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Introduction
This is part (B) of project 4, in which you implement an interpreter for MicroCaml.
In particular, you will implement two functions, eval_expr and eval_mutop. Each of these takes an environment (defined in microCamlTypes.ml) as a parameter, which acts as a map from variables to values. The eval_expr function evaluates an expression in the
given environment, returning a value, while eval_mutop takes a mutop — a top-level directive — and returns a possibly updated environment and any additional result. You will need to use Imperative OCaml — notably references — to implement this project. This use is small, but important. More details below.
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Ground Rules and Extra Info
The interpreter must be implemented in eval.ml in accordance with the signatures for eval_expr and eval_mutop found in eval.mli. eval.ml is the only file you will write code in.
In your code, you may use any standard library functions, but the ones that will be useful to you will be found in the Stdlib module. If you come asking for help using something we have not taught we will direct you to use methods taught in this class.
Compilation, Tests, and Running
You can submit through gradescope-submit from the project directory and the project will be automatically submitted. You can also manually submit to Gradescope. You may
only submit the eval.ml file.
You do not need a working parser and lexer to implement this project — all testing can be done on abstract syntax trees directly.
To test locally, run dune runtest -f. To test from the toplevel, run dune utop src. The necessary functions and types will automatically be imported for you. For example,
from utop, you can write:
eval_expr [] (Let (“x”, false, Value (Bool true), ID “x”));; – : value = Bool true
Running Mutop
If you do have a working parser and lexer, you can run them and your interpreter together in mutop (Micro-utop), a version of utop for MicroCaml. Run the
command dune exec bin/mutop.exe in your terminal or use the shell script bash mutop.sh to start the mutop toplevel. The toplevel uses your implementations
for parse_mutop and eval_mutop to execute MicroCaml expressions. Here is an example of its use:
Note: If you are having issues running mutop, run the command dune build before starting the mutop toplevel.
Operational Semantics
We are going to describe how to implement your interpreter using examples, below. A more succinct description is this operational semantics. Even if you don’t use it much to do the project, we expect you to understand it — we may take questions from it for the exam.
Part 1: Evaluating Expressions
eval_expr : environment -> expr -> value
This function takes an environment env and an expression e, which is type expr, and produces the result of evaluating e, which is something of type value. All of the types mentioned here are defined in microCamlTypes; do not change any of them!
The environment env is a (var * value ref) list, where var refers to an variable name (which is a string), and the value ref refers to its corresponding value in
the environment; it’s a ref because the value could change, due to implementing recursion, as discussed for Let below. Elements earlier in the list shadow elements later in the list.
There are three possible error cases, represented by three different exceptions
(in eval.ml — do not change): exception TypeError of string exception DeclareError of string exception DivByZeroError
A TypeError happens when an operation receives an argument of the wrong type;
a DeclareError happens when an ID is seen that has not been declared; and
a DivByZeroError happens on attempted division by zero. We do not enforce what messages you use when raising the TypeError or DeclareError exceptions. That’s up to you.
Evaluation of subexpressions should be done from left to right to ensure that lines with multiple possible errors match up with our expected errors.
Now we describe what your interpreter should do for each kind of expr, i.e., type expr =
| Value of value
| ID of var
| Fun of var * expr
| Not of expr
| Binop of op * expr * expr
| If of expr * expr * expr
| FunctionCall of expr * expr
| Let of var * bool * expr * expr
A value is defined as type value =
| Int of int
| Bool of bool
| String of string
| Closure of environment * var * expr
Values (often literals in the original source program) evaluate to themselves, i.e.,
eval_expr [] (Value(Int 1)) = Int 1 eval_expr [] (Value(Bool false)) = Bool false eval_expr [] (Value(String “x”)) = String “x”
A closure is the result of evaluating an anonymous function; it, too, evaluates to itself. We will discuss closures in detail when considering anonymous functions, and function calls, below.
eval_expr [] (Value(Closure ([], “x”, Fun (“y”, Binop (Add, ID “x”, ID “y”))))) = Closure ([], “x”, Fun (“y”, Binop (Add, ID “x”, ID “y”)))
An identifier evaluates to whatever value it is mapped to by the environment. Should
raise a DeclareError if the identifier has no binding.
eval_expr [(“x”, ref (Int 1))] (ID “x”) = Int 1
eval_expr [] (ID “x”) (* DeclareError “Unbound variable x” *)
See the discussion of Let below for advice about managing environments. Not
The unary not operator operates only on booleans and produces a Bool containing the
negated value of the contained expression. If the expression in the Not is not a boolean
(or does not evaluate to a boolean), a TypeError should be raised. eval_expr [(“x”, ref (Bool true))] (Not (ID “x”)) = Bool false eval_expr [(“x”, ref (Bool true))] (Not (Not (ID “x”))) = Bool true eval_expr [] (Not (Value(Int 1))) (* TypeError “Expected type bool” *)
There are five sorts of binary operator: Those carrying out integer arithmetic; those carrying out integer ordering comparisons; one carrying out string concatenation; and one carrying out equality (and inequality) comparisons; and those implementing boolean logic.
