Subprograms =========== Subprogram Declarations ----------------------- We distinguish the *declaration view* introduced by a ``subprogram_declaration`` from the *implementation view* introduced by a ``subprogram_body`` or an ``expression_function_declaration``. For subprograms that are not declared by a ``subprogram_declaration``, the ``subprogram_body`` or ``expression_function_declaration`` also introduces a declaration view which may be in |SPARK| even if the implementation view is not. .. index:: subprogram with side effects A *subprogram with side effects* is either a procedure, a protected entry, or a function with side effects (see :ref:`Functions With Side Effects`). A subprogram with side effects may have output parameters, write global variables, raise exceptions and not terminate. Rules are imposed in |SPARK| to ensure that the execution of a function call does not modify any variables declared outside of the function, unless it is a function with side effects. Outside of this special case, it follows as a consequence of these rules that the evaluation of any |SPARK| expression is side-effect free. .. index:: global item We also introduce the notion of a *global item*, which is a name that denotes a global object or a state abstraction (see :ref:`Abstract_State Aspects`). Global items are presented in Global aspects (see :ref:`Global Aspects`). .. index:: entire object An *entire object* is an object which is not a subcomponent of a larger containing object. More specifically, an *entire object* is an object declared by an ``object_declaration`` (as opposed to, for example, a slice or the result object of a function call) or a formal parameter of a subprogram. In particular, a component of a protected unit is not an *entire object*. .. container:: heading Static Semantics 1. The *exit* value of a global item or parameter of a subprogram is its value immediately following the call of the subprogram. 2. The *entry* value of a global item or parameter of a subprogram is its value at the call of the subprogram. .. index:: subprogram output 3. An *output* of a subprogram is a global item or parameter whose final value, or the final value of any of its reachable parts (see :ref:`Access Types`), may be updated by a successful call to the subprogram. The result of a function is also an output. A global item or parameter which is an external state with the property Async_Readers => True, and for which intermediate values are written during an execution leading to a successful call, is also an output even if the final state is the same as the initial state. (see :ref:`External State`). [On the contrary, a global item or parameter is not an output of the subprogram if it is updated only on paths that lead to a statement raising an unexpected exception or to a ``pragma Assert (statically_False)``.] .. index:: subprogram input 4. An *input* of a subprogram is a global item or parameter whose initial value (or that of any of its reachable parts - see :ref:`Access Types`) may be used in determining the exit value of an output of the subprogram. For a global item or parameter which is an external state with Async_Writers => True, each successive value read from the external state is also an input of the subprogram (see :ref:`External State`). As a special case, a global item or parameter is also an input if it is mentioned in a ``null_dependency_clause`` in the Depends aspect of the subprogram (see :ref:`Depends Aspects`). 5. An output of a subprogram is said to be *fully initialized* by a call if all parts of the output are initialized as a result of any successful execution of a call of the subprogram. In the case of a parameter X of a class-wide type T'Class, this set of "all parts" is not limited to the (statically known) parts of T. For example, if the underlying dynamic tag of X is T2'Tag, where T2 is an extension of T that declares a component C, then C would be included in the set. In this case, this set of "all parts" is not known statically. [In order to fully initialize such a parameter, it is necessary to use some form of dispatching assignment. This can be done by either a direct (class-wide) assignment to X, passing X as an actual out-mode parameter in a call where the formal parameter is of a class-wide type, or passing X as a controlling out-mode parameter in a dispatching call.] The meaning of "all parts" in the case of a parameter of a specific tagged type is determined by the applicable Extensions_Visible aspect (see :ref:`Extensions_Visible Aspects`). [A state abstraction cannot be fully initialized by initializing individual constituents unless its refinement is visible.] .. container:: heading Legality Rules 6. The declaration of a function without side effects shall not have a ``parameter_specification`` with a mode of **out** or **in out** unless it has a mode of **in out** and is the first parameter of a borrowing traversal function (see :ref:`Access Types`). This rule also applies to a ``subprogram_body`` for a function without side effects for which no explicit declaration is given. A function without side effects shall have no outputs other than its result. [A subprogram parameter of mode **in out** shall not be an output of its borrowing traversal function]. 7. A subprogram parameter of mode **in** shall not be an output of its subprogram unless the type of the parameter is an access type and the subprogram is a subprogram with side effects. .. container:: heading Verification Rules 8. At the point of a call, all inputs of the callee except for those that have relaxed initialization (see :ref:`Relaxed Initialization`) shall be fully initialized. Similarly, upon return from a call all outputs of the callee except for those that have relaxed initialization shall be fully initialized. 9. If a call propagates an exception, all global outputs of the callee and all output parameters which either have a *by reference* type or are marked as aliased shall be fully initialized when the exception is propagated except for those that have relaxed initialization. 10. If a call exits the whole program, all global outputs of the callee mentioned in the boolean expression of its aspect Program_Exit outside of a reference to the Old attribute shall be fully initialized when the program is exited except for those that have relaxed initialization. 11. A function without side effects shall always return normally. 12. A call to a ghost procedure occurring outside of a ghost context shall always return normally. .. index:: precondition, postcondition Preconditions and Postconditions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. container:: heading Legality Rules 1. The corresponding expression for an inherited Pre'Class or Post'Class of an inherited subprogram S of a tagged type T shall not call a non-inherited primitive function of type T. [The notion of corresponding expression is defined in Ada RM 6.1.1(18/4) as follows: If a Pre'Class or Post'Class aspect is specified for a primitive subprogram S of a tagged type T, or such an aspect defaults to True, then a corresponding expression also applies to the corresponding primitive subprogram S of each descendant of T.] [The rationale for this rule is that, otherwise, if the contract applicable to an inherited subprogram changes due to called subprograms in its contract being overridden, then the inherited subprogram would have to be re-verified for the derived type. This rule forbids the cases that require re-verification.] 2. The Pre aspect shall not be specified for a primitive operation of a type T at a point where T is tagged. [Pre'Class should be used instead to express preconditions.] [The rationale for this rule is that, otherwise, the combination of dynamic semantics and verification rules below would force an identical Pre'Class each time Pre is used on a dispatching operation.] 3. A subprogram_renaming_declaration shall not declare a primitive operation of a tagged type. [Consider .. code-block:: ada package Outer is type T is tagged null record; package Nested is procedure Op (X : T) with Pre => ..., Post => ... ; -- not a primitive, so Pre/Post specs are ok end Nested; procedure Renamed_Op (X : T) renames Nested.Op; -- illegal end Outer; Allowing this example in SPARK would introduce a case of a dispatching operation which is subject to a Pre (and Post) aspect specification. This rule is also intended to avoid problematic interactions between the Pre/Pre'Class/Post/Post'Class aspects of the renamed subprogram and the Pre'Class/Post'Class inheritance associated with the declaration of a primitive operation of a tagged type. Note that a dispatching subprogram can be renamed as long as the renaming does not itself declare a dispatching operation. Note also that this rule would never apply to a renaming-as-body.] .. container:: heading Verification Rules For a call on a nondispatching operation, a verification condition is introduced (as for any run-time check) to ensure that the specific precondition check associated with the statically denoted callee will succeed. Upon entry to such a subprogram, the specific preconditions of the subprogram may then be assumed. For a call (dispatching or not) on a dispatching operation, a verification condition is introduced (as for any run-time check) to ensure that the class-wide precondition check associated with the statically denoted callee will succeed. The verification condition associated with the specific precondition of a dispatching subprogram is imposed on the callee, as opposed to on callers of the subprogram. Upon entry to a subprogram, the class-wide preconditions of the subprogram may be assumed. Given this, the specific preconditions of the subprogram must be proven. The callee is responsible for discharging the verification conditions associated with any postcondition checks, class-wide or specific. The success of these checks may then be assumed by the caller. .. index:: verification condition; on dispatching operation In the case of an overriding dispatching operation whose Pre'Class attribute is explicitly specified, a verification condition is introduced to ensure that the specified Pre'Class condition is implied by the Pre'Class condition of the overridden inherited subprogram(s). Similarly, in the case of an overriding dispatching operation whose Post'Class attribute is explicitly specified, a verification condition is introduced to ensure that the specified Post'Class condition implies the Post'Class condition of the overridden inherited subprogram(s). [These verification conditions do not correspond to any run-time check. They are intended to, in effect, require users to make explicit the implicit disjunction/conjunction of class-wide preconditions/postconditions that is described in Ada RM 6.1.1.] Subprogram Contracts ~~~~~~~~~~~~~~~~~~~~ The syntax of all language-defined subprogram contracts is extended to allow splitting the contract into one or more parts associated with an assertion level (see :ref:`Pragma Assertion_Level`): .. container:: heading Syntax :: level_and_expression ::= assertion_level => boolean_expression level_and_expression_list ::= level_and_expression[, level_and_expression_list] The ``aspect_definition`` of subprogram contracts can be either a boolean expression or a ``level_and_expression_list``. In the second case, the boolean expressions are handled similarly to the boolean expression of the first case with respect to legality rules and name resolution. In order to extend Ada's support for specification of subprogram contracts (e.g., the Pre and Post) by providing more precise and/or concise contracts, the |SPARK| aspects, Global, Depends, and Contract_Cases are defined. .. container:: heading Legality Rules 1. The Global, Depends and Contract_Cases aspects may be specified for a subprogram with an ``aspect_specification``. More specifically, such aspect specifications are allowed in the same contexts as Pre or Post aspect specifications. [In particular, these aspects may be specified for a generic subprogram but not for an instance of a generic subprogram.] 