# Writing a MiniC-to-MSIL compiler in F# - Part 1 - Defining the abstract syntax tree

### Introduction

So we’re going to write a compiler - great. Let’s start by deciding on the language we want to compile. The standard way to do this is by defining a language grammar. The grammar will define precisely what source code our compiler will accept as valid input - and implicitly, what isn’t valid input.

I chose to use a grammar I found in this paper (which looks like a university course assignment). It defines a language it calls Mini-C, which is a subset of C that omits macros, pointers and structs (and probably lots of other things). There’s enough in MiniC to making writing a compiler for it an interesting exercise.

Here’s an example of Mini-C source code. By the end of this series, our compiler will be able to turn this source code into an executable .NET application:

int fib(int n) {
if (n == 0)
return 0;
if (n == 1)
return 1;
return fib(n - 1) + fib(n - 2);
}

int main(void) {
return fib(10);
}


### The Mini-C grammar

Enough talking. Here’s the MiniC grammar, from the paper I mentioned above. It consists of multiple rules. Each rule starts with the rule name, followed by an arrow, followed by one or more tokens. Capital letters indicate a literal - i.e. BOOL means the literal string “bool”.

program       → decl_list
decl_list     → decl_list decl | decl
decl          → var_decl | fun_decl
var_decl      → type_spec IDENT  ; | type_spec IDENT [ ] ;
type_spec     → VOID | BOOL | INT | FLOAT
fun_decl      → type_spec IDENT ( params ) compound_stmt
params        → param_list | VOID
param_list    → param_list , param | param
param         → type_spec IDENT | type_spec IDENT [ ]
stmt_list     → stmt_list stmt | ε
stmt          → expr_stmt | compound_stmt | if_stmt | while_stmt |
return_stmt | break_stmt
expr_stmt     → expr ; | ;
while_stmt    → WHILE ( expr ) stmt
compound_stmt → { local_decls stmt_list }
local_decls   → local_decls local_decl | ε
local_decl    → type_spec IDENT ; | type_spec IDENT [ ] ;
if_stmt       → IF ( expr ) stmt | IF ( expr ) stmt ELSE stmt
return_stmt   → RETURN ; | RETURN expr ;

The following expressions are listed in order of increasing precedence:
expr → IDENT = expr | IDENT [ expr ] = expr
→ expr OR expr
→ expr EQ expr | expr NE expr
→ expr LE expr | expr < expr | expr GE expr  | expr > expr
→ expr AND expr
→ expr + expr | expr - expr
→ expr * expr | expr / expr  | expr % expr
→ ! expr | - expr | + expr
→ ( expr )
→ IDENT | IDENT [ expr ] | IDENT ( args ) | IDENT . size
→ BOOL_LIT | INT_LIT  | FLOAT_LIT | NEW type_spec [ expr ]

arg_list → arg_list , expr | expr
args     → arg_list | ε


If that makes your eyes hurt, don’t worry. Let’s break it down, taking the var_decl rule as an example:

var_decl → type_spec IDENT  ; | type_spec IDENT [ ] ;


And here’s a line of Mini-C code, which is valid according to the var_decl rule:

bool MyVar[];


The vertical bar (|) in the middle of the var_decl rule indicates an OR relationship: source code will match the rule if it looks like the left side OR the right side. Let’s look at the right side:

• First we have a type_spec. The type_spec rule is defined in the grammar just below var_decl. A type_spec can be any of the following strings: void, bool, int or float.
• Then there’s an identifier. Mini-C uses the same rules as standard C for valid identifiers.
• Finally, there’s a pair of square brackets: [ followed by ].

This level of precision in the grammar will be necessary when we come to write the parser. But before we can write the parser, we need to define the hierarchy of objects that the parser will store its results in. This is called the abstract syntax tree (AST).

### The Abstract Syntax Tree (AST)

Now that we have a grammar for Mini-C, we need to turn it into code. The code won’t do anything yet - it’s just how we will represent source code after it has been parsed.

Wikipedia defines an abstract syntax tree (AST) as

… a tree representation of the abstract syntactic structure of source code written in a programming language.

When you’re writing an F# program, as soon as you hear the word “tree”, you can smile. F# was built for such things. In C#, we’d probably use a hierarchy of classes, but F#’s discriminated unions provide a more elegant solution. Hopefully you’ll see that F# lets us write code that looks surprisingly similar to the grammar. You’ll find this code in Ast.fs in the Mini-C GitHub repository.

