Make proofreading-based fixes.

code/compiler/12/ast.cpp

@@ -302,7 +302,7 @@ void ast_let::translate(global_scope& scope) {
         mangled_env->bind(def.first, env->lookup(def.first), visibility::global);
         mangled_env->set_mangled_name(def.first, global_definition.name);
 
-        ast_ptr global_app(new ast_lid(global_definition.name));
+        ast_ptr global_app(new ast_lid(original_name));
         global_app->env = mangled_env;
         for(auto& param : global_definition.params) {
             if(!(captured--)) break;

content/blog/12_compiler_let_in_lambda/index.md

@@ -6,9 +6,9 @@ description: "In this post, we extend our language with let/in expressions and l
 draft: true
 ---
 
-Now that our language's type system is more fleshed out and pleasant to use, it's time to shift our focus to the ergonomics of the language itself. I've been mentioning `let/in` expressions and __lambda expressions__ for a while now. The former will let us create names for expressions that are limited to a certain scope (without having to create global variable bindings), while the latter will allow us to create functions without giving them any name at all.
+Now that our language's type system is more fleshed out and pleasant to use, it's time to shift our focus to the ergonomics of the language itself. I've been mentioning `let/in` and __lambda__ expressions for a while now. The former will let us create names for expressions that are limited to a certain scope (without having to create global variable bindings), while the latter will allow us to create functions without giving them any name at all.
 
-Let's take a look at `let/in` expressions first, to make sure we're all on the same page about what it is we're trying to implement. Let's start with some rather basic examples, and then move on to more complex examples. The most basic use of a `let/in` expression is, in Haskell:
+Let's take a look at `let/in` expressions first, to make sure we're all on the same page about what it is we're trying to implement. Let's start with some rather basic examples, and then move on to more complex ones. A very basic use of a `let/in` expression is, in Haskell:
 
 ```Haskell
 let x = 5 in x + x
@@ -93,7 +93,7 @@ addSingle6 x = 6 + x
 -- ... and so on ...
 ```
 