2. The Global and Depends (but not Contract_Cases) aspects may be specified for an abstract subprogram. 3. The Global, Depends and Contract_Cases aspects shall not be specified for a null procedure. See section :ref:`Contract Cases` for further detail on Contract_Case aspects, section :ref:`Global Aspects` for further detail on Global aspects and section :ref:`Depends Aspects` for further detail on Depends aspects. .. container:: heading Dynamic Semantics 4. The checks associated with a contract containing assertion levels are performed in a similar fashion to regular contracts for each boolean expression. The associated assertion level is taken into account when determining whether each expression is enabled. [Intuitively, the boolean expressions of a contract containing assertion levels are joined together using a conjunction.] .. index:: Contract_Cases Contract Cases ~~~~~~~~~~~~~~ The Contract_Cases aspect provides a structured way of defining a subprogram contract using mutually exclusive subcontract cases. The final case in the Contract_Case aspect may be the keyword **others** which means that, in a specific call to the subprogram, if all the ``conditions`` are False this ``contract_case`` is taken. If an **others** ``contract_case`` is not specified, then in a specific call of the subprogram exactly one of the guarding ``conditions`` should be True. A Contract_Cases aspect may be used in conjunction with the language-defined aspects Pre and Post in which case the precondition specified by the Pre aspect is augmented with a check that exactly one of the ``conditions`` of the ``contract_case_list`` is satisfied and the postcondition specified by the Post aspect is conjoined with conditional expressions representing each of the ``contract_cases``. For example: .. code-block:: ada procedure P (...) with Pre => General_Precondition, Post => General_Postcondition, Contract_Cases => (A1 => B1, A2 => B2, ... An => Bn); is short hand for .. code-block:: ada procedure P (...) with Pre => General_Precondition and then Exactly_One_Of (A1, A2, ..., An), Post => General_Postcondition and then (if A1'Old then B1) and then (if A2'Old then B2) and then ... and then (if An'Old then Bn); where A1 .. An are Boolean expressions involving the entry values of formal parameters and global objects and B1 .. Bn are Boolean expressions that may also use the exit values of formal parameters, global objects and results. ``Exactly_One_Of(A1,A2...An)`` evaluates to True if exactly one of its inputs evaluates to True and all other of its inputs evaluate to False. The Contract_Cases aspect is specified with an ``aspect_specification`` where the ``aspect_mark`` is Contract_Cases and the ``aspect_definition`` must follow the grammar of ``contract_case_list`` given below. .. container:: heading Syntax :: contract_case_list ::= (contract_case {, contract_case}) contract_case ::= condition => consequence | others => consequence where ``consequence ::=`` *Boolean_*\ ``expression`` Similarly to other subprogram contracts, the ``aspect_specification`` of a Contract_Cases aspect can be a list of associations of an assertion level and a ``contract_case_list`` instead. In this case, each ``contract_case_list`` is handled as for simple Contract_Cases aspects, but their execution semantic is governed by the associated assertion level. .. container:: heading Legality Rules 1. A Contract_Cases aspect may have at most one **others** ``contract_case`` and if it exists it shall be the last one in the ``contract_case_list``. 2. A ``consequence`` expression is considered to be a postcondition expression for purposes of determining the legality of Old or Result ``attribute_references``. .. container:: heading Static Semantics 3. A Contract_Cases aspect is an assertion (as defined in RM 11.4.2(1.1/3)); its assertion expressions are as described below. Contract_Cases may be specified as an ``assertion_aspect_mark`` in an Assertion_Policy pragma. .. container:: heading Dynamic Semantics 4. Upon a call of a subprogram which is subject to an enabled Contract_Cases aspect, Contract_Cases checks are performed as follows: * Immediately after the specific precondition expression is evaluated and checked (or, if that check is disabled, at the point where the check would have been performed if it were enabled), all of the ``conditions`` of the ``contract_case_list`` are evaluated in textual order. A check is performed that exactly one (if no **others** ``contract_case`` is provided) or at most one (if an **others** ``contract_case`` is provided) of these ``conditions`` evaluates to True; Assertions.Assertion_Error is raised if this check fails. * Immediately after the specific postcondition expression is evaluated and checked (or, if that check is disabled, at the point where the check would have been performed if it were enabled), exactly one of the ``consequences`` is evaluated. The ``consequence`` to be evaluated is the one corresponding to the one ``condition`` whose evaluation yielded True (if such a ``condition`` exists), or to the **others** ``contract_case`` (if every ``condition``\ 's evaluation yielded False). A check is performed that the evaluation of the selected ``consequence`` evaluates to True; Assertions.Assertion_Error is raised if this check fails. 5. If an Old ``attribute_reference`` occurs within a ``consequence`` other than the ``consequence`` selected for (later) evaluation as described above, then the associated implicit constant declaration (see Ada RM 6.1.1) is not elaborated. [In particular, the prefix of the Old ``attribute_reference`` is not evaluated]. .. container:: heading Verification Rules The verification conditions associated with the Contract_Cases runtime checks performed at the beginning of a call are assigned in the same way as those associated with a specific precondition check. More specifically, the verification condition is imposed on the caller or on the callee depending on whether the subprogram in question is a dispatching operation. .. container:: heading Examples .. code-block:: ada -- This subprogram is specified using a Contract_Cases aspect. -- The prover will check that the cases are disjoint and -- cover the domain of X. procedure Incr_Threshold (X : in out Integer; Threshold : in Integer) with Contract_Cases => (X < Threshold => X = X'Old + 1, X >= Threshold => X = X'Old); -- This is the equivalent specification not using Contract_Cases. -- It is noticeably more complex and the prover is not able to check -- for disjoint cases or that the domain of X is covered. procedure Incr_Threshold_1 (X : in out Integer; Threshold : in Integer) with Pre => (X < Threshold and not (X >= Threshold)) or else (not (X < Threshold) and X >= Threshold), Post => (if X'Old < Threshold then X = X'Old + 1 elsif X'Old >= Threshold then X = X'Old); -- Contract_Cases can be used in conjunction with pre and postconditions. procedure Incr_Threshold_2 (X : in out Integer; Threshold : in Integer) with Pre => X in 0 .. Threshold, Post => X >= X'Old, Contract_Cases => (X < Threshold => X = X'Old + 1, X = Threshold => X = X'Old); .. index:: Global Global Aspects ~~~~~~~~~~~~~~ A Global aspect of a subprogram lists the global items whose values are used or affected by a call of the subprogram. The Global aspect shall only be specified for the initial declaration of a subprogram (which may be a declaration, a body or a body stub), of a protected entry, or of a task unit. The implementation of a subprogram body shall be consistent with the subprogram's Global aspect. Similarly, the implementation of an entry or task body shall be consistent with the entry or task's Global aspect. Note that a Refined_Global aspect may be applied to a subprogram body when using state abstraction; see section :ref:`Refined_Global Aspects` for further details. The Global aspect is introduced by an ``aspect_specification`` where the ``aspect_mark`` is Global and the ``aspect_definition`` must follow the grammar of ``global_specification`` For purposes of the rules concerning the Global, Depends, Refined_Global, and Refined_Depends aspects, when any of these aspects are specified for a task unit the task unit's body is considered to be the body of a nonreturning procedure and the current instance of the task unit is considered to be a formal parameter (of that notional procedure) of mode **in out**. [For example, rules which refer to the "subprogram body" refer, in the case of a task unit, to the task body.] [Because a task (even a discriminated task) is effectively a constant, one might think that a mode of **in** would make more sense. However, the current instance of a task unit is, strictly speaking, a variable; for example, it may be passed as an actual **out** or **in out** mode parameter in a call.] The Depends and Refined_Depends aspect of a task unit T need not mention this implicit parameter; an implicit specification of "T => T" is assumed, although this may be confirmed explicitly. Similarly, for purposes of the rules concerning the Global, Refined_Global, Depends, and Refined_Depends aspects as they apply to protected operations, the current instance of the enclosing protected unit is considered to be a formal parameter (of mode **in** for a protected function, of mode **in out** otherwise) and a protected entry is considered to be a protected procedure. [For example, rules which refer to the "subprogram body" refer, in the case of a protected entry, to the entry body. As another example, the Global aspect of a subprogram nested within a protected operation might name the current instance of the protected unit as a global in the same way that it might name any other parameter of the protected operation.] [Note that AI12-0169 modifies the Ada RM syntax for an ``entry_body`` to allow an optional ``aspect_specification`` immediately before the ``entry_barrier``. This is relevant for aspects such as Refined_Global and Refined_Depends.] .. container:: heading Syntax :: global_specification ::= (moded_global_list {, moded_global_list}) | global_list | null_global_specification moded_global_list ::= mode_selector => global_list global_list ::= global_item | (global_item {, global_item}) mode_selector ::= Input | Output | In_Out | Proof_In global_item ::= name null_global_specification ::= null .. container:: heading Static Semantics 1. A ``global_specification`` that is a ``global_list`` is shorthand for a ``moded_global_list`` with the ``mode_selector`` Input. 