# Retrofitting Strong Typing Rules¶

The Annex C of MISRA-C:2012 document puts it in the clearest terms:

"ISO C may be considered to exhibit poor type safety as it permits a wide range of implicit type conversions to take place. These type conversions can compromise safety as their implementation-defined aspects can cause developer confusion."

The most severe consequences come from inappropriate conversions involving pointer types, as they result in general in memory safety violations. Two sections of MISRA-C are dedicated to these issues: a section on "Pointer type conversions" (9 rules) and a section on "Pointers and arrays" (8 rules).

Inappropriate conversions between scalar type are only slightly less severe, as they may introduce arbitrary violations of the intended functionality. MISRA-C has gone to great length to improve the situation here, by defining a stricter type system on top of the C language, which is described in Appendix D of MISRA-C:2012 and in the dedicated section on "The essential type model" (8 rules).

## Enforcing Strong Typing for Pointers¶

Pointers in C provide a low-level view of the addressable memory as a set of integer addresses. Want to write at address 42? Just say so:

int main() {
int *p = 42;
*p = 0;
return 0;
}


Running this program is likely to hit a segmentation fault on an operating system, or to cause havoc in an embedded system, both because address 42 will not be correctly aligned on a 32-bit or 64-bit machine and because this address is unlikely to correspond to valid addressable data for the application. The compiler might issue a helpful warning on the above code (with option -Wint-conversion implied by -Wall in GCC or LLVM), but note that the warning disappears when converting explicitly value 42 to the target pointer type, although the problem is still present.

Beyond their ability to denote memory addresses, pointers are also used in C to pass references to inputs and outputs to function calls, to construct complex data structures with indirection or sharing, and to denote arrays of elements. Pointers are thus at once pervasive, powerful and fragile.

In an attempt to rule out issues that come from direct addressing of memory with pointers, MISRA-C states in Rule 11.4 that "A conversion should not be performed between a pointer to object and an integer type". As this rule is classified as only Advisory, MISRA-C completes it with two Required rules that state: "A cast shall not be performed between pointer to void and an arithmetic type" (Rule 11.6) and "A cast shall not be performed between pointer to object and a non-integer arithmetic type" (Rule 11.7).

In Ada, pointers are not addresses, and addresses are not integers. An opaque standard type System.Address defines addresses, and conversions to/from integers are provided by standard unit System.Storage_Elements. The previous wrong C code can be written as follows in Ada:

with System; with System.Storage_Elements; procedure Pointer is A : constant System.Address := System.Storage_Elements.To_Address (42); M : aliased Integer with Address => A; P : access Integer := M'Access; begin P.all := 0; end Pointer;

The integer value 42 is converted into a memory address A by calling System.Storage_Elements.To_Address, which is then used as the address of integer variable M, and pointer variable P is set to point to M (which is only allowed because M is declared as aliased).

Note that it requires far more typing to convince the compiler in Ada that this is a valid program, which hopefully gives more time for programmers to rethink their typing (pun intended) if it's incorrect.

We only mentioned Ada above because SPARK does not support pointers. But SPARK allows addresses.

### Pointers Are Not References¶

Passing parameters by reference is critical for efficient programs, but the absence of references distinct from pointers in C means that this incurs a serious risk in C. Any parameter of pointer type can be copied freely to a variable whose lifetime is larger than the memory pointed to, a problem known as dangling pointers. MISRA-C forbids such uses in Rule 18.6: "The address of an object with automatic storage shall not be copied to another object that persists after the first object has ceased to exist". Unfortunately, enforcing this rule is difficult, as it is one of the undecidable ones.

