A flat reachability-based measure


    fun yes = (print "yes"; yes)

\[\neg\]

💥

🙂

You can prove it!

🙃

It's complicated...

The aim of this work is to simplify this process

size_of_heap s

=

size_of reachabe_values s.refs {}


       <|s.locals|> ++ <|s.stack|> ++ <|s.global|>

size_of vals refs seen

Precise measurements
Handles aliasing
Trivial to evaluate given concrete values


├─── ftail [1,2,3] ───┤ <= heap_limit

├─── ftail [2,3] ───┤ <= heap_limit

├─── ftail [3]  ───┤ <= heap_limit

├─── ftail []  ───┤ <= heap_limit


    ├──[2,...,n]──┼───rest───┤

    <=

    ├──[1,2,...,n]──┼───rest───┤

🤦

size_of vals refs seen

Traversal-base measurement
No algebraic properties over ++
Relies on the well-formedness of its arguments

A flat reachability-based measure

The set of all reachable values


    <|s.locals|> ++ <|s.stack|> ++ <|s.global|>


    [
     Block 71 some_tag [Number 1; Block 74 ...];
     Number 57;
     Word64 0xF5CA15;
     Word64 0x01368E;
     Word64 0xC81026;
     RefPtr 45;
     Block 75 some_tag [RefPtr 84; ...];
    ]

The set of all reachable values addresses

The set of all reachable addresses

`=`


      reachable_addrs refs blocks roots =
        { y | ∃x. x ∈ roots ∧ RTC (next refs blocks) x y }

Once we have that, we measure!

🎉

flat_size_of refs blocks roots

Precise measurements
Handles aliasing
Simpler reasoning

Proven equivalent to size_of
Published on IFL2021