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docs/lectures/compilers/10_if_then_else.md

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+# Compiling Branches
+
+**Mini Triangle Programs** -$parse$-> **AST** -$Code\space Generation$-> **TAM Programs** -$execute$ -> **Output**
+
+Before we could generate a list of instructions to be executed in sequence, now we need to implement code thats conditionally executed or executed multiple times.
+
+```haskell
+--Code for dealing with functions and commands
+commCode :: VarEnv -> Command -> TAMProg
+```
+
+We will assume an if statement looks like this
+
+IF $e$ THEN $c_1$ ELSE $c_2$
+
+```python
+if e then c1 else c2
+IfThenElse e c1 c2
+```
+
+```haskell
+expCode ve e
+commCode ve c1
+commCode ve c2
+-- We dont want to execute both
+```
+
+- We can use `JUMPIFZ R1`, a branching function supplied by the TAM language.
+
+- This means `commCode ve c1` & `commCode ve c2` need labels and a `JUMPA` after
+
+```
+MINI TRIANGLE PROGRAM
+
+let var := 5
+in
+begin
+	if 1
+		then n := 6
+		else n := 7;
+    if 0
+    	then n := 8
+    	else n := 9;
+end
+```
+
+```assembly
+COMPILED VERSION
+
+LOADL 5
+
+
+LOAD 1 --if 1
+JUMPIFZ "label1" --jump to else
+LOAD 6 --load the number
+STORE 0 --store 0 (stack[0] is 6 from line above) in the place of variable n, for other variables you would have to check the variable enviroment to get the stack address
+JUMP "label2"
+Label "label1"
+
+LOAD 7
+STORE 0
+
+Label "label2"
+LOAD 0
+JUMPIFZ "label3"
+```
+
+![img](img/i.png)
+
+### Generating Labels
+
+Labels must **always** be **unique**.
+
+This would require a global variable in our compiler to count the number of labels, haskell doesnt not allow global variables.
+
+We can use the `stateMonad` instead.
+
+```haskell
+type LabelName = String
+
+fresh :: ST Int LabelName
+-- Whenever we call fresh, it generates a new label name
+-- We can use do (because fresh is element of ST Monad)
+
+fresh = do
+	n <- stGet --checks current state (which is num of labels)
+	stUpdate(n+1) --update number of labels
+	return ("#" : (show n)) -- # symbol to denote labels
+	-- show converts integer to string (fresh returns string)
+	
+commCode :: VarEnv -> Command -> ST Int [TAMInsrt]
+-- TAMPrgm is interchangable with [TAMInstr]
+commCode ve (IFTHENELSE e c1 c2) = 
+		do l1 <- fresh
+		   l2 <- fresh --generate the two labels needed for an if
+		   let te = expCode ve e --the condition expression
+		   tc1 <- commCode ve c1 --compile success branch
+		   tc2 <- commCode ve c2 --compile else branch
+		   return (te ++ [JUMPIFZ l1] ++ tc1 ++ [JUMP l2]
+		   			++ [Label l1] ++ tc2 ++ [Label l2])
+--then return the tam instructions
+```
+
+**REMINDER**: `expCode` is a function that takes a variable environment `ve` and an expression `e` and generates a list of TAM instructions.