Add, Sub, Mult, and Div
Arithmetic operators work on integers; if either argument evaluates to a non-Int, a TypeError should be raised. An attempt to divide by zero should raise
a DivByZeroError exceptio.
eval_expr [] (Binop (Add, Value(Int 1), Value(Int 2))) = Int 3
eval_expr [] (Binop (Add, Value(Int 1), Value(Bool false))) (* TypeError “Expected type int” *)
eval_expr [] (Binop (Div, Value(Int 1), Value(Int 0))) (* DivByZeroError *)
Greater, Less, GreaterEqual, and LessEqual
These relational operators operate only on integers and produce a Bool containing the result of the operation. If either argument evaluates to a non-Int, a TypeError should
be raised.
eval_expr [] (Binop(Greater, Value(Int 1), Value(Int 2))) = Bool false
eval_expr [] (Binop(LessEqual, Value(Bool false), Value(Bool true))) (* TypeError “Expected type int” *)
This operation returns the result of concatenating two strings; if either argument
evaluates to a non-String, a TypeError should be raised.
eval_expr [] (Binop (Concat, Value(Int 1), Value(Int 2))) (* TypeError “Expected type string” *)
eval_expr [] (Binop (Concat, Value(String “hello “), Value(String “ocaml”))) =
String “hello ocaml”
Equal and NotEqual
The equality operators require both arguments to be of the same type. The operators produce a Bool containing the result of the operation. If the two arguments to these operators do not evaluate to the same type (e.g., one boolean and one integer),
a TypeError should be raised. Moreover, we cannot compare two closures for equality — to do so risks an infinite loop because of the way recursive functions are implemented; trying to compare them also raises TypeError (OCaml does the same thing in its
implementation, BTW).
eval_expr [] (Binop(NotEqual, Value(Int 1), Value(Int 2))) = Bool true
eval_expr [] (Binop(Equal, Value(Bool false), Value(Bool true))) = Bool false eval_expr [] (Binop(Equal, Value(String “hi”), Value(String “hi”))) = Bool true eval_expr [] (Binop(NotEqual, Value(Int 1), Value(Bool false))) (* TypeError “Cannot compare types” *)
Or and And
These logical operations operate only on booleans and produce a Bool result. If either
argument evaluates to a non-Bool, a TypeError should be raised.
eval_expr [] (Binop(Or, Value(Int 1), Value(Int 2))) (* TypeError “Expected type bool” *)
eval_expr [] (Binop(Or, Value(Bool false), Value(Bool true))) = Bool true
The If expression consists of three subexpressions – a guard, the true branch, and the false branch. The guard expression must evaluate to a Bool – if it does not,
a TypeError should be raised. If it evaluates to Bool true, the true branch should be
evaluated; else the false branch should be.
eval_expr [] (If (Binop (Equal, Value (Int 3), Value (Int 3)), Value (Bool true), Value (Bool false))) = Bool true
eval_expr [] (If (Binop (Equal, Value (Int 3), Value (Int 2)), Value (Int 5), Value (Bool false))) = Bool false
• Only one branch should be evaluated, not both.
• The true and false branches could evaluate to values having different types. This is an effect of MicroCaml being dynamically typed.
The Let consists of four components – an ID’s name var (which is a string); a boolean indicating whether or not the bound variable is referenced in its own definition (i.e., whether it’s recursive); the initialization expression; and the body expression.
Non-recursive bindings
For a non-recursive Let, we first evaluate the initialization expression, which produces a value v or raises an error. If the former, we then return the result of evaluating the body expression in an environment extended with a mapping from the Let’s ID variable to v.
(Evaluating the body might cause an exception to be raised.)
eval_expr [] (Let (“x”, false,
Binop (Add, Binop (Mult, Value (Int 2),
Binop (Div, Value (Int 3), Value (Int 5))), Value (Int 4)), Binop (Sub, ID “x”, Value (Int 5)))) = Int (-1)
Recursive bindings
For a recursive Let, we evaluate the initialization expression in an environment extended with a mapping from the ID we are binding to a temporary placeholder; this
way, the initialization expression is permitted to refer to itself, the ID being bound. Then, we update that placeholder to v, the result, before evaluating the body.
