# Example: SimPL

As a running example for the next few sections, we'll use a very simple programming language that we call SimPL. Here is its syntax in BNF:

e ::= x | i | b | e1 bop e2
| if e1 then e2 else e3
| let x = e1 in e2

bop ::= + | * | <=

x ::= <identifiers>

i ::= <integers>

b ::= true | false


Obviously there's a lot missing from this language, especially functions. But there's enough in it for us to study the important concepts of interpreters without getting too distracted by lots of language features. Later, we will consider a larger fragment of OCaml.

As we go through this chapter, we're going to develop a complete interpreter for SimPL. You can download the finished interpreter here, or just follow along as we build each piece of it.

## The AST

Since the AST is the most important data structure in an interpreter, let's design it first:

type bop =
| Mult
| Leq

type expr =
| Var of string
| Int of int
| Bool of bool
| Binop of bop * expr * expr
| Let of string * expr * expr
| If of expr * expr * expr


There is one constructor for each of the syntactic forms of expressions in the BNF. For the underlying primitive syntactic classes of identifiers, integers, and booleans, we're using OCaml's own string, int, and bool types.

Instead of defining the bop type and a single Binop constructor, we could have defined three separate constructors for the three binary operators:

type expr =
...
| Add of expr * expr
| Mult of expr * expr
| Leq of expr * expr
...


But by factoring out the bop type we will be able to avoid a lot of code duplication later in our implementation.