The CIVL-IR language. A program in this language is also known as a "CIVL model".

Properties of the language:

• the language is not intended to be written by humans; it is an intermediate form constructed by CIVL. However it should be readable to help debug things
• a CIVL-IR program represents a guarded-transition system explicitly
• as in CIVL-C, there are functions, scopes, and functions can be defined in any scope
• all blocks (including a function body) consist of the following elements, in this order:
  • a sequence of type definitions
  • a sequence of variable declarations with no initializers
  • a sequence of function definitions
  • a sequence of labeled statements. Each clause in the labeled statement is a \when statement with some guard and a primitive statement, followed by a \goto statement
• an array is declared without any length expression. When it is initialized it can specify length.
• curly braces are used only to indicate scopes

Example:

f(u:Integer, a:Array[Real]): Integer {
  x: Real;
  y: Real;
  z: Float[16,23];
 
L1 :
    when (g1) stmt1; goto L2;
    when (g2) stmt2; goto L3;

  { // begin new scope
    Real x;
L2 :
      when (g3) stmt3; goto L4;
      ...
  } // end new scope
...
}
// etc.

Example:

{
  int x=3*y;
  int a[x+1];
}

translates to:

{
  x: Integer;
  a_t : Dytype[Array[Integer]];
  a: Array[Integer];
L1:
  when (\true) x:=3*y; goto L2;
L2:
  when(\true) a_t:=\dytype(Array[Integer, x+1]); goto L3; // Array[Integer] is refined here using x+1
L3:
  when (\true) a:=\new(a_t); goto L4;
L4:
}

Types

The types are:

• Bool : boolean type, values are \true and \false
• Proc : process type
• Scope : scope type
• Char : character type
• Bundle : type representing some un-typed chunk of data
• Heap : heap type
• Range : ordered set of integers
• Domain : ordered set of tuples of integers
• Domain[n], n is an integer at least 1; subtype of Domain in which all tuples have arity n.
• Enum types.
  • different from integers or like C?
• Integer : the mathematical integers
• Int[lo,hi,wrap]
  • lo, hi are integers, wrap is boolean
  • finite interval of integers [lo,hi]. If wrap is true then all operations "wrap", otherwise, any operation resulting in a value outside of the interval results in an exception being thrown.
  • Do we want to allow lo and hi to be any values of type Integer, which means they are dynamic types, like complete array types?
• HerbrandInt : Herbrand integers. Values are unsimplified symbolic expressions.
• Real : the mathematical real numbers
• Float[e,f], e, f are integers, each at least 1. Same question for e and f as for lo and hi.
  • IEEE754 floating point numbers
• HerbrandReal : Herbrand real numbers. Values are unsimplified symbolic expressions.
• Tuple[T0, T1, ...]: a tuple type, the Cartesian product of T0, T1, ...
  • What about bit-widths?
• Union[T0, T1, ...]: union type, the disjoint union of T0, T1, ...
• Array[T] : arrays of any length whose elements belong to T
• Function[(T0,T1,...),T] : functions consuming T0,T1,... and returning T. T can be void to indicate nothing is returned.
• Mem : type representing a memory set. May be thought of as a set of pointers.
• Pointer : all pointers, a subtype of Mem
• Pointer[T] : pointer-to-T, subtype of Pointer
• Dytype : the set of all dynamic types
• Dytype[T]: dynamic types refining T. Values of this type represent dynamic types that refine T. For example \dytype(Array[Integer,24]) has type Dytype[Array[Integer]]

Type facts:

Static types are the types assigned to variables in a program statically. A static type contains no values anywhere in the type tree. That is, there is no array length expression in the type. These are the types that are used in declarations. Each variable is declared to have some static type.

Value types are the types associated to values. They include all the static types plus possible length expressions. A value type refines a static type if when you delete the values from the value type you get the static type.

A type name is a syntactic element that names a (static or value) type. Examples of type names include Array[Integer] and Array[Integer,24].

The expression \new(t) takes a Dytype and returns the initial value for an object of that type. The initial value of Integer and other primitive (non-compound) types is "undefined". The initial value of Array[Integer] is an array of length 0 of Integer. The initial value of Pointer[Real] is the undefined pointer to Real. The initial value of Array[Real, 10] is the array of length 10 in which each element is undefined. In general, the initial value of an array of length n is the sequence of length n in which every element is the initial value of the element type of the array. The initial value of a tuple type is the tuple in which each component is assigned the initial value for its type.

Example: the C code

int n = 10;
struct S { int a[n]; };
struct S x1;
n=20;
struct S x2;

may be translated as

// type definitions
typedef S=Tuple[Array[Integer]];

// variable decls
n: Integer;
S_d: Dytype[S];
x1: S;
x2: S;

// statements (leaving out the chooses and whens for brevity)
n:=10;
S_d:=\dytype(Tuple[Array[Integer, n]]);
x1:=\new(S_d);
n:=20;
x2:=\new(S_d);

Expressions

In the following list of expressions, e, e0, e1, etc., are expressions. T is a type name. t is an expression of type Dytype.