-But now, we end up creating several functions with almost identical bodies, with the exception of the free variables themselves. Wouldn't it be better to perform the well-known strategy of reducing code duplication by factoring out parameters, and leaving only instance of the repeated code? We would end up with:
+But now, we end up creating several functions with almost identical bodies, with the exception of the free variables themselves. Wouldn't it be better to perform the well-known strategy of reducing code duplication by factoring out parameters, and leaving only one instance of the repeated code? We would end up with:
 
 ```Haskell {linenos=table}
 addToAll n xs = map (addSingle n) xs
@@ -145,11 +145,48 @@ to `let/in`, and that's what we'll be using in our language.
 
 This technique of replacing captured variables with arguments, and pulling closures into the global scope to aid compilation, is called [Lambda Lifting](https://en.wikipedia.org/wiki/Lambda_lifting). Its name is no coincidence - lambda functions need to undergo the same kind of transformation as our nested definitions (unlike nested definitions, though, lambda functions need to be named). This is why they are included in this post together with `let/in`!
 
+What are lambda functions, by the way? A lambda function is just a function
+expression that doesn't have a name. For example, if we had Haskell code like
+this:
+
+```Haskell
+double x = x + x
+doubleList xs = map double xs
+```
+
+We could rewrite it using a lambda function as follows:
+
+```Haskell
+doubleList xs = map (\x -> x + x) xs
+```
+
+As you can see, a lambda is an expression in the form `\x -> y` where `x` can
+be any variable and `y` can be any expression (including another lambda).
+This represents a function that, when applied to a value `x`, will perform
+the computation given by `y`. Lambdas are useful when creating single-use
+functions that we don't want to make globally available.
+
+Lifting lambda functions will effectively rewrite our program in the
+opposite direction to the one shown, replacing the lambda with a reference
+to a global declaration which will hold the function's body. Just like
+with `let/in`, we will represent captured variables using arguments
+and partial appliciation. For instance, when starting with:
+
+```Haskell
+addToAll n xs = map (\x -> n + x) xs
+```
+
+We would output the following:
+
+```Haskell
+addToAll n xs = map (lambda n) xs
+lambda n x = n + x
+```
+
 ### Implementation
 Now that we understand what we have to do, it's time to jump straight into
-doing it. First, we need to refactor our current code so allow for the changes 
+doing it. First, we need to refactor our current code to allow for the changes 
-we're going to make; then, we can implement `let/in` expressions; finally,
+we're going to make; then, we will use the new tools we defined to implement `let/in` expressions and lambda functions.
-we'll tackle lambda functions.
 
 #### Infrastructure Changes
 When finding captured variables, the notion of _free variables_ once again
@@ -168,8 +205,8 @@ since it's not defined locally.
 The algorithm that we used for computing free variables was rather biased.
 Previously, we only cared about the difference between a local variable
 (defined somewhere in a function's body, or referring to one of the function's
-parameters) and a global variable (referring to a function name). This shows in
+parameters) and a global variable (referring to a global function).
-our code for `find_free`. Consider, for example, this segment:
+This shows in our code for `find_free`. Consider, for example, this snippet:
 
 {{< codelines "C++" "compiler/11/ast.cpp" 33 36 >}}
 
@@ -536,7 +573,7 @@ And the latter:
 
 {{< codelines "C++" "compiler/12/type_env.cpp" 39 45 >}}
 
-We don't allow the `set_mangled_name` to affect variables that are declared
+We don't allow `set_mangled_name` to affect variables that are declared
 above the receiving `type_env`, and use the empty string as a 'none' value.
 Now, when lifting data type constructors, we'll be able to use
 `set_mangled_name` to make sure constructor calls are made correctly. We
@@ -630,7 +667,7 @@ void ast::translate(global_scope& scope);
 
 The `scope` parameter and its `add_function` and `add_constructor` methods will
 be used to add definitions to the global scope. Each AST node will also
-uses this method to implement the second step. Currently, only
+use this method to implement the second step. Currently, only
 `ast_let` and `ast_lambda` will need to modify themselves - all other
 nodes will simply recursively call this method on their children. Let's jump
 straight into implementing this method for `ast_let`:
@@ -639,7 +676,7 @@ straight into implementing this method for `ast_let`:
 
 Since data type definitions don't really depend on anything else, we process
 them first. This amounts to simply calling the `definition_data::into_globals`
-methd, which itself simply calls `global_scope::add_constructor`:
+method, which itself simply calls `global_scope::add_constructor`:
 
 {{< codelines "C++" "compiler/12/definition.cpp" 86 92 >}}
 
@@ -659,7 +696,7 @@ First, this method collects all the non-global free variables in
 its body, which will need to be passed to the global definition
 as arguments. It then combines this list with the arguments
 the user explicitly added to it, recursively translates
-its body, creates a new global definition using `add_function`.
+its body, and creates a new global definition using `add_function`.
 
 We return to `ast_let::translate` at line 299. Here,
 we determine how many variables ended up being captured, by
@@ -675,7 +712,7 @@ of the function, but this seems inelegant, especially since we
 alreaady keep track of mangling information in `type_env`. Instead,
 we create a new, local environment, in which we place an updated
 binding for the function, marking it global, and setting
-its mangled name to one generated by `global_sope`. This work is done
+its mangled name to the one generated by `global_sope`. This work is done
 on lines 301-303. We create a reference to the global function
 using the new environment on lines 305 and 306, and apply it to
 all the implict arguments on lines 307-313. Finally, we
@@ -730,7 +767,7 @@ closer to the top of the G-machine stack. Thus, when we
 iterate the definitions again, this time to compile their
 bodies, we have to do so starting with the highest offset,
 and working our way down to __Update__-ing the top of the stack.
-One the definitions have been compiled, we proceed to compiling
+Once the definitions have been compiled, we proceed to compiling
 the `in` part of the expression as normal, using our updated
 environment. Finally, we use __Slide__ to get rid of the definition
 graphs, cleaning up the stack.
@@ -738,16 +775,16 @@ graphs, cleaning up the stack.
 Compiling the `ast_lambda` is far more straightforward. We just
 compile the resulting partial application as we normally would have:
 
-{{< codelines "C++" "compiler/12/ast.cpp" 393 395 >}}
+{{< codelines "C++" "compiler/12/ast.cpp" 394 396 >}}
 
 One more thing. Let's adopt the convention of storing __mangled__
-names into the environment. This way, rather than looking up
+names into the compilation environment. This way, rather than looking up
 mangled names only for global functions, which would be a 'gotcha'
 for anyone working on the compiler, we will always use the mangled
 names during compilation. To make this change, we make sure that
 `ast_case` also uses `mangled_name`:
 
-{{< codelines "C++" "compiler/12/ast.cpp" 228 228 >}}
+{{< codelines "C++" "compiler/12/ast.cpp" 242 242 >}}
 
 We also update the logic for `ast_lid::compile` to use the mangled
 name information:
@@ -859,7 +896,7 @@ in our language, perhaps to create an infinite list of ones:
 
 We want `sumTwo` to take the first two elements from the list,
 and return their sum. For an infinite list of ones, we expect
-this sum to equal to 2, and so it does:
+this sum to be equal to 2, and it is:
 
 ```
 Result: 2
@@ -873,9 +910,9 @@ dependency tracking works as expected:
 {{< codeblock "text" "compiler/12/examples/letin.txt" >}}
 
 Here, we have a function `mergeUntil` which, given two lists
-and a predicate, combines the two lists until as long as
+and a predicate, combines the two lists as long as
 the predicate returns `True`. It does so using a convoluted
-pair of two mutually recursive functions, one of which
+pair of mutually recursive functions, one of which
 unpacks the left list, and the other the right. Each of the
 functions calls the global function `if`. We also use two
 definitions inside of `main` to create the two lists we're