2. A ``global_item`` is *referenced* by a subprogram if: * It denotes an input or an output of the subprogram, or; * Its entry value is used to determine the value of an assertion expression within the subprogram, or; * Its entry value is used to determine the value of an assertion expression within another subprogram that is called either directly or indirectly by this subprogram. 3. A ``null_global_specification`` indicates that the subprogram does not reference any ``global_item`` directly or indirectly. 4. If a subprogram's Global aspect is not otherwise specified and either * the subprogram is a library-level subprogram declared in a library unit that is declared pure (i.e., a subprogram to which the implementation permissions of Ada RM 10.2.1 apply); or * a Pure_Function pragma applies to the subprogram then a Global aspect of *null* is implicitly specified for the subprogram. .. container:: heading Name Resolution Rules 5. A ``global_item`` shall denote an entire object or a state abstraction. [This is a name resolution rule because a ``global_item`` can unambiguously denote a state abstraction even if a function having the same fully qualified name is also present]. .. container:: heading Legality Rules 6. The Global aspect may only be specified for the initial declaration of a subprogram (which may be a declaration, a body or a body stub), of a protected entry, or of a task unit. 7. A ``global_item`` occurring in a Global aspect specification of a subprogram shall not denote a formal parameter of the subprogram. 8. A ``global_item`` shall not denote a state abstraction whose refinement is visible. [A state abstraction cannot be named within its enclosing package's body other than in its refinement. Its constituents shall be used rather than the state abstraction.] 9. Each ``mode_selector`` shall occur at most once in a single Global aspect. 10. A function without side effects shall not have a ``mode_selector`` of Output or In_Out in its Global aspect. 11. A user-defined primitive equality operation on a record type shall have a Global aspect of ``null``, unless the record type has only limited views (see :ref:`Overloading of Operators`). [This avoids the case where such a record type is a component of another composite type, whose predefined equality operation now depends on variables through the primitive equality operation on its component.] 12. The ``global_items`` in a single Global aspect specification shall denote distinct entities. Additionally, if a ``global_item`` is a state abstraction, none of its constituents shall appear as a ``global_item`` in the same Global aspect specification. 13. If a subprogram is nested within another and if the ``global_specification`` of the outer subprogram has an entity denoted by a ``global_item`` with a ``mode_specification`` of Input or the entity is a formal parameter with a mode of **in**, then a ``global_item`` of the ``global_specification`` of the inner subprogram shall not denote the same entity with a ``mode_selector`` of In_Out or Output. 14. A ``global_item`` occurring with mode Input in the Global aspect specification of a function annotated with Pure_Function aspect or pragma shall denote a constant object whose type is not an owning type (see :ref:`Access Types`). [This restriction ensures that two calls to the function with the same parameters return the same value, so that the compiler can safely apply corresponding optimizations.] .. container:: heading Dynamic Semantics There are no dynamic semantics associated with a Global aspect as it is used purely for static analysis purposes and is not executed. .. container:: heading Verification Rules 15. For a subprogram that has a ``global_specification``, an object (except a constant without variable inputs) or state abstraction that is declared outside the scope of the subprogram, shall only be referenced within its implementation if it is a ``global_item`` in the ``global_specification``. 16. A ``global_item`` shall occur in a Global aspect of a subprogram if and only if it denotes an entity (except for a constant without variable inputs) that is referenced by the subprogram. 17. Where the refinement of a state abstraction is not visible (see :ref:`State Refinement`) and a subprogram references one or more of its constituents, the constituents may be represented by a ``global_item`` that denotes the state abstraction in the ``global_specification`` of the subprogram. [The state abstraction encapsulating a constituent is known from the Part_Of indicator on the declaration of the constituent.] 18. Each entity denoted by a ``global_item`` in a ``global_specification`` of a subprogram that is an input or output of the subprogram shall satisfy the following mode specification rules [which are checked during analysis of the subprogram body]: * a ``global_item`` that denotes an input but not an output has a ``mode_selector`` of Input; * a ``global_item`` has a ``mode_selector`` of Output if: - it denotes an output but not an input, other than the use of a discriminant or an attribute related to a property, not its value, of the ``global_item`` [examples of attributes that may be used are A'Last, A'First and A'Length; examples of attributes that are dependent on the value of the object and shall not be used are X'Old and X'Loop_Entry] and - it does not have relaxed initialization (see :ref:`Relaxed Initialization`); * a ``global_item`` that denotes an output which is not an input and which has relaxed initialization may have a ``mode_selector`` of Output or In_Out; * otherwise the ``global_item`` denotes both an input and an output, and has a ``mode_selector`` of In_Out. [For purposes of determining whether an output of a subprogram shall have a ``mode_selector`` of Output or In_Out, reads of array bounds, discriminants, or tags of the output are ignored. Reads of array bounds, discriminants, or tag of any reachable part of the output are not considered either if they are constrained by their subtype. Similarly, for purposes of determining whether an entity is fully initialized as a result of any successful execution of the call, the mutable discriminants of the output itself are not considered. This implies that given an output of a discriminated type that is not known to be constrained ("known to be constrained" is defined in Ada RM 3.3), the discriminants of the output might or might not be updated by the call.] 19. An entity that is denoted by a ``global_item`` which is referenced by a subprogram but is neither an input nor an output but is only referenced directly, or indirectly in assertion expressions has a ``mode_selector`` of Proof_In. .. index:: constant with variable inputs; in Global 20. A ``global_item`` shall not denote a constant object other than a formal parameter [of an enclosing subprogram] of mode **in**, a generic formal object of mode **in**, a constant of (named or anonymous) access-to-variable type, or a *constant with variable inputs*. If a ``global_item`` denotes a generic formal object of mode **in**, then the corresponding ``global_item`` in an instance of the generic unit may denote a constant which has no variable inputs. [This can occur if the corresponding actual parameter is an expression which has no variable inputs]. Outside of the instance, such a ``global_item`` is ignored. For example, .. literalinclude:: ../../../testsuite/gnatprove/tests/RM_Examples/global_and_generics.ads :language: ada :linenos: .. literalinclude:: ../../../testsuite/gnatprove/tests/RM_Examples/global_and_generics.adb :language: ada :linenos: 21. The ``mode_selector`` of a ``global_item`` denoting a *constant with variable inputs* shall be ``Input`` or ``Proof_In``. .. index:: Constant_After_Elaboration; in Global 22. The ``mode_selector`` of a ``global_item`` denoting a variable marked as a *constant after elaboration* shall be ``Input`` or ``Proof_In`` [, to ensure that such variables are only updated directly by package elaboration code]. A subprogram or entry having such a ``global_item`` shall not be called during library unit elaboration[, to ensure only the final ("constant") value of the object is referenced]. .. container:: heading Examples .. code-block:: ada with Global => null; -- Indicates that the subprogram does not reference -- any global items. with Global => V; -- Indicates that V is an input of the subprogram. with Global => (X, Y, Z); -- X, Y and Z are inputs of the subprogram. with Global => (Input => V); -- Indicates that V is an input of the subprogram. with Global => (Input => (X, Y, Z)); -- X, Y and Z are inputs of the subprogram. with Global => (Output => (A, B, C)); -- A, B and C are outputs of -- the subprogram. with Global => (In_Out => (D, E, F)); -- D, E and F are both inputs and -- outputs of the subprogram with Global => (Proof_In => (G, H)); -- G and H are only used in -- assertion expressions within -- the subprogram with Global => (Input => (X, Y, Z), Output => (A, B, C), In_Out => (P, Q, R), Proof_In => (T, U)); -- A global aspect with all types of global specification .. index:: Depends Depends Aspects ~~~~~~~~~~~~~~~ A Depends aspect defines a *dependency relation* for a subprogram which may be given in the ``aspect_specification`` of the subprogram. A dependency relation is a sort of formal specification which specifies a simple relationship between inputs and outputs of the subprogram. It may be used with or without a postcondition. The Depends aspect shall only be specified for the initial declaration of a subprogram (which may be a declaration, a body or a body stub), of a protected entry, or of a task unit. Unlike a postcondition, the Depends aspect must be complete in the sense that every input and output of the subprogram must appear in it. A postcondition need only specify properties of particular interest. Like a postcondition, the dependency relation may be omitted from a subprogram declaration when it defaults to the conservative relation that each output depends on every input of the subprogram. A particular |SPARK| tool may synthesize a more accurate approximation from the subprogram implementation if it is present (see :ref:`Synthesis of |SPARK| Aspects`). For accurate information flow analysis the Depends aspect should be present on every subprogram. A Depends aspect for a subprogram specifies for each output every input on which it depends. The meaning of *X depends on Y* in this context is that the input value(s) of *Y* may affect: * the exit value of *X*; and * the intermediate values of *X* if it is an external state (see section :ref:`External State`), or if the subprogram is a nonreturning procedure [, possibly the notional nonreturning procedure corresponding to a task body]. This is written *X => Y*. As in UML, the entity at the tail of the arrow depends on the entity at the head of the arrow. If an output does not depend on any input this is indicated using a **null**, e.g., *X =>* **null**. An output may be self-dependent but not dependent on any other input. The shorthand notation denoting self-dependence is useful here, X =>+ **null**. Note that a Refined_Depends aspect may be applied to a subprogram body when using state abstraction; see section :ref:`Refined_Depends Aspects` for further details. See section :ref:`Global Aspects` regarding how the rules given in this section apply to protected operations and to task bodies. The Depends aspect is introduced by an ``aspect_specification`` where the ``aspect_mark`` is Depends and the ``aspect_definition`` must follow the grammar of ``dependency_relation`` given below. .. container:: heading Syntax :: dependency_relation ::= null | (dependency_clause {, dependency_clause}) dependency_clause ::= output_list =>[+] input_list | null_dependency_clause null_dependency_clause ::= null => input_list output_list ::= output | (output {, output}) input_list ::= input | (input {, input}) | null input ::= name output ::= name | function_result where ``function_result`` is a function Result ``attribute_reference``. .. container:: heading Name Resolution Rules 1. An ``input`` or ``output`` of a ``dependency_relation`` shall denote only an entire object or a state abstraction. [This is a name resolution rule because an ``input`` or ``output`` can unambiguously denote a state abstraction even if a function having the same fully qualified name is also present.] .. container:: heading Legality Rules 2. The Depends aspect shall only be specified for the initial declaration of a subprogram (which may be a declaration, a body or a body stub), of a protected entry, or of a task unit. 3. An ``input`` or ``output`` of a ``dependency_relation`` shall not denote a state abstraction whose refinement is visible [a state abstraction cannot be named within its enclosing package's body other than in its refinement]. 4. The *explicit input set* of a subprogram is the set of formal parameters of the subprogram of mode **in** and **in out** along with the entities denoted by ``global_items`` of the Global aspect of the subprogram with a ``mode_selector`` of Input and In_Out. 5. The *input set* of a subprogram is the explicit input set of the subprogram augmented with those formal parameters of mode **out** and those ``global_items`` with a ``mode_selector`` of Output having discriminants, array bounds, or a tag which can be read and whose values are not implied by the subtype of the parameter. More specifically, it includes formal parameters of mode **out** and ``global_items`` with a ``mode_selector`` of Output which are of an unconstrained array subtype, an unconstrained discriminated subtype, or a tagged type (with one exception). The exception mentioned in the previous sentence is in the case where the formal parameter is of a specific tagged type and the applicable Extensions_Visible aspect is False. In that case, the tag of the parameter cannot be read and so the fact that the parameter is tagged does not cause it to included in the subprogram's *input_set*, although it may be included for some other reason (e.g., if the parameter is of an unconstrained discriminated subtype). 6. The *output set* of a subprogram is the set of formal parameters of the subprogram of mode **in out** and **out** along with the entities denoted by ``global_items`` of the Global aspect of the subprogram with a ``mode_selector`` of In_Out and Output and (for a function) the ``function_result`` or (for a subprogram with side effects) the set of formal parameters of the subprogram of mode **in** of an access-to-variable type. 7. The entity denoted by each ``input`` of a ``dependency_relation`` of a subprogram shall be a member of the input set of the subprogram. 8. Every member of the explicit input set of a subprogram shall be denoted by at least one ``input`` of the ``dependency_relation`` of the subprogram. 9. The entity denoted by each ``output`` of a ``dependency_relation`` of a subprogram shall be a member of the output set of the subprogram. 10. Every member of the output set of a subprogram shall be denoted by exactly one ``output`` in the ``dependency_relation`` of the subprogram. 11. For the purposes of determining the legality of a Result ``attribute_reference``, a ``dependency_relation`` is considered to be a postcondition of the function to which the enclosing ``aspect_specification`` applies. 12. In a ``dependency_relation`` there can be at most one ``dependency_clause`` which is a ``null_dependency_clause`` and if it exists it shall be the last ``dependency_clause`` in the ``dependency_relation``. 13. An entity denoted by an ``input`` which is in an ``input_list`` of a ``null_dependency_clause`` shall not be denoted by an ``input`` in another ``input_list`` of the same ``dependency_relation``. 14. The ``inputs`` in a single ``input_list`` shall denote distinct entities. 15. A ``null_dependency_clause`` shall not have an ``input_list`` of **null**. .. container:: heading Static Semantics 16. A ``dependency_clause`` with a "+" symbol in the syntax ``output_list`` =>+ ``input_list`` means that each ``output`` in the ``output_list`` has a *self-dependency*, that is, it is dependent on itself. [The text (A, B, C) =>+ Z is shorthand for (A => (A, Z), B => (B, Z), C => (C, Z)).] 17. A ``dependency_clause`` of the form A =>+ A has the same meaning as A => A. [The reason for this rule is to allow the short hand: ((A, B) =>+ (A, C)) which is equivalent to (A => (A, C), B => (A, B, C)).] 18. A ``dependency_clause`` with a **null** ``input_list`` means that the final value of the entity denoted by each ``output`` in the ``output_list`` does not depend on any member of the input set of the subprogram (other than itself, if the ``output_list`` =>+ **null** self-dependency syntax is used). 19. The ``inputs`` in the ``input_list`` of a ``null_dependency_clause`` may be read by the subprogram but play no role in determining the values of any outputs of the subprogram. 20. A Depends aspect of a subprogram with a **null** ``dependency_relation`` indicates that the subprogram has no ``inputs`` or ``outputs``. [From an information flow analysis viewpoint it is a null operation (a no-op).] 21. A function without side effects without an explicit Depends aspect specification has the default ``dependency_relation`` that its result is dependent on all of its inputs. [Generally an explicit Depends aspect is not required for a function declaration.] 22. A subprogram with side effects without an explicit Depends aspect specification has a default ``dependency_relation`` that each member of its output set is dependent on every member of its input set. [This conservative approximation may be improved by analyzing the body of the subprogram if it is present.] .. container:: heading Dynamic Semantics There are no dynamic semantics associated with a Depends aspect as it is used purely for static analysis purposes and is not executed. .. container:: heading Verification Rules 23. Each entity denoted by an ``output`` given in the Depends aspect of a subprogram shall be an output in the implementation of the subprogram body and the output shall depend on all, but only, the entities denoted by the ``inputs`` given in the ``input_list`` associated with the ``output``. 24. Each output of the implementation of the subprogram body is denoted by an ``output`` in the Depends aspect of the subprogram. 25. Each input of the implementation of a subprogram body is denoted by an ``input`` of the Depends aspect of the subprogram. 26. If not all parts of an output are updated, then the updated entity is dependent on itself as the parts that are not updated have their current value preserved. [In the case of a parameter of a tagged type (specific or class-wide), see the definition of "fully initialized" for a clarification of what the phrase "all parts" means in the preceding sentence.] .. container:: heading Examples .. code-block:: ada procedure P (X, Y, Z in : Integer; Result : out Boolean) with Depends => (Result => (X, Y, Z)); -- The exit value of Result depends on the entry values of X, Y and Z procedure Q (X, Y, Z in : Integer; A, B, C, D, E : out Integer) with Depends => ((A, B) => (X, Y), C => (X, Z), D => Y, E => null); -- The exit values of A and B depend on the entry values of X and Y. -- The exit value of C depends on the entry values of X and Z. -- The exit value of D depends on the entry value of Y. -- The exit value of E does not depend on any input value. procedure R (X, Y, Z : in Integer; A, B, C, D : in out Integer) with Depends => ((A, B) =>+ (A, X, Y), C =>+ Z, D =>+ null); -- The "+" sign attached to the arrow indicates self-dependency, that is -- the exit value of A depends on the entry value of A as well as the -- entry values of X and Y. -- Similarly, the exit value of B depends on the entry value of B -- as well as the entry values of A, X and Y. -- The exit value of C depends on the entry value of C and Z. -- The exit value of D depends only on the entry value of D. procedure S with Global => (Input => (X, Y, Z), In_Out => (A, B, C, D)), Depends => ((A, B) =>+ (A, X, Y, Z), C =>+ Y, D =>+ null); -- Here globals are used rather than parameters and global items may appear -- in the Depends aspect as well as formal parameters. function F (X, Y : Integer) return Integer with Global => G, Depends => (F'Result => (G, X), null => Y); -- Depends aspects on functions are only needed for special cases like here where the -- parameter Y has no discernible effect on the result of the function. Global and Depends Aspects of Dispatching Subprograms ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Additional rules apply to the Global and Depends aspects on a dispatching subprogram, in order to ensure that the effects of dynamically calling an overriding subprogram are properly captured by the aspects of the statically denoted callee. .. container:: heading Static Semantics 1. A Global aspect specification G2 is said to be a *valid overriding* of another such specification, G1, if the following conditions are met: * each Input-mode item of G2 is an Input-mode or an In_Out-mode item of G1 or a direct or indirect constituent thereof; and * each In_Out-mode item of G2 is an In_Out-mode item of G1 or a direct or indirect constituent thereof; and * each Output-mode item of G2 is an Output-mode or In_Out-mode item of G1 or a direct or indirect constituent thereof; and * each Output-mode item of G1 which is not a state abstraction whose refinement is visible at the point of G2 is an Output-mode item of G2; and * for each Output-mode item of G1 which is a state abstraction whose refinement is visible at the point of G2, each direct or indirect constituent thereof is an Output-mode item of G2. 