In SPARK, parameters can be passed by reference, but no pointer to the parameter can be stored, which completely solves this issue. In fact, the decision to pass a parameter by copy or by reference lays in many cases with the compiler, but such compiler dependency has no effect on the functional behavior of a SPARK program. For example, the compiler may decide to pass parameter P of procedure Rotate_X by copy or by parameter, but in any case the postcondition of Rotate_X will hold: the resulting value of P will be modified by rotation around the X axis.

package Geometry is type Point_3D is record X, Y, Z : Float; end record; procedure Rotate_X (P : in out Point_3D) with Post => P = P'Old'Update (Y => P.Z'Old, Z => -P.Y'Old); end Geometry;
package body Geometry is procedure Rotate_X (P : in out Point_3D) is Tmp : constant Float := P.Y; begin P.Y := P.Z; P.Z := -Tmp; end Rotate_X; end Geometry;

SPARK analysis can mathematically prove this fact, and it issues a message that the postcondition is proved here.

### Pointers Are Not Arrays¶

The greatest source of vulnerabilities regarding pointers is their use as substitutes for arrays. Although the C language has a syntax for declaring and accessing arrays, this is just a thin syntactic layer on top of pointers. From that follows that array access is just pointer arithmetic, array length must be separately passed around by the programmer, and all the vulnerabilities originating in that confusion of pointers and arrays, like buffer overflows.

Consider a function that counts the number of times a value is present in an array. In C, this could be written:

#include <stdio.h>

int count(int *p, int len, int v) {
int count = 0;
while (len--) {
if (*p++ == v) {
count++;
}
}
return count;
}

int main() {
int p[5] = {0, 3, 9, 3, 3};
int c = count(p, 5, 3);
printf("value 3 is seen %d times in p\n", c);
return 0;
}


Function count has no control over the range of addresses accessed from pointer p. The critical property that len parameter is a valid length for an array of integers pointed to by parameter p rests completely with the caller of count, and count has no way to check that this is true.

To mitigate the risks associated with pointers being used for arrays, MISRA-C contains 8 rules in a section on "Pointers and arrays", which in particular forbid pointer arithmetic (Rule 18.4) or, if this Advisory rule is not followed, require pointer arithmetic to stay within bounds (Rule 18.1). But, even if we rewrite the loop in count to respect all decidable MISRA-C rules, the complete dependency of count on its caller for passing a correct value of len remains:

#include <stdio.h>

int count(int *p, int len, int v) {
int count = 0;
for (int i = 0; i < len; i++) {
if (p[i] == v) {
count++;
}
}
return count;
}

int main() {
int p[5] = {0, 3, 9, 3, 3};
int c = count(p, 5, 3);
printf("value 3 is seen %d times in p\n", c);
return 0;
}


The resulting code is more readable, but still vulnerable to incorrect values of parameter len passed by the caller of count, which violates undecidable MISRA-C Rules 18.1 (pointer arithmetic should stay within bounds) and 1.3 (no undefined behavior). Contrast this with the same function in SPARK:

package Types is type Int_Array is array (Positive range <>) of Integer; end Types;
with Types; use Types; function Count (P : Int_Array; V : Integer) return Natural is Count : Natural := 0; begin for I in P'Range loop if P (I) = V then Count := Count + 1; end if; end loop; return Count; end Count;
with Ada.Text_IO; use Ada.Text_IO; with Types; use Types; with Count; procedure Test_Count is P : Int_Array := (0, 3, 9, 3, 3); C : Integer := Count (P, 3); begin Put_Line ("value 3 is seen" & C'Img & "times in p"); end Test_Count;

Here, array parameter P contains its own length P'Length as well as its first index P'First and last index P'Last, so function Count can simply loop over the range of valid array indexes P'First .. P'Last (or P'Range for short). As a result, function Count can be verified in isolation to be free of vulnerabilities such as buffer overflows, as it does not depend on the values of parameters passed by its callers. In fact, we can go further in SPARK and show that the value returned by Count is no greater than the length of parameter P by stating this property in postcondition of Count and asking SPARK analysis to prove it:

package Types is type Int_Array is array (Positive range <>) of Integer; end Types;
with Types; use Types; function Count (P : Int_Array; V : Integer) return Natural with Post => Count'Result <= P'Length is Count : Natural := 0; begin for I in P'Range loop pragma Loop_Invariant (Count <= I - P'First); if P (I) = V then Count := Count + 1; end if; end loop; return Count; end Count;

The only help that SPARK analysis required from us is to state how Count evolves at each iteration in a loop invariant (a special kind of assertion).