• literals
  • \true, \false : values of type Bool
  • 123, -123, 3.1415, etc. : values of type Integer, Int, Real, Float. NEED TO BE MORE SPECIFIC
  • 'a', 'b', ... : Char values. UNICODE?
  • \array(T, (e0, ..., en-1)): value of type Array[T, n], a literal array
  • \array(T, n, e): value of type Array[T,n] in which each of the n elements is e
  • \tuple(S, (e0, e1, ...)) : value of tuple type S (tuple literal)
  • \range(e1,e2,e3) : value of type Range consisting of the integers e1, e1+e3, e1+2*e3, ... that are less than or equal to e2.
  • \domain(r1,...,rn) : value of type Domain[n], the ordered Cartesian product of the n ranges (dictionary order)
  • "abc" : string literals: value of type Array[Char, n+1], where n is the length of the string (the last element is the character \0)
  • \root, \here : values of type Scope
  • \self, \proc_null : values of type Proc
  • NULL : value of type void*
• variables
• \sizeof_type(t) : the size of the dynamic type t
• \sizeof_expr(e) : the size of the value of expression e
• \new(t) : new (default) value of dynamic type t
• \defined(e) : is e defined? Type is Bool
• \has_next(dom, (i, j, …)): an expression of boolean type, testing if the domain dom contains any element after (i, j, ...)
• \add(e1, e2) : numeric addition.
  • e1 and e2 have the same numeric type. Note that there are no "automatic conversions" as there are in C. If the original expressions have different types, explicit casts must be inserted.
• \padd(e1, e2): pointer addition. e1 has pointer type and e2 has an integer type.
• \sub(e1, e2) : subtraction
• \mul(e1, e2) : multiplication
• \div(e1, e2) : division
  • If both are integer types, the result is integer division. Otherwise it is real division. Need to define what happens for negative integers.
• \mod(e1, e2) : modulus
• \asub(e1, e2) : array subscript expression. Note that e1 must have array type, not pointer type. (This is different from C.) If e1 has pointer type, use \deref(\padd(e1, e2)) instead.
• \deref(e) : pointer dereference
• \addressof(e) : address-of operator
• \not(e) : logical not
• \neg(e) : negative
• \cast(T, e) : casts e to a value of the named type
  • need to list all of the legal casts and what they mean exactly
  • cast of integer to array-of-boolean, and vice-versa?
  • Instead of casts would it be better to have explicit functions for each legal kind of cast?
• \eq(e1, e2), \neq(e1, e2): equality/inequality test
• \and(e1, e2), \or(e1, e2): logical and/or operation
• \cond(e1, e2, e3): conditional expression, equivalent to e1?e2:e3 in C.
• \lt(e1, e2), \lte(e1, e2): less than/less than or equal to
• e0(e1,...,en) : a function invocation where e must evaluate to an abstract or pure system function
• \forall, \exists : \forall {Integer i | e0} e1. \exists is similar. Is this the best notation?
• \tuple_read(e1, i), some natural number i (tuple read)
• \bit_and(e1, e2), \bit_or(e1, e2), \bit_xor(e1, e2), \bit_comp(e1) : bit-wise operations: arguments are arrays of booleans
• a left-hand-side expression, when used in certain contexts, is automatically converted to Mem. The contexts are: arguments to the built-in functions \access, \read, and \write described below, or occurrence in the list of an \assigns clause
• \array_chunk(a, dom), where a is an expression of array type and dom is an expression of Domain type. The dimension of the array must match the dimension of the domain. This represents all memory units which are the cells in the array indexed by a tuple in dom.
• \region(ptr), where ptr is an expression with a pointer type. This represents the set of all memory units reachable from ptr, including the memory unit pointed to by ptr itself.
  • \mem_reach ?
• \mem_union(mem1, mem2), where mem1 and mem2 are expressions of type Memory. This is the union of the two sets.
  • could we use Frama-C notation p+(e1..e2) for example?

Pointers: unlike C, there is no "array-pointer pun". If an array a needs to be converted to a pointer, you must use \address_of(\address_of(\array_subscript(a, 0))).