2. A Depends aspect specification D2 is said to be a *valid overriding* of another such specification, D1, if the set of dependencies of D2 is a subset of the dependencies of D1 or, in the case where D1 mentions a state abstraction whose refinement is visible at the point of D2, if D2 is derivable from such a subset as described in :ref:`Refined_Depends Aspects`. .. container:: heading Legality Rules 3. The Global aspect of an overriding subprogram shall be a valid overriding of the Global aspect(s) of the overridden inherited subprogram(s). 4. The Depends aspect of an overriding subprogram shall be a valid overriding of the Depends aspect(s) of the overridden inherited subprogram(s). .. index:: Extensions_Visible Extensions_Visible Aspects ~~~~~~~~~~~~~~~~~~~~~~~~~~ The Extensions_Visible aspect provides a mechanism for ensuring that "hidden" components of a formal parameter of a specific tagged type are unreferenced. For example, if a formal parameter of a specific tagged type T is converted to a class-wide type and then used as a controlling operand in a dispatching call, then the (dynamic) callee might reference components of the parameter which are declared in some extension of T. Such a use of the formal parameter could be forbidden via an Extensions_Visible aspect specification as described below. The aspect also plays a corresponding role in the analysis of callers of the subprogram. .. container:: heading Static Semantics 1. Extensions_Visible is a Boolean-valued aspect which may be specified for a noninstance subprogram or a generic subprogram. If directly specified, the aspect_definition shall be a static [Boolean] expression. The aspect is inherited by an inherited primitive subprogram. If the aspect is neither inherited nor directly specified for a subprogram, then the aspect is False, except in the case of the predefined equality operator of a type extension. In that case, the aspect value is that of the primitive [(possibly user-defined)] equality operator for the parent type. .. container:: heading Legality Rules 2. If the Extensions_Visible aspect is False for a subprogram, then certain restrictions are imposed on the use of any parameter of the subprogram which is of a specific tagged type (or of a private type whose full view is a specific tagged type). Such a parameter shall not be converted (implicitly or explicitly) to a class-wide type. Such a parameter shall not be passed as an actual parameter in a call to a subprogram whose Extensions_Visible aspect is True. These restrictions also apply to any parenthesized expression, qualified expression, or type conversion whose operand is subject to these restrictions, to any Old or Loop_Entry ``attribute_reference`` whose prefix is subject to these restrictions, to any delta aggregate whose expression is subject to these restrictions, and to any conditional expression having at least one dependent_expression which is subject to these restrictions. [A subcomponent of a parameter is not itself a parameter and is therefore not subject to these restrictions. A parameter whose type is class-wide is not subject to these restrictions. An Old or Loop_Entry ``attribute_reference`` does not itself violate these restrictions (despite the fact that (in the tagged case) each of these attributes yields a result having the same underlying dynamic tag as their prefix).] 3. A subprogram whose Extensions_Visible aspect is True shall not override an inherited primitive operation of a tagged type whose Extensions_Visible aspect is False. [The reverse is allowed.] 4. If a nonnull type extension inherits a procedure having both a False Extensions_Visible aspect and one or more controlling out-mode parameters, then the inherited procedure requires overriding. [This is because the inherited procedure would not initialize the noninherited component(s).] 5. The Extensions_Visible aspect shall not be specified for a subprogram which has no parameters of either a specific tagged type or a private type unless the subprogram is declared in an instance of a generic unit and the corresponding subprogram in the generic unit satisfies this rule. [Such an aspect specification, if allowed, would be ineffective.] 6. [These rules ensure that the value of the underlying tag (at run time) of the actual parameter of a call to a subprogram whose Extensions_Visible aspect is False will have no effect on the behavior of that call. In particular, if the actual parameter has any additional components which are not components of the type of the formal parameter, then these components are unreferenced by the execution of the call.] .. container:: heading Verification Rules 7. [|SPARK| typically requires that an actual parameter corresponding to an in mode or in out mode formal parameter in a call shall be fully initialized before the call; similarly, the callee is typically responsible for fully initializing any out-mode formal parameters before returning. For details (including interactions with relaxed initialization), see the verification rule about full initialization of subprogram inputs and outputs (which include parameters) in :ref:`Subprogram Declarations` and then :ref:`Relaxed Initialization`]. 8. In the case of a formal parameter of a specific tagged type T (or of a private type whose full view is a specific tagged type), the set of components which shall be initialized in order to meet these requirements depends on the Extensions_Visible aspect of the callee. If the aspect is False, then that set of components is the [statically known] set of nondiscriminant components of T. If the aspect is True, then this set is the set of nondiscriminant components of the specific type associated with the tag of the corresponding actual parameter. [In general, this is not statically known. This set will always include the nondiscriminant components of T, but it may also include additional components.] 9. [To put it another way, if the applicable Extensions_Visible aspect is True, then the initialization requirements (for both the caller and the callee) for a parameter of a specific tagged type T are the same as if the formal parameter's type were T'Class. If the aspect is False, then components declared in proper descendants of T need not be initialized. In the case of an out mode parameter, such initialization by the callee is not only not required, it is effectively forbidden because such an out-mode parameter could not be fully initialized without some form of dispatching (e.g., a class-wide assignment or a dispatching call in which an out-mode parameter is a controlling operand). Such a dispatching assignment will always fully initialize its controlling out-mode parameters, regardless of the Extensions_Visible aspect of the callee. An assignment statement whose target is of a class-wide type T'Class is treated, for purposes of formal verification, like a call to a procedure with two parameters of type T'Class, one of mode out and one of mode in.] 10. [In the case of an actual parameter of a call to a subprogram whose Extensions_Visible aspect is False where the corresponding formal parameter is of a specific tagged type T, these rules imply that formal verification can safely assume that any components of the actual parameter which are not components of T will be neither read nor written by the call.] .. index:: Subprogram_Variant termination; of subprogram Subprogram_Variant Aspects ~~~~~~~~~~~~~~~~~~~~~~~~~~ The aspect Subprogram_Variant may be specified for subprograms; it can be used to ensure termination of recursive subprograms in a way that is similar to how pragma Loop_Variant can be used to ensure termination of loops. .. container:: heading Syntax :: subprogram_variant_list ::= structural_subprogram_variant_item | numeric_subprogram_variant_items numeric_subprogram_variant_items ::= numeric_subprogram_variant_item {, numeric_subprogram_variant_item} numeric_subprogram_variant_item ::= change_direction => expression structural_subprogram_variant_item ::= Structural => expression change_direction ::= Increases | Decreases The aspect_definition for a Subprogram_Variant aspect_specification shall be a subprogram_variant_list. The Subprogram_Variant aspect of an inherited subprogram for a derived type is always unspecified. Two Subprogram_Variant aspects are said to be `compatible` if either both are structural subprogram variants or both are numeric subprogram variants, the lengths of the two ``numeric_subprogram_variant_items`` are equal, and corresponding pairs of the elements of the two lists agree with respect to both ``change_direction`` and the type of their respective ``expressions``. An unspecified Subprogram_Variant aspect is compatible with, and only with, another unspecified Subprogram_Variant aspect (including itself). .. index:: recursive subprograms Two subprograms are said to be `statically mutually recursive`, if they are mutually recursive taking into account only direct calls (that is, ignoring dispatching calls and calls through access-to-subprogram values). For example, if subprogram Aa calls Bb (that is, Aa statically contains a direct call to Bb), Bb calls Cc, Cc calls Dd, and Dd calls Aa, then any 2 of those 4 subprograms (e.g., Bb and Dd) are statically mutually recursive. The case of a direct recursive call is just a special case of a statically mutually recursive call; thus, it is possible [and not unusual] for a subprogram to be statically mutually recursive with itself and with no other subprogram. In some cases (described in more detail below) involving a call where the calling subprogram and the called subprogram have compatible (specified) Subprogram_Variant aspects, a runtime check (or a verification condition corresponding to such a runtime check) may be be introduced to ensure that the "variant of the call progresses". For numeric subprogram variants, this means that the values of the caller's ``expressions`` (which were saved upon entry to the caller, as will be described below) are compared in textual order with those of the callee (which are evaluated only as needed as part of the check) until either a pair of unequal values is encountered or until all pairs have been compared. In either case, a check is performed that the last pair of values to be compared satisfies the following condition: if the ``change_direction`` for the associated ``subprogram_variant_item`` is Increases (respectively, Decreases) then the expression value obtained for the call is greater (respectively, less) than the value that was saved upon entry to the caller. .. container:: heading Static Semantics 1. [Aspect Subprogram_Variant can be used to demonstrate that execution of any of a set of statically mutually recursive subprogram(s) will not result in unbounded recursion. This is accomplished by specifying expressions that will increase or decrease at each (mutually) recursive call.] 2. Subprogram_Variant is an assertion aspect [and may be used in an Assertion_Policy pragma]. Subprogram_Variant is an assertion (as defined in Ada RM 11.4.2(1.1/3)); any Subprogram_Variant runtime checking associated with a call (see below) is governed by the Subprogram_Variant assertion policy that is in effect at the point of the call. .. container:: heading Legality Rules 3. A Subprogram_Variant aspect may be specified for the same subprograms that a Pre aspect may be specified for. [This implies, for example, that the Subprogram_Variant aspect cannot be specified for an abstract subprogram.] 