### Pointers Should Be Typed¶

The C language defines a special pointer type void* that corresponds to an untyped pointer. It is legal to convert any pointer type to and from void*, which makes it a convenient replacement for templates. Consider the following code which indirectly applies assign_int to integer i and assign_float to floating-point f by calling assign on both:

#include <stdio.h>

void assign_int (int *p) {
*p = 42;
}

void assign_float (float *p) {
*p = 42.0;
}

typedef void (*assign_fun)(void *p);

void assign(assign_fun fun, void *p) {
fun(p);
}

int main() {
int i;
float f;
assign((assign_fun)&assign_int, &i);
assign((assign_fun)&assign_float, &f);
printf("i = %d; f = %f\n", i, f);
}


Variables i and f are implicitly converted to void* type as a way to apply assign to any second parameter p whose type matches the argument type of its first argument fun. The use of an untyped argument means that the responsibility for the correction of typing rests completely with programmers. Switch variables i and f in the calls to assign and you still get a compilable program without warnings, that runs and produces completely bogus output:

i = 1109917696; f = 0.000000


i = 42; f = 42.000000


It is possible to use generics in SPARK to obtain the same result in a fully typed way, where procedure Assign applies its parameter procedure Initialize to its parameter V:

generic type T is private; with procedure Initialize (V : out T); procedure Assign (V : out T);
procedure Assign (V : out T) is begin Initialize (V); end Assign;
with Ada.Text_IO; use Ada.Text_IO; with Assign; procedure Apply_Assign is procedure Assign_Int (V : out Integer) is begin V := 42; end Assign_Int; procedure Assign_Float (V : out Float) is begin V := 42.0; end Assign_Float; procedure Assign_I is new Assign (Integer, Assign_Int); procedure Assign_F is new Assign (Float, Assign_Float); I : Integer; F : Float; begin Assign_I (I); Assign_F (F); Put_Line ("I =" & I'Img & "; F =" & F'Img); end Apply_Assign;

The generic procedure Assign must be instantiated with specific values of type T and parameter procedure Initialize, and the resulting instantiated procedures apply to a unique possible type. So switching I and F here results in a compiler error.

## Enforcing Strong Typing for Scalars¶

In C, all scalar types can be converted both implicitly and explicitly to any other scalar type. The process for doing that is defined by the rules of promotion and conversion, which trick even experts. See the Preface for an example which tricked the MISRA-C committee. For another example, see this article introducing a safe library for manipulating scalars by Microsoft expert David LeBlanc. In its conclusion, the author acknowledges the inherent difficulty in understanding scalar type conversions in C, by showing an early buggy version of the code he wrote to produce the minimum signed integer:

return (T)(1 << (BitCount()-1));


The issue here is that the literal 1 on the left-hand side of the shift is an int, so on a 64-bit machine with 32-bit int and 64-bit type T, the above is shifting 32-bit value 1 by 63 bits, a case of undefined behavior producing an unexpected output with Microsoft compiler. The fix is to convert first literal 1 to T before the shift:

return (T)((T)1 << (BitCount()-1));


Although he'd asked some excellent programmers to review the code, no one found this problem. Did you?

To avoid as much as possible these issues, MISRA-C defines its own type system on top of C types, presented in the section on "The essential type model" (8 rules). It can be seen as additional typing rules, as all rules in this section are decidable, and can be decided at the scope of a single translation unit. These rules forbid in particular the two tricky cases of confusion that we mentioned above. They can be divided in three blocks of rules for:

• restricting operations on types
• restricting explicit conversions
• restricting implicit conversions

### Restricting Operations on Types¶

Apart from the application of some operations to floating-point arguments (the bitwise, mod and array access operations) which are invalid and reported by the compiler, all operations apply to all scalar types in C. MISRA-C Rule 10.1 constrains the types on which each operation is possible as follows.