Let’s write some code. I’m not going to explain F#’s syntax, because there are plenty of other places that do a better job than I could. If you’re not familiar with F#, it might look a bit weird at first, but it grows on you.

type Program = Declaration list


This makes Program essentially an alias for a list of declarations. (In C#, we’d write List<Declaration>.)

and Declaration =
| StaticVariableDeclaration of VariableDeclaration
| FunctionDeclaration of FunctionDeclaration


A declaration is either a static variable declaration or a function declaration.

and TypeSpec =
| Void
| Bool
| Int
| Float


The supported types in Mini-C are void, bool, int and float.

and VariableDeclaration =
| ScalarVariableDeclaration of TypeSpec * Identifier
| ArrayVariableDeclaration of TypeSpec * Identifier


A variable declaration can either be a scalar variable declaration or an array variable declaration. Both types of variable declaration consist of a type and an identifier. The * character is what F# uses to define tuples. In C#, we might write Tuple<TypeSpec, Identifier> (except we wouldn’t because nobody uses tuples in C#).

and FunctionDeclaration = TypeSpec * Identifier * Parameters * CompoundStatement


A function declaration consists of a type, an identifier, some function parameters, and a “compound statement”. We’ll see what compound statements are shortly.

and Identifier = string

and Parameters = VariableDeclaration list

and IdentifierRef = { Identifier : string; }


An identifier is simply a string. The Parameters type (as used in FunctionDeclaration) is an alias for a list of variable declarations. It’s worth noting that the VariableDeclaration type is used for both function parameters and global variable declarations. Although the grammar is a bit different in these two contexts, the actual data we need to store after parsing is the same.

and Statement =
| ExpressionStatement of ExpressionStatement
| CompoundStatement of CompoundStatement
| IfStatement of IfStatement
| WhileStatement of WhileStatement
| ReturnStatement of Expression option
| BreakStatement


Here are examples of each type of Mini-C statement:

Statement Type Mini-C Code
Expression Statement i = 2 + 3;
Compound Statement { int j; j = 5; j = j + 1; }
If Statement if (i == 2) { return 3; }
While Statement while (i < 3) { i = i + 1; }
Return Statement return true;
Break Statement break;
and ExpressionStatement =
| Expression of Expression
| Nop


Many languages, including Mini-C, differentiate between expressions and statements. At a very high level:

• Expressions evaluate to a value.
• Statements do something.

Expression statements are where the two come together. An expression statement is simply a statement composed of an expression. We’ll soon see what expressions are.

and CompoundStatement = LocalDeclarations * Statement list

and LocalDeclarations = VariableDeclaration list


A compound statement is composed of a list of local variable declarations, and a list of statements. You might notice that there’s some recursion going on here: one of the Statement types is CompoundStatement, which itself is composed of a list of Statements. That simplifies AST construction, and will also make working with the AST easier later on.

and IfStatement = Expression * Statement * Statement option


An if statement is composed of:

• an expression - i.e. the condition to test
• a statement to execute if the condition evaluates to true, which could be either a single statement or a compound statement
• an optional statement to execute if the condition evaluates to false - this is what you’d write in the else part of the if statement

Note that adding option after a type such as Statement is roughly analogous to writing Statement? or Nullable<Statement> in C#, except that F# is more awesome and allows the use of option for reference types too.

and WhileStatement = Expression * Statement


While statements, at least far as the AST goes, are similar to if statements. They are composed of an expression - which is the condition to test on each time through the loop, and a statement (which again, could be a compound statement).

and Expression =
| ScalarAssignmentExpression of IdentifierRef * Expression
| ArrayAssignmentExpression of IdentifierRef * Expression * Expression
| BinaryExpression of Expression * BinaryOperator * Expression
| UnaryExpression of UnaryOperator * Expression
| IdentifierExpression of IdentifierRef
| ArrayIdentifierExpression of IdentifierRef * Expression
| FunctionCallExpression of Identifier * Arguments
| ArraySizeExpression of IdentifierRef
| LiteralExpression of Literal
| ArrayAllocationExpression of TypeSpec * Expression


In partnership with statements, expressions make up the core of most languages. Mini-C has a simple grammar, and correspondingly few expression types. Here are examples of each type of Mini-C expression:

Expression Type Mini-C Code
Scalar assignment i = 2 + 3
Array assignment j[0] = 2 + 3;
Binary i == 2
Unary -i
Identifier i
Array identifier j[0]
Function call myFunc(0, true)
Array size j.size
Literal true
Array allocation new int[3]

Note that many of these definitions are recursive. ScalarAssignmentExpression, for example, is composed of an IdentifierRef and an Expression. If you think about it, this makes sense - on the right hand side of an assignment, you want to be able to use any arbitrary expression, including other assignments (at least in C-like languages).

and BinaryOperator =
| ConditionalOr
| Equal
| NotEqual
| LessEqual
| Less
| GreaterEqual
| Greater
| ConditionalAnd
| Add
| Subtract
| Multiply
| Divide
| Modulus

and UnaryOperator =
| LogicalNegate
| Negate
| Identity


Binary and unary operators are hopefully self-explanatory, and comparable to the operators in most C-based languages.

and Literal =
| BoolLiteral of bool
| IntLiteral of int
| FloatLiteral of float


Mini-C supports these literals:

• BoolLiteral - true or false
• IntLiteral - 1, -2, etc.
• FloatLiteral - 1.23, -0.5, etc.

### Until next time…

And that’s it! You’ll find all that code in Ast.fs in the GitHub repository. F#’s discriminated unions are perfectly suited for defining an abstract syntax tree.

Next time, we’ll build a parser capable of turning Mini-C source code into a tree of objects, using the AST we’ve defined here.