Tidy up

docs/lectures/compilers/08_variables.md

@@ -1,6 +1,6 @@
 # Compiling Variables
 
-A variable is identified by a alphanumeric string. We can store this as a list of pairs, with the variables identifier and its value.
+A variable is identified by an alphanumeric string. We can store this as a list of pairs, with the variable's identifier and its value.
 
 Variable Environment or VarEnv - `[(Identifier, Stack Address)]`
 
@@ -8,7 +8,7 @@ A stack address is an integer value that specifies where in the stack that varia
 
 The bottom of the stack is indexed `0`.
 
-Lets say our environment consists of 3 variables named x,y,z. It would look like:
+Let's say our environment consists of 3 variables named x, y, z. It would look like:
 
 `[("z",2), ("y",1), ("x",0)]`
 
@@ -18,13 +18,13 @@ Lets say our environment consists of 3 variables named x,y,z. It would look like
 |     y     |       2        |   1   |
 |     z     |       9        |   2   |
 
-To get the value of a variable from the stackk, TAM uses the instruction `LOADL a` where `a` is a stack address. `LOADL` will get the value and copy the value to the top of the stack.
+To get the value of a variable from the stack, TAM uses the instruction `LOADL a` where `a` is a stack address. `LOADL` will get the value and copy the value to the top of the stack.
 
 `LOAD a` - copy address a to top of stack
 
 `STORE a` - pop top of stack to address a
 
-For example if `LOADL 2` is called, it will effect the stack in the following way:
+For example, if `LOADL 2` is called, it will affect the stack in the following way:
 
 | Variables | Stack (Values) | Index |
 | :-------: | :------------: | :---: |
@@ -38,7 +38,7 @@ For example if `LOADL 2` is called, it will effect the stack in the following wa
 expCode :: VarEnv -> Expr -> [TAMInst]
 ```
 
-Before we just called the abstract syntax tree `AST` however with the extended grammar now we will have multiple ASTs, one for programs, one for commands, expressions. The AST for expressions we call `Expr`.
+Before, we just called the abstract syntax tree `AST`; however, with the extended grammar, we will now have multiple ASTs: one for programs, one for commands and one for expressions. The AST for expressions we call `Expr`.
 
 Remember in our compiler, the stack is represented and stored as a list, with the top of the stack being the head of the list.
 
@@ -87,10 +87,10 @@ $$
 Example: $s_n$ could be your bank balance and $a_n$ could be the purchase history.
 
 - In our case:
-  - States are VarEnv & next free address space for next variable
-  - Outputs are TAM instructions
+    - States are VarEnv & next free address space for next variable
+    - Outputs are TAM instructions
 
-We to define a type that models a state transform, while at the same time producing a result. This is where a state monad comes in.
+We need to define a type that models a state transform, while at the same time producing a result. This is where a state monad comes in.
 
 ```haskell
 newtype ST st a = S (\st -> (a, st))