#### Arithmetic Operations on Arithmetic Types¶

Ever tried to add two Booleans or an Apple and an Orange? Let's do it in C:

#include <stdbool.h>
#include <stdio.h>

int main() {
bool b1 = true;
bool b2 = false;
bool b3 = b1 + b2;

typedef enum {Apple, Orange} fruit;
fruit f1 = Apple;
fruit f2 = Orange;
fruit f3 = f1 + f2;

printf("b3 = %d; f3 = %d\n", b3, f3);

return 0;
}


No error from the compiler here. In fact, there is no undefined behavior in the above code. Variable b3 and f3 both end up with value 1. Of course it makes no sense to add up Boolean or enumerated values, which is why MISRA-C Rule 18.1 forbids the use of all arithmetic operations on Boolean and enumerated values, while forbidding most arithmetic operations on characters. That leaves the use of arithmetic operations for signed or unsigned integers as well as floating-point types.

Let's try to do the same in SPARK:

package Bad_Arith is B1 : Boolean := True; B2 : Boolean := False; B3 : Boolean := B1 + B2; type Fruit is (Apple, Orange); F1 : Fruit := Apple; F2 : Fruit := Orange; F3 : Fruit := F1 + F2; end Bad_Arith;

The compiler reports that there is no applicable operator in both cases. It is possible however to get the predecessor of a Boolean or enumerated value with Value'Pred and its successor with Value'Succ, as well as to iterate over all values of the type:

with Ada.Text_IO; use Ada.Text_IO; procedure Ok_Arith is B1 : Boolean := False; B2 : Boolean := Boolean'Succ (B1); B3 : Boolean := Boolean'Pred (B2); type Fruit is (Apple, Orange); F1 : Fruit := Apple; F2 : Fruit := Fruit'Succ (F1); F3 : Fruit := Fruit'Pred (F2); begin pragma Assert (B1 = B3); pragma Assert (F1 = F3); for B in Boolean loop Put_Line (B'Img); end loop; for F in Fruit loop Put_Line (F'Img); end loop; end Ok_Arith;

#### Modular Operation on Integers¶

Do you wonder if a false statement is a round number of true ones, or if a pineapple can be divided evenly in oranges? Again, we can ask the question in C:

#include <stdbool.h>
#include <stdio.h>

int main() {
bool b1 = true;
bool b2 = false;
bool b3 = b2 % b1;

typedef enum {Apple, Orange, Pineapple} fruit;
fruit f1 = Orange;
fruit f2 = Pineapple;
fruit f3 = f2 % f1;

printf("b3 = %d; f3 = %d\n", b3, f3);

return 0;
}


There are no compiler errors and no undefined behavior in the above code. Variable b3 and f3 both end up with value 0, showing that a false statement is indeed a round number of true ones and that a pineapple can be divided evenly in oranges. Like before, both the questions and the answers make no sense, which is why MISRA-C Rule 18.1 forbids the use of modulo operation on Boolean, character and enumerated values. That leaves the use of modulo operation for signed or unsigned integers.

Let's try to do the same in SPARK, where the modulo operator is called mod:

package Bad_Modulo is B1 : Boolean := True; B2 : Boolean := False; B3 : Boolean := B2 mod B1; type Fruit is (Apple, Orange, Pineapple); F1 : Fruit := Orange; F2 : Fruit := Pineapple; F3 : Fruit := F2 mod F1; end Bad_Modulo;

The compiler reports that there is no applicable operator in both cases.

#### No Comparison Operation on Boolean¶

Is truth greater than falsity? Probably in moral, but not necessarily in programs, where these values have symmetric roles. Yet, the C language imposes an ordering on Boolean values inherited from their identification with integers, false being the same as integer 0 and true being the same as integer 1:

#include <stdbool.h>
#include <stdio.h>

int main() {
bool ff = false <= false;
bool ft = false <= true;
bool tf = true <= false;
bool tt = true <= true;

printf("false implies false? %d\n", ff);
printf("false implies true? %d\n", ft);
printf("true implies false? %d\n", tf);
printf("true implies true? %d\n", tt);

return 0;
}


The above code shows the so-called truth table of the logical implication operator, which is paradoxically identified with the less-than-or-equal (which unfortunately resembles graphically a reverse implication arrow) on Boolean values. This is rather obscure, which is why MISRA-C Rule 18.1 forbids the use of ordering operations on Boolean values. That leaves the use of ordering operations for all other scalar types.

