carbon-lang/executable_semantics

Executable Semantics

This directory contains a work-in-progress executable semantics. It started as an executable semantics for Featherweight C and it is migrating into an executable semantics for the Carbon language. It includes a parser, type checker, and abstract machine.

This language currently includes several kinds of values: integer, booleans, functions, and structs. A kind of safe union, called a choice, is in progress. Regarding control-flow, it includes if statements, while loops, break, continue, function calls, and a variant of switch called match is in progress.

The grammar of the language matches the one in Proposal #162. The type checker and abstract machine do not yet have a corresponding proposal. Nevertheless they are present here to help test the parser but should not be considered definitive.

The parser is implemented using the flex and bison parser generator tools.

• syntax.lpp the lexer specification
• syntax.ypp the grammar

The parser translates program text into an abstract syntax tree (AST), defined in the ast subdirectory.

The type checker defines what it means for an AST to be a valid program. The type checker prints an error and exits if the AST is invalid.

The parser and type checker together specify the static (compile-time) semantics.

The dynamic (run-time) semantics is specified by an abstract machine. Abstract machines have several positive characteristics that make them good for specification:

• abstract machines operate on the AST of the program (and not some lower-level representation such as bytecode) so they directly connect the program to its behavior

• abstract machines can easily handle language features with complex control-flow, such as goto, exceptions, coroutines, and even first-class continuations.

The one down-side of abstract machines is that they are not as simple as a definitional interpreter (a recursive function that interprets the program), but it is more difficult to handle complex control flow in a definitional interpreter.

InterpProgram() runs an abstract machine using the interpreter, as described below.

Abstract Machine

The abstract machine implements a state-transition system. The state is defined by the State structure, which includes three components: the procedure call stack, the heap, and the function definitions. The Step function updates the state by executing a little bit of the program. The Step function is called repeatedly to execute the entire program.

An implementation of the language (such as a compiler) must be observationally equivalent to this abstract machine. The notion of observation is different for each language, and can include things like input and output. This language is currently so simple that the only thing that is observable is the final result, an integer. So an implementation must produce the same final result as the one produces by the abstract machine. In particular, an implementation does not have to mimic each step of the abstract machine and does not have to use the same kinds of data structures to store the state of the program.

A procedure call frame, defined by the Frame structure, includes a pointer to the function being called, the environment that maps variables to their addresses, and a to-do list of actions. Each action corresponds to an expression or statement in the program. The Action structure represents an action. An action often spawns other actions that needs to be completed first and afterwards uses their results to complete its action. To keep track of this process, each action includes a position field pos that stores an integer that starts at -1 and increments as the action makes progress. For example, suppose the action associated with an addition expression e1 + e2 is at the top of the to-do list:

(e1 + e2) [-1] :: ...

When this action kicks off (in the StepExp function), it increments pos to 0 and pushes e1 onto the to-do list, so the top of the todo list now looks like:

e1 [-1] :: (e1 + e2) [0] :: ...

Skipping over the processing of e1, it eventually turns into an integer value n1:

n1 :: (e1 + e2) [0]

Because there is a value at the top of the to-do list, the Step function invokes HandleValue which then dispatches on the next action on the to-do list, in this case the addition. The addition action spawns an action for subexpression e2, increments pos to 1, and remembers n1.

e2 [-1] :: (e1 + e2) [1](n1) :: ...

Skipping over the processing of e2, it eventually turns into an integer value n2:

n2 :: (e1 + e2) [1](n1) :: ...

Again the Step function invokes HandleValue and dispatches to the addition action which performs the arithmetic and pushes the result on the to-do list. Let n3 be the sum of n1 and n2.

n3 :: ...

The heap is an array of values. It is used to store anything that is mutable, including function parameters and local variables. An address is simply an index into the array. The assignment operation stores the value of the right-hand side into the heap at the index specified by the address of the left-hand side lvalue.

Function calls push a new frame on the stack and the return statement pops a frame off the stack. The parameter passing semantics is call-by-value, so the machine applies CopyVal to the incoming arguments and the outgoing return value. Also, the machine kills the values stored in the parameters and local variables when the function call is complete.

Experimental: Delimited Continuations

Delimited continuations provide a kind of resumable exception with first-class continuations. The point of experimenting with this feature is not to say that we want delimited continuations in Carbon, but this represents a place-holder for other powerful control-flow features that might eventually be in Carbon, such as coroutines, threads, exceptions, etc. As we refactor the executable semantics, having this feature in place will keep us honest and prevent us from accidentally simplifying the interpreter to the point where it can't handle features like this one.

Instead of delimited continuations, we could have instead done regular continuations with callcc. However, there seems to be a consensus amongst the experts that delimited continuations are better than regular ones.

So what are delimited continuations? Recall that a continuation is a representation of what happens next in a computation. In the abstract machine, the procedure call stack represents the current continuation. A delimited continuation is also about what happens next, but it doesn't go all the way to the end of the execution. Instead it represents what happens up until control reaches the nearest enclosing __continuation statement.

The statement

__continuation <identifier> <statement>

creates a continuation object from the given statement and binds the continuation object to the given identifier. The given statement is not yet executed.

The statement

__run <expression>;

starts or resumes execution of the continuation object that results from the given expression.

The statement

__await;

pauses the current continuation, saving the control state in the continuation object. Control is then returned to the statement after the __run that initiated the current continuation.

These three language features are demonstrated in the following example, where we create a continuation and bind it to k. We then run the continuation twice. The first time increments x to 1 and the second time increments x to 2, so the expected result of this program is 2.

fn main() -> Int {
  var Int: x = 0;
  __continuation k {
    x = x + 1;
    __await;
    x = x + 1;
  }
  __run k;
  __run k;
  return x;
}

Note that the control state of the continuation object bound to k mutates as the program executes. Upon creation, the control state is at the beginning of the continuation. After the first __run, the control state is just after the __await. After the second __run, the control state is at the end of the continuation.

The delimited continuation feature described here is based on the shift/reset style of delimited continuations created by Danvy and Filinsky (Abstracting control, ACM Conference on Lisp and Functional Programming, 1990). We adapted the feature to operate in a more imperative manner. The __continuation feature is equivalent to a reset followed immediately by a shift to pause and capture the continuation object. The __run feature is equivalent to calling the continuation. The __await feature is equivalent to a shift except that it updates the continuation in place.

Example Programs (Regression Tests)

The testdata/ subdirectory includes some example programs with golden output.