4. The expression of a ``numeric_subprogram_variant_item`` shall be either of a discrete type, of a subtype of ``Ada.Numerics.Big_Numbers.Big_Integers.Big_Integer``, of a subtype of ``Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer`` or of a subtype of ``SPARK.Big_Numbers.Big_Integer``. In the second and third cases the associated ``change_direction`` shall be Decreases. 5. The expression of a ``structural_subprogram_variant_item`` shall denote a formal parameter of the subprogram. 6. The Subprogram_Variant assertion policy in effect at the point of a direct recursive call (i.e., a call where the calling subprogram is the same as the callee) and at the point where the subprogram is declared shall agree. 7. For purposes of the rules given in this section (including static semantics, dynamic semantics, legality rules, and verification rules), a call to an inherited subprogram associated with a derived type is treated as if the call were replaced with the equivalent call to the corresponding primitive subprogram of the parent or progenitor type described in the "Dynamic Semantics" section of Ada RM 3.4. This notional transformation is applied repeatedly in the case of multiple levels of subprogram inheritance. .. container:: heading Dynamic Semantics 8. At the beginning of a subprogram with a specified numeric Subprogram_Variant aspect, the ``expressions`` are evaluated in textual order and their values are each saved in a constant that is implicitly declared at the beginning of the subprogram body[, in the same way as for an unconditionally evaluated Old attribute reference (see Ada RM 6.1.1)]. For every expression whose type is a subtype of ``Ada.Numerics.Big_Numbers.Big_Integers.Big_Integer``, a check is performed that it is non-negative. 9. For a direct recursive call (i.e., the calling subprogram is the same as the callee), if the subprogram variant is numeric, for every expression in the variant of the call whose type is a subtype of ``Ada.Numerics.Big_Numbers.Big_Integers.Big_Integer``, a check is performed that it is non-negative. Then, a check is made that the variant of the call progresses (as described above). If the check fails, Assertion_Error is raised. [No runtime check is performed in the case of a direct call from one subprogram to a different subprogram, even if the two subprograms are statically mutually recursive. No runtime check is performed for a dispatching call or a call through an access-to-subprogram value.] No runtime check is performed if the Subprogram_Variant assertion policy in effect at the point of the call is not Check. .. container:: heading Verification Rules 10. Statically mutually recursive subprograms shall have compatible variants. 11. A statically mutually recursive call (that is, a direct call where the caller and the callee are statically mutually recursive) where the Subprogram_Variant aspects of the two subprograms are specified shall not occur with a precondition expression, within a subtype predicate expression, within a type invariant expression, within a Default_Initial_Condition expression, within a discrete_expression of a Subprogram_Variant aspect specification, or as part of the default initialization of a type. Such a call shall also not occur inside the elaboration of a package unless the package is located within a subprogram and not within a declare block. 12. For a statically mutually recursive call to a subprogram whose numeric Subprogram_Variant aspect is specified, a verification condition is introduced to ensure that the evaluation of the ``expressions`` of the ``subprogram_variant_list`` of the callee does not a raise any exception. Then, for every expression in the variant of the called subprogram whose type is a subtype of ``Ada.Numerics.Big_Numbers.Big_Integers.Big_Integer``, a check is performed that it is non-negative. Finally, a verification condition is generated to ensure that the variant of the call progresses. This verification condition is already implicitly generated in the case where the caller and the callee are the same (a direct recursive call) as a consequence of the runtime check taking place in that case. It is also generated in the case of other mutually recursive calls, although no checks are introduced at runtime due to compiler implementation constraints. 13. For a statically mutually recursive call to a subprogram whose structural Subprogram_Variant aspect is specified, a verification condition is generated to ensure that the actual parameter corresponding to the formal parameter denoted by the ``expression`` is a path rooted either at the formal parameter of the enclosing subprogram denoted by the expression of its Subprogram_Variant aspect or at a local object of an anonymous access-to-object type ultimately borrowing or observing a part of this formal parameter, that this path corresponds to a strict subcomponent of the structure denoted by the formal parameter of the enclosing subprogram, and that no deep parts of this structure are updated before the call. [This ensures that the rule is sufficient to prove recursion termination on acyclic data structures.] Exceptional Cases ~~~~~~~~~~~~~~~~~ The aspect Exceptional_Cases may be specified for procedures and functions with side effects; it can be used to list exceptions that might be propagated by the subprogram with side effects in the context of its precondition, and associate them with a specific postcondition. The Exceptional_Cases aspect is specified with an aspect_specification where the ``aspect_mark`` is Exceptional_Cases and the ``aspect_definition`` must follow the grammar of ``exceptional_case_list`` given below. .. container:: heading Syntax :: exceptional_case_list ::= ( exceptional_case {, exceptional_case }) exceptional_case ::= exception_choice {'|' exception_choice} => consequence where ``consequence`` is a boolean expression. .. container:: heading Name Resolution Rules The boolean expression in the consequences should be resolved as regular postconditions. In particular, references to the Old attribute are allowed to occur in them. .. container:: heading Static Semantics An Exceptional_Cases aspect is an assertion (as defined in RM 11.4.2(1.1/3)); its assertion expressions are the consequences of its exceptional cases. All prefixes of references to the Old attribute in exceptional cases are expected to be evaluated at the beginning of the call regardless of whether or not the particular exception is raised. This allows to introduce constants for these prefixes at the beginning of the subprogram together with the ones introduced for the regular postcondition. .. container:: heading Dynamic Semantics Exceptional_Cases aspects are ignored for execution. .. container:: heading Legality Rules 1. Parameters of modes *out* or *in out* of the subprogram which are neither of a *by-reference* type nor marked as aliased shall only occur in the consequences of an exceptional case: * directly or indirectly in the prefix of a reference to the Old attribute, or * directly as a prefix of the Constrained, First, Last, Length, or Range attributes. References to attribute Result shall not occur in the consequences of an exceptional case. .. container:: heading Verification Rules 2. If an exception raised in a subprogram annotated with Exceptional_Cases is not handled and causes the subprogram body to complete, then a verification condition is introduced to make sure that the consequence associated to the exceptional case covering the exception evaluates to True. [Because of the verification conditions introduced when raising unexpected exceptions, there is always an exceptional case covering the propagated exception.] Program_Exit Aspects ~~~~~~~~~~~~~~~~~~~~ The aspect Program_Exit may be specified for subprograms with side effects; it can be used to indicate that a subprogram might exit the whole program, and provide a specific postcondition. The Program_Exit aspect is specified with an aspect_specification where the aspect_mark is Program_Exit and the optional aspect_definition is a boolean expression. A Program_Exit aspect with no aspect_definition is equivalent to a Program_Exit aspect with an aspect_definition of True. .. container:: heading Name Resolution Rules The boolean expression in the aspect_definition should be resolved as a postcondition. In particular, references to the Old attribute are allowed to occur in it. .. container:: heading Static Semantics A Program_Exit aspect is an assertion (as defined in RM 11.4.2(1.1/3)); its assertion expression is its boolean expression. 1. If an output of a subprogram with side effects is mentioned in the boolean expression of its aspect Program_Exit, then it shall either occur inside the prefix of a reference to the Old attribute or be a stand-alone object. .. container:: heading Dynamic Semantics Program_Exit aspects are ignored for execution. .. container:: heading Legality Rules 2. The Program_Exit aspect may only be specified for the initial declaration of a subprogram with side effects (which may be a declaration, a body or a body stub). .. container:: heading Verification Rules 3. A verification condition is introduced on calls to subprograms annotated with the Program_Exit aspect. For calls occuring directly inside subprograms also annotated with the Program_Exit aspect, it ensures that the boolean expression of the Program_Exit aspect of the caller evaluates to True if the callee exits the whole program. For other calls, it ensures that the callee does not exit the whole program. Exit Cases ~~~~~~~~~~ The aspect Exit_Cases may be specified for procedures and functions with side effects; it can be used to partition the input state into a list of cases and specify, for each case, how the subprogram is allowed to terminate (i.e. return normally, propagate an exception, or exit the whole program). The Exit_Cases aspect is specified with an ``aspect_specification`` where the ``aspect_mark`` is Exit_Cases and the ``aspect_definition`` must follow the grammar of ``exit_case_list`` given below. .. container:: heading Syntax :: EXIT_CASE_LIST ::= EXIT_CASE {, EXIT_CASE} EXIT_CASE ::= GUARD => EXIT_KIND EXIT_KIND ::= Normal_Return | Exception_Raised | (Exception_Raised => exception_name) | Program_Exit GUARD ::= Boolean_expression | OTHERS .. container:: heading Name Resolution Rules The boolean expressions in the guards should be resolved as regular preconditions. .. container:: heading Static Semantics An Exit_Cases aspect is an assertion (as defined in RM 11.4.2(1.1/3)); its assertion expressions are the guards of its exit cases. .. container:: heading Dynamic Semantics Exit_Cases aspects are ignored for execution. .. container:: heading Legality Rules 1. A guard **others**, if present, shall appear in the last exit case. 2. If all the exit cases of the Exit_Cases aspect of a subprogram are associated with Normal_Return, then the subprogram shall have either an Exceptional_Cases contract that does not contain only consequences which are known to be False at compile time or a Program_Exit contract whose postcondition is not known to be False at compile time. [A subprogram annotated with Exit_Cases shall be allowed to either propagate an exception or exit the program.] 