This is one case where SPARK adopts the same convention as C of ordering the false and true values, so the above code can be also be expressed in SPARK:

with Ada.Text_IO; use Ada.Text_IO; procedure Truth_Table is FF : Boolean := False <= False; FT : Boolean := False <= True; TF : Boolean := True <= False; TT : Boolean := True <= True; begin Put_Line ("false implies false? " & FF'Img); Put_Line ("false implies true? " & FT'Img); Put_Line ("true implies false? " & TF'Img); Put_Line ("true implies true? " & TT'Img); end Truth_Table;

#### Boolean Operations on Boolean¶

Two bee or not two bee? Let's try to C:

#include <stdbool.h>
#include <stdio.h>

int main() {
typedef enum {Ape, Bee, Cat} Animal;
bool answer = (2 * Bee) || ! (2 * Bee);
printf("two bee or not two bee? %d\n", answer);
return 0;
}


Did you guess the answer? It's 1 of course! Which is the correct logical answer to Shakespeare's existential questioning, as it reduces to A or not A which is true in classical logic.

We saw previously that MISRA-C forbids the use of the multiplication operator with an operand of enumerated type like Bee. It also forbids in Rule 18.1 the use of Boolean operations and/or/not (in C: &&, ||, !) on anything else than Boolean operands, as misused in our Shakespearian code above.

Let's try to do the same in SPARK, where the Boolean operators are called and, or, not (for the strict operators that always evaluate both operands); and then, or else (for the shortcut operators):

package Bad_Hamlet is type Animal is (Ape, Bee, Cat); Answer : Boolean := Bee or not Bee; end Bad_Hamlet;

As expected, the compiler reports that there is no applicable operator.

#### Bitwise Operations on Unsigned Integers¶

Fancy genetic engineering? Look at how one can transform a Bee into a Cat by manipulating individual genes (really, bits) of their matrix:

#include <stdbool.h>
#include <assert.h>

int main() {
typedef enum {Ape, Bee, Cat} Animal;
Animal mutant = Bee << 1;
assert (mutant == Cat);
return 0;
}


This genetic algorithm works by accessing the underlying bitwise representation of a Bee and transforming it into the underlying bitwise representation of a Cat. While very powerful, fiddling with the bitwise representation of values is best left to computations on the so-called unsigned integers as beautifully done in the well-known book Hacker's Delight. For that reason, MISRA-C Rule 18.1 forbids the use of all bitwise operations on anything else than unsigned integers.

Let's try to do the same in SPARK, where the bitwise operators are called and, or, xor, not, Shift_Left, Shift_Right, Shift_Right_Arithmetic, Rotate_Left and Rotate_Right:

package Bad_Genetics is type Animal is (Ape, Bee, Cat); function Shift_Left (A : Animal; V : Natural) return Animal with Import, Convention => Intrinsic; Mutant : Animal := Shift_Left (Bee, 1); end Bad_Genetics;

Operator Shift_Left must be declared explicitly for it to be available for a type. This is to no use here, as the compiler reports that Shift_Left cannot be used on an enumerated type like Animal. All the previously mentioned operators are available for unsigned integers only in SPARK, also called modular types.

Note that and, or, not are used both as logical operators and as bitwise operators, but there is no possible confusion between these two uses in SPARK, as logical operators apply only to Boolean, bitwise operators apply only to modular types, and there are no implicit conversions between these two types.

### Restricting Explicit Conversions¶

A simple way to bypass the restrictions of Rule 10.1 consists in explicitly converting the arguments of an operation to a type allowed by Rule 10.1. While it can make sense sometimes to cast a value from one type to another, many casts that are allowed in C make no sense in general, or are poor replacements for clearer syntax.