The AST given in this example corresponds to the MicroCaml program let rec f = fun
x -> if x = 0 then x else (x + (f (x-1))) in f 8: eval_expr [] (Let (“f”, true,
If (Binop (Equal, ID “x”, Value (Int 0)), ID “x”,
Binop (Add, ID “x”,
FunctionCall (ID “f”, Binop (Sub, ID “x”, Value (Int 1)))))),
FunctionCall (ID “f”, Value (Int 8)))) = Int 36
Environments
Being able to modify the placeholder is made possibly by using references; this is why the type environment given in microCamlTypes.ml is (var * value ref) list and not (var
* value) list. To make it easy to work with this kind of environment, we recommend you use the functions given at the top of eval.ml:
• extend env x v produces an environment that extends env with a mapping fromxtov
• lookup env x returns v if x maps to v in env; if there are multiple mappings, it chooses the most recent.
• extend_tmp x produces an environment that extends env with a mapping
from x to a temporary placeholder.
• update env x v produces an environment that updates env in place, modifying its
most recent mapping for x to be v instead (removing the placeholder).
The Fun is used for anonymous functions, which consist of two components – a parameter, which is a string as an ID’s name, and a body, which is an expression.
A Fun evaluates to a Closure that captures the current environment, so as to implement
lexical (aka static) scoping.
eval_expr [(“x”, ref (Bool true))] (Fun (“y”, Binop (And, ID “x”, ID “y”))) = Closure ([(“x”, ref (Bool true))], “y”, Binop (And, ID “x”, ID “y”))
eval_expr [] (Fun (“x”, Fun (“y”, Binop (And, ID “x”, ID “y”))))
= Closure ([], “x”, Fun (“y”, Binop (And, ID “x”, ID “y”)))
FunctionCall
The FunctionCall has two subexpressions. We evaluate the first to
a Closure(A,x,e) (otherwise, a TypeError should be raised) and the second to a value v.
Then we evaluate e (the closure’s body) in environment A (the closure’s environment),
returning the result.
eval_expr [] (FunctionCall (Value (Int 1), Value (Int 1))) (* TypeError “Not a function” *)
eval_expr [] (Let (“f”, false, Fun (“x”, Fun (“y”, Binop (Add, ID “x”, ID “y”))),
FunctionCall (FunctionCall (ID “f”, Value (Int 1)), Value (Int 2)))) = Int 3 The AST in the second example is equivalent to the MicroCaml expression let f = fun
x -> fun y -> x + y in (f 1) 2.
Part 2: Evaluating Mutop Directive
eval_mutop : environment -> mutop -> environment * (value option)
This function evaluates the given mutop directive in the given environment, returning an updated environment with an optional value as the result. There are three kinds
of mutop directive (as defined in microCamlTypes.ml): type mutop =
| Def of var * expr | Expr of expr
For a Def, we evaluate its expr in the given environment, but with a placeholder set for var (see the discussion of recursive Let, above, for more about environment placeholders), producing value v. We then update the binding for var to be v and
return the extended environment, along with the value itself.
eval_mutop [] (Def (“x”, Value(Bool(true)))) = ([(“x”, {contents = Bool true})], Some (Bool true))
eval_mutop [] (Def (“f”,
If (Binop (Equal, ID “y”, Value (Int 0)), Value (Int 1),
FunctionCall (ID “f”, Binop (Sub, ID “y”, Value (Int 1))))))) = ([(“f”,
{contents =
Closure (
If (Binop (Equal, ID “y”, Value (Int 0)), Value (Int 1), FunctionCall (ID “f”, Binop (Sub, ID “y”, Value (Int 1)))))})],
(Closure ([(“f”, {contents =
If (Binop (Equal, ID “y”, Value (Int 0)), Value (Int 1), FunctionCall (ID “f”, Binop (Sub, ID “y”, Value (Int 1)))))))
For a Expr, we should evaluate the expression in the given environment, and return that
environment and the resulting value.
eval_mutop [] (Expr (FunctionCall (Fun (“x”,
Binop (Concat, Value (String “(“),
Binop (Concat, ID “x”, Value (String “)”)))),
Value (String “parenthesis”)))) = ([], Some (String “(parenthesis)”))
The NoOp should return the original environment and no value (None). eval_mutop [] NoOp = ([], None)
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