3. All exceptions mentioned in the Exit_Cases aspect of a subprogram shall be allowed by the Exceptional_Cases contract of the subprogram, if any. 4. If the Exit_Cases aspect has at least one exit case associated with Program_Exit, then the Program_Exit contract for the subprogram, if any, shall not have a postcondition which is known to be False at compile time. .. container:: heading Verification Rules 5. If a subprogram is annotated with Exit_Cases and there are at least two exit cases whose guards are not the **others** choice, then a verification condition is introduced to make sure that all the non-**others** guards are disjoint in the context of the precondition. 6. If a subprogram annotated with Exit_Cases returns normally, then a verification condition is introduced to make sure that the exit kind of the exit case whose guard evaluates to True is Normal_Return, if there is one. 7. If an exception raised in a subprogram annotated with Exit_Cases is not handled and causes the subprogram body to complete, then a verification condition is introduced to make sure that the exit kind of the exit case whose guard evaluates to True, if there is one, is either Exception_Raised or (Exception_Raised => E), where E is resolved to the exception that is propagated. 8. If a subprogram annotated with Exit_Cases exits the whole program, then a verification condition is introduced to make sure that the exit kind of the exit case whose guard evaluates to True is Program_Exit, if there is one. Always_Terminates Aspects ~~~~~~~~~~~~~~~~~~~~~~~~~ The aspect Always_Terminates may be specified for subprograms with side effects; it can be used to provide a condition under which the subprogram shall necessarily complete (either return normally, raise an exception, or exit the whole program). This aspect may also be specified on packages to provide a default for all subprograms with side effects declared in the package or in one of its nested packages. The Always_Terminates aspect is specified with an aspect_specification where the aspect_mark is Always_Terminates and the optional aspect_definition is a boolean expression. An Always_Terminates aspect with no aspect_definition is equivalent to an Always_Terminates aspect with an aspect_definition of True. [The execution of a SPARK subprogram which does not complete necessarily runs forever. Other behaviors cannot be modeled in SPARK.] .. container:: heading Name Resolution Rules The boolean expression in the aspect_definition should be resolved as a precondition. .. container:: heading Static Semantics An Always_Terminates aspect is an assertion (as defined in RM 11.4.2(1.1/3)); its assertion expression is its boolean expression. 1. If the aspect Always_Terminates is specified for a package, it shall not have an aspect definition. 2. If the aspect Always_Terminates for a package specification or a subprogram with side effects P is not otherwise specified and P is declared directly inside a package (explicitly or implicitly) annotated with an aspect Always_Terminates then an Always_Terminates aspect of True is implicitly specified for P. .. container:: heading Dynamic Semantics Always_Terminates aspects are ignored for execution. .. container:: heading Legality Rules 3. The Always_Terminates aspect may only be specified for the initial declaration of a subprogram with side effects (which may be a declaration, a body or a body stub), or of a package specification. .. container:: heading Verification Rules 4. A verification condition is introduced on loops and calls occuring inside functions without side effects or package elaborations to make sure that they necessarily complete. 5. A verification condition is introduced on loops and calls occuring inside subprograms with side effects annotated with an Always_Terminates aspect to make sure that they necessarily complete in cases where the boolean condition mentioned in the Always_Terminates aspect evaluates to True on entry of the subprogram with side effects. Functions With Side Effects ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The aspect Side_Effects may be specified for functions; it can be used to indicate that a function should be handled like a procedure with respect to parameter modes, Global contract, exceptional contract and termination: it may have output parameters, write global variables, raise exceptions and not terminate. Such a function is called a *function with side effects*. Note that a function with side effects is also a volatile function (see section :ref:`External State`). .. container:: heading Static Semantics 1. Side_Effects is a Boolean-valued aspect which may be specified for a noninstance function or a generic function. If directly specified, the aspect_definition shall be a static [Boolean] expression. The aspect is inherited by an inherited primitive function. If the aspect is neither inherited nor directly specified for a function, then the aspect is False. .. container:: heading Legality Rules 2. [Redundant: The declaration of a function with side effects may have a ``parameter_specification`` with a mode of **out** or **in out**. This rule also applies to a ``subprogram_body`` for a function with side effects for which no explicit declaration is given.] 3. [Redundant: A function with side effects may have a ``mode_selector`` of Output or In_Out in its Global aspect.] 4. A call to a function with side effects may only occur as the [right-hand side] expression of an assignment statement or of a local object declaration witout a block. [Redundant: In particular, functions with side effects cannot be called inside assertions.] 5. A function with side effects shall not have a Pure_Function aspect or pragma. 6. A function with side effects shall not be an expression function. 7. A function with side effects shall not be a traversal function (see section :ref:`Access Types`). 8. A user-defined primitive equality operation on a record type shall not be a function with side effects, unless the record type has only limited views (see :ref:`Overloading of Operators`). [This avoids the case where such a record type is a component of another composite type, whose predefined equality operation now has side effects through the primitive equality operation on its component.] Formal Parameter Modes ---------------------- In flow analysis, particularly information flow analysis, the update of a component of composite object is treated as updating the whole of the composite object with the component set to its new value and the remaining components of the composite object with their value preserved. This means that if a formal parameter of a subprogram is a composite type and only individual components, but not all, are updated, then the mode of the formal parameter should be **in out**. In general, it is not possible to statically determine whether all elements of an array have been updated by a subprogram if individual array elements are updated. The mode of a formal parameter of an array with such updates should be **in out**. .. todo: Consider providing a way of proving that all elements of an array have been updated individually and providing a means to specify that a composite object is updated but not read by a subprogram. A formal parameter with a mode of **out** is treated as not having an entry value (apart from any discriminant or attributes of properties of the formal parameter). Hence, a subprogram cannot read a value of a formal parameter of mode **out** until the subprogram has updated it. .. container:: heading Verification Rules 1. A subprogram formal parameter of a composite type which is updated but not fully initialized by the subprogram shall have a mode of **in out**, unless it has relaxed initialization (see section :ref:`Relaxed Initialization`). 2. A subprogram formal parameter of mode **out** shall not be read by the subprogram until it has been updated by the subprogram. The use of a discriminant or an attribute related to a property, not its value, of the formal parameter is not considered to be a read of the formal parameter. [Examples of attributes that may be used are A'First, A'Last and A'Length; examples of attributes that are dependent on the value of the formal parameter and shall not be used are X'Old and X'Loop_Entry.] Subprogram Bodies ----------------- Conformance Rules ~~~~~~~~~~~~~~~~~ No extensions or restrictions. Inline Expansion of Subprograms ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ No extensions or restrictions. Subprogram Calls ---------------- No extensions or restrictions. Parameter Associations ~~~~~~~~~~~~~~~~~~~~~~ No extensions or restrictions. .. index:: aliasing Anti-Aliasing ~~~~~~~~~~~~~ An alias is a name which refers to the same object as another name. The presence of aliasing is inconsistent with the underlying flow analysis and proof models used by the tools which assume that different names represent different entities. In general, it is not possible or is difficult to deduce that two names refer to the same object and problems arise when one of the names is used to update the object (although object renaming declarations are not problematic in |SPARK|). A common place for aliasing to be introduced is through the actual parameters and between actual parameters and global variables in a call to a subprogram with side effects. Extra verification rules are given that avoid the possibility of problematic aliasing through actual parameters and global variables. Except for functions with side effects (see :ref:`Functions With Side Effects`), a function is not allowed to have side effects and cannot update an actual parameter or global variable. Therefore, such function calls cannot introduce problematic aliasing and are excluded from the anti-aliasing rules given below for calls to subprograms with side effects. .. container:: heading Static Semantics .. index:: interfering object 1. An object is said to be *interfering* if it is unsynchronized (see section :ref:`Tasks and Synchronization`) or it is synchronized only due to being *constant after elaboration* (see section :ref:`Object Declarations`). Two names that potentially overlap (see section :ref:`Access Types`) and which each denotes an interfering object are said to *potentially introduce aliasing via parameter passing*. [This definition has the effect of exempting most synchronized objects from the anti-aliasing rules given below; aliasing of most synchronized objects via parameter passing is allowed.] .. index:: immutable parameter 2. A formal parameter is said to be *immutable* if it is of mode **in** and neither of an access-to-variable type nor of an anonymous access-to-constant type. [Note that access parameters are of mode **in** too.] Otherwise, the formal parameter is said to be *mutable*. .. container:: heading Verification Rules 3. A call to a subprogram with side effects shall only pass two actual parameters which potentially introduce aliasing via parameter passing when either * both of the corresponding formal parameters are either * immutable; or * of mode **in** and of an anonymous access-to-constant type; or * at least one of the corresponding formal parameters is immutable and is of a by-copy type. [Note that this includes parameters of named access-to-constant and (named or anonymous) access-to-subprograms types. Ownership rules prevent other problematic aliasing, see section :ref:`Access Types`.] 