function, that's also
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a list. Otherwise, it could be anything.
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My Haskell linter actually suggested a pretty clever way of writing
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the whole "add a base case if this function returns a list" code.
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Check it out:
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{{< codelines "Haskell" "cs325-langs/src/LanguageOne.hs" 299 305 >}}
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Specifically, look at the line with `let fastReturn = ...`. It
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uses a list comprehension: we take a parameter `p` from the list of
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parameter `ps`, but only produce the statements for the base case
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if the possible type computed using `p` is `List`.
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### The Output
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What kind of beast have we created? Take a look for yourself:
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```Python
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def qselect(xs,k):
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if xs==[]:
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return xs
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cache = {}
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def pivot():
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if ("pivot") not in (cache):
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cache["pivot"] = xs.pop(0)
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return cache["pivot"]
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def left():
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def temp2(arg):
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out = []
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for arg0 in arg:
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if arg0<=pivot():
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out.append(arg0)
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return out
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pivot()
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if ("left") not in (cache):
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cache["left"] = temp2(xs)
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return cache["left"]
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def right():
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def temp3(arg):
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out = []
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for arg0 in arg:
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if arg0>pivot():
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out.append(arg0)
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return out
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left()
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pivot()
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if ("right") not in (cache):
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cache["right"] = temp3(xs)
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return cache["right"]
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if k>(len(left())+1):
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temp4 = qselect(right(), k-len(left())-1)
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else:
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if k==(len(left())+1):
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temp5 = [pivot()]
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else:
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temp5 = qselect(left(), k)
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temp4 = temp5
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return temp4
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def _search(xs,k):
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if xs==[]:
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return xs
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if xs[1]==k:
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temp6 = xs
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else:
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if xs[1]>k:
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temp8 = _search(xs[0], k)
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else:
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temp8 = _search(xs[2], k)
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temp6 = temp8
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return temp6
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def sorted(xs):
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if xs==[]:
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return xs
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return sorted(xs[0])+[xs[1]]+sorted(xs[2])
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def search(xs,k):
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return len(_search(xs, k))!=0
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def insert(xs,k):
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return _insert(k, _search(xs, k))
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def _insert(k,xs):
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if k==[]:
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return k
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if len(xs)==0:
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temp16 = xs
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temp16.append([])
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temp17 = temp16
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temp17.append(k)
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temp18 = temp17
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temp18.append([])
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temp15 = temp18
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else:
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temp15 = xs
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return temp15
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```
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It's...horrible! All the `tempX` variables, __three layers of nested function declarations__, hardcoded cache access. This is not something you'd ever want to write.
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Even to get this code, I had to come up with hacks __in a language I created__.
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The first is the hack is to make the `qselect` function use the `xs == []` base
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case. This doesn't happen by default, because `qselect` doesn't return a list!
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To "fix" this, I made `qselect` return the number it found, wrapped in a
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list literal. This is not up to spec, and would require another function
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to unwrap this list.
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While `qselect` was struggling with not having the base case, `insert` had
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a base case it didn't need: `insert` shouldn't return the list itself
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when it's empty, it should insert into it! However, when we use the `<<`
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list insertion operator, the language infers `insert` to be a list-returning
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function itself, inserting into an empty list will always fail. So, we
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make a function `_insert`, which __takes the arguments in reverse__.
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The base case will still be generated, but the first argument (against
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which the base case is checked) will be a number, so the `k == []` check
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will always fail.
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That concludes this post. I'll be working on more solutions to homework
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assignments in self-made languages, so keep an eye out!
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