The Primitive Statements

• Assign: e1:=e2;
• Call: \call f, (e1,...,en); and \call e, f, (e1,...,en);
  • regular function (one with flow graph)
  • distinguish this kind of call from an expression involving a pure system or abstract call???
• Spawn: \spawn f, (e1,...,en); and \spawn e, f, (e1,...,en);
• Wait: \wait e;
• Wailtall: \waitall e, n where e is a pointer to a process reference and n is the number of processes to be waited for
• Allocation
  • \allocate e, h, t, e0;, where
    • e has type Pointer
    • h has type Heap
    • t has type Dytype
    • e0 has integer type.
  • Allocates e0 objects of type t on heap h
  • To translate the C malloc you first need to figure out the type of the elements being malloced. If the argument to malloc is n, then you first need to insert an assertion \eq(\mod(n, \sizeof_type(t)), 0), and then \allocate e, h, t, \div(n, \sizeof_type(t)).
• Free: \free p;
• Expression statement: e;, where e is side effect free except that it might contain error/exception (e.g., array index out of bound, division by zero);
• Noop: ;
  • Is there a need to add annotations for "true" or "false" branch, etc.? If so, we can just make these parameters to the Noop.
• Return: \return; and \return e;
• Atomic_enter: \atomic_enter;
• Atomic_exit: \atomic_exit;
• Parfor_spawn: \parspawn p, d, f; where p is pointer to process reference, d has Domain type and f has Function type.
• Domain iterator: \next dom, (i,j,…) updates i, j, ... to be the value of the inter tuple in dom after (i, j, ...)
• For_dom_enter (for domains): \for_enter dom;

Declarations and Function Definitions

Declarations follow the C notation. Function prototypes are considered to be declarations similar to variable declarations.

Example of declaration of a function:

f(Real x, Bool y; Integer);

Additional modifiers that may be placed on any of above:

• \pure : the function has no side effects, but may be nondeterministic
• \abstract: function is a pure, mathematical function: deterministic function of inputs
• \atomic_f: function definition is atomic, and it never blocks

System functions:

• A function declaration which is not abstract and for which no definition is provided is a system function.
• If the system function is called anywhere in the program, it must be defined by providing Java code in an Enabler and Executor. Failure to do so will result in an exception.
• A system function may modify any memory it can reach. This includes allocating new data on heaps it can reach.
• A system function may have a guard.

Example of a declaration of a system function with guard.

g(Real x, Bool y; Bool) { ... }
f(Real x, Bool y; Integer) \guard {g};

Function Contracts

• event set expressions:

  EventSetExpression
   : \read(MemorySetExpression)
   | \write(MemorySetExpression)
   | \access(MemorySetExpression)
   | \calls(FunctionCallExpression)
   | \nothing
   | \everything
   | ‘(’ EventSetExpression ‘)’
   | EventSetExpression + EventSetExpression
   | EventSetExpression - EventSetExpression
   | EventSetExpression & EventSetExpression
  

• depends clause: \depends [condition] { event1, event2, ...}
  • Example:

    \depends {
      \access(n) - (\calls(inc(MemorySetExpression)) + \calls(dec(MemorySetExpression)))
    }
    

  • absence of \depends clause:
• assigns-or-reads clause
  • assigns clause: \assigns [condition] {memory-list}
  • reads clause: \reads [condition] {memory-list}
  • \reads {\nothing} implies \assigns {\nothing}
  • \reads {\nothing} is equivalent to: \reads {\nothing} \assigns {\nothing}
  • \assigns {X} where X != \nothing, implies \reads {X}
  • \assigns {X} is equivalent to: \assigns{X} \reads{X}
  • absence:
    • absence of \reads clause: there is no assumption about the read access of the function, i.e., the function could read anything
    • absence of \assigns clause: similar to the absence of \reads clause
  • \reads/\assigns {\nothing} doesn’t necessarily means that the function never reads or assigns any variable. The function could still reads/assigns its “local” variables, including function parameters and any variable declared inside the function body.

• For an independent function which has \depends {\nothing}, usually we also need to specify \reads{nothing}, for the purpose of reachability analysis.

e.g.,

/* Returns the size of the given bundle b. */
\bundle_size(Bundle b; Int)
  \depends {\nothing}
  \reads {\nothing}
  ;

• Example of a function declaration with contracts:

  \atomic_f sendRecv(Int cmd, Pointer buf; Int)
    \depends [\eq(cmd, SEND)] {\write(buf)}
    \depends [\eq(cmd, RECV)] {\access(\deref(buf))}
    \assigns [\eq(cmd, SEND)] {\nothing}
    \assigns [\eq(cmd, RECV)] {\deref(buf)}
    \reads {\deref(buf)}
  {
  L0:
    when (\eq(cmd, SEND))
       send(\deref(buf), ...); goto L1;
    when (\eq(cmd, RECV))
      \deref(buf):=recv(...); goto L1;
    when (\and(\neq(cmd, SEND), \neq(cmd, RECV)))
      ; goto L1;
  L1:
  }
  

Program

A program consists of a sequence of global variable declarations, which may include declarations annotated by $input and $output, followed by a sequence of function declarations and definitions.

Semantics

Semantics issues

• define every possible cast
• define every possible +, etc.
• define every kind of pointer value and casts between pointer types
• casts between pointer and integer types?

Values

Transitions

Libraries