Consider the case of casting from any scalar type to Boolean. A better way to express (bool)x is to compare x to the null value of its type: x != 0 for integers, x != 0.0 for floats, x != \0 for characters, x != Enum where Enum is the first enumerated value of the type. Thus, MISRA-C Rule 10.5 advises to avoid casting non-Boolean values to Boolean.

Rule 10.5 also advises to avoid nonsensical casts:

• from a Boolean to any other scalar type
• from a floating-point value to an enumeration or a character
• from any scalar type to an enumeration

The rules are not symmetric, so although it is advised not to cast a float into an enum, it is allowed to cast an enum into a float. Similarly, it is advised not to cast a character into an enum, it is allowed to cast an enum into a character.

The rules in SPARK are simpler. There are no conversions between numeric types (integers, fixed-point and floating-point) and non-numeric types (Boolean, characters, enumerations). There are no conversions between different non-numeric types. Any numeric type can be converted to any other numeric type. So the rules are symmetric and restricted to numeric types, with precise rules for rounding/truncating values when needed and runtime checks that the conversion is meaningful for the given value.

### Restricting Implicit Conversions¶

We have seen that Rules 10.1 and 10.5 restrict operations on types and explicit conversions. That's not enough to avoid problematic C programs, as any program violating one of these rules can be reexpressed using only implicit type conversions. Take for example the Shakespearian code we saw in section Boolean Operations on Boolean. It can be reexpressed in a way that satisfies both Rules 10.1 and 10.5:

#include <stdbool.h>
#include <stdio.h>

int main() {
typedef enum {Ape, Bee, Cat} Animal;
int b = Bee;
bool t = 2 * b;
bool answer = t || ! t;
printf("two bee or not two bee? %d\n", answer);
return 0;
}


Here, we're implicitly converting the enumerated value Bee to an integer, and then implicitly converting the integer value 2 * b to a Boolean. Both of these are forbidden by MISRA-C Rule 10.3 stating that "The value of an expression shall not be assigned to an object with a narrower essential type or of a different essential type category".

Rule 10.1 also does not prevent arguments of an operation to be somwhat at odds, for example comparing a floating-point value and an enumerated value. Hence MISRA-C Rule 10.4 forces some type consistency between arguments, stating that "Both operands of an operator in which the usual arithmetic conversions are performed shall have the same essential type category".

In addition, MISRA-C contains 3 rules in a section on "Composite operators and expressions" to avoid common mistakes related to the combination of explicit/implicit conversions and operations.

The rules in SPARK are far simpler: there are no implicit conversions! This applies both between types of a different essential type category as MISRA-C puts it, as well as between types that are essentially the same but defined as different.

procedure Bad_Conversions is F : Float := 0.0; I : Integer := 0; type Animal is (Ape, Bee, Cat); E : Animal := Cat; B : Boolean := True; C : Character := 'a'; begin F := I; I := E; E := B; B := C; C := F; end Bad_Conversions;

The compiler reports a mismatch on every line in the above procedure. Adding explicit conversions only makes the first line valid, as SPARK only allows converting between numeric types:

procedure Bad_Conversions is F : Float := 0.0; I : Integer := 0; type Animal is (Ape, Bee, Cat); E : Animal := Cat; B : Boolean := True; C : Character := 'a'; begin F := Float (I); I := Integer (E); E := Animal (B); B := Boolean (C); C := Character (F); end Bad_Conversions;

However, it is possible to get the position of an enumerated value in the enumeration with attribute Pos which starts from value 0. This applies to user-defined enumerations like Animal above, as well as Boolean (defined as an enumeration with values False and True) and characters (defined as an enumeration with character values). Hence, the following is valid SPARK code:

procedure Ok_Conversions is F : Float := 0.0; I : Integer := 0; type Animal is (Ape, Bee, Cat); E : Animal := Cat; B : Boolean := True; C : Character := 'a'; begin F := Float (I); I := Animal'Pos (E); I := Boolean'Pos (B); I := Character'Pos (C); I := Integer (F); end Ok_Conversions;