4. If an actual parameter in a call to a subprogram with side effects and a ``global_item`` referenced by the called subprogram potentially introduce aliasing via parameter passing, then * the corresponding formal parameter shall be either * immutable; or * of mode **in** and of an anonymous access-to-constant type; and * if the ``global_item``'s mode is Output or In_Out, then the corresponding formal parameter shall be immutable and of a by-copy type. 5. A call to a function with side effects shall only pass an actual parameter which potentially introduces aliasing via parameter passing with an object referenced from the [left-hand side] name of the enclosing assignment statement, when the corresponding formal parameter is either * immutable; or * of mode **in** and of an anonymous access-to-constant type. [The rationale for this rule is that, otherwise, the result of the evaluation of the assignment statement would depend on the order of evaluation chosen by the compiler, as the object assigned to might depend on this choice.] 6. A call to a function with side effects shall not reference a ``global_item`` of mode Output or In_Out which potentially introduces aliasing via parameter passing with an object referenced from the [left-hand side] name of the enclosing assignment statement. [The rationale for this rule is the same as for the previous rule.] 7. A call to a function with side effects shall not reference the symbol ``@`` to refer to the target name of the assignment. [The rationale for this rule is the same as for the previous rule.] 8. Where one of these rules prohibits the occurrence of an object V or any of its subcomponents as an actual parameter, the following constructs are also prohibited in this context: * A type conversion whose operand is a prohibited construct; * A call to an instance of Unchecked_Conversion whose operand is a prohibited construct; * A qualified expression whose operand is a prohibited construct; * A prohibited construct enclosed in parentheses. .. container:: heading Examples .. literalinclude:: ../../../testsuite/gnatprove/tests/RM_Examples/anti_aliasing.adb :language: ada :linenos: Exception Propagation ~~~~~~~~~~~~~~~~~~~~~ .. container:: heading Verification Rules 1. A call to a procedure annotated with an aspect Exceptional_Cases (see :ref:`Exceptional Cases`) introduces an obligation to prove that potentially raised exceptions are expected as defined in :ref:`Raise Statements and Raise Expressions`. Return Statements ----------------- No extensions or restrictions. Overloading of Operators ------------------------ .. container:: heading Legality Rules 1. [A user-defined primitive equality operation on a record type shall have a Global aspect of ``null``, unless the record type has only limited views; see :ref:`Global Aspects` for the statement of this rule.] 2. [A user-defined primitive equality operation on a record type shall not be a volatile function, unless the record type has only limited views; see :ref:`External State - Variables and Types` for the statement of this rule.] 3. [A user-defined primitive equality operation on a record type shall not be a function with side effects, unless the record type has only limited views; see :ref:`Functions With Side Effects` for the statement of this rule.] 4. [A user-defined primitive equality operation on a non-ghost record type shall not be ghost, unless the record type has only limited views; see :ref:`Ghost Entities` for the statement of this rule.] Null Procedures --------------- No extensions or restrictions. .. index:: expression function Expression Functions -------------------- .. container:: heading Legality Rules 1. Contract_Cases, Global and Depends aspects may be applied to an expression function as for any other function declaration if it does not have a separate declaration. If it has a separate declaration then the aspects are applied to that. It may have refined aspects applied (see :ref:`State Refinement`). .. index:: ghost code see: Ghost; ghost code Ghost Entities -------------- Ghost entities are intended for use in discharging verification conditions and in making it easier to express assertions about a program. The essential property of ghost entities is that they have no effect on the dynamic behavior of a valid SPARK program. More specifically, if one were to take a valid SPARK program and remove all ghost entity declarations from it (considering the association of a ghost formal parameter in a generic instantiation as a declaration) and all "innermost" statements, declarations, and pragmas which refer to those declarations (replacing removed statements with null statements when syntactically required), then the resulting program might no longer be a valid SPARK program (e.g., it might no longer be possible to discharge all of the program's verification conditions) but its dynamic semantics (when viewed as an Ada program) should be unaffected by this transformation. [This transformation might affect the performance characteristics of the program (e.g., due to no longer evaluating provably true assertions), but that is not what we are talking about here. In rare cases, it might be necessary to make a small additional change after the removals (e.g., adding an Elaborate_Body pragma) in order to avoid producing a library package that no longer needs a body (see Ada RM 7.2(4))]. .. container:: heading Static Semantics 1. |SPARK| defines the representation aspect Ghost. It can be associated with either a boolean value or an assertion level (see :ref:`Pragma Assertion_Level`). Ghost is an aspect of all entities (e.g., subprograms, types, objects). An entity whose Ghost aspect is either True or an assertion level is said to be a ghost entity; terms such as "ghost function" or "ghost variable" are defined analogously (e.g., a function whose Ghost aspect is either True or an assertion level is said to be a ghost function). In addition, a subcomponent of a ghost object is a ghost object. Ghost is an assertion aspect. [This means that Ghost can be named in an Assertion_Policy pragma.] [The assertion policy applicable to the declaration of a Ghost entity may be associated either with an assertion level, if the entity has an associated assertion level, or with the Ghost assertion kind otherwise.] 2. Unless explicitly provided, the Ghost aspect of an entity declared inside of a ghost entity (e.g., within the body of a ghost subprogram) is defined to be the Ghost aspect of its enclosing entity. The Ghost aspect of an entity implicitly declared as part of the explicit declaration of a ghost entity (e.g., an implicitly declared subprogram associated with the declaration of a ghost type) is defined to be the Ghost aspect of the declared object. Unless explicitly provided, the Ghost aspect of a child of a ghost library unit is defined to be Ghost aspect of the library unit. 3. A statement or pragma is said to be a "ghost statement" if * it occurs within a ghost subprogram or package; or * it is a call to a ghost procedure; or * it is an assignment statement whose target is a ghost variable; or * it is a pragma which specifies an aspect of a ghost entity; or * it is an assertion pragma which encloses a name denoting a ghost entity. The assertion policy applicable to an assignment statement whose target is a ghost variable is the assertion policy applicable to the ghost variable at the point of assignment. The assertion policy applicable to a call to a ghost procedure is the assertion policy applicable to the ghost procedure at the point of call. Assertion pragmas and specification aspects occurring inside a disabled ghost entity or that apply to a disabled ghost entity are considered to be disabled. Otherwise, the assertion policy applicable to an assertion pragma or specification aspect may come either from its assertion level if any, or from an assertion kind (e.g., Pre for a precondition expression, Assert for the argument of an Assert pragma...). The applicable assertion policy for other ghost statements is the assertion policy applicable to the enclosing ghost subprogram or package. 4. If the assertion policy applicable to a ghost statement or the declaration of a ghost entity is Ignore, then the elaboration of that construct (at run time) has no effect, other Ada or |SPARK| rules notwithstanding. Similarly, the elaboration of the completion of a ghost entity has no effect if the assertion policy applicable to the entity's initial declaration is Ignore. [Assertion policy Ignore can be used to ensure that a compiler generates no code for ghost constructs.] Such a declaration is said to be a *disabled ghost declaration*; terms such as "disabled ghost type" and "disabled ghost subprogram" are defined analogously. 5. A ghost entity A is said to be *assertion-level-dependent* on a ghost entity B if either: * A or B does not have an associated assertion level or * both A and B have an associated assertion level and either: * the associated assertion level of A depends on the associated assertion level of B or * the associated assertion level of A cannot be enabled. [It is Static or depends on Static.] In the same way, an assertion expression or specification aspect is said to be *assertion-level-dependent* on a ghost entity if either: * the ghost entity or the assertion or aspect does not have an associated assertion level or * both the ghost entity and the assertion or aspect have an associated assertion level and either: * the assertion level of the assertion or aspect depends on the assertion level of the ghost entity or * the assertion level of the assertion cannot be enabled. [The following rules enforce that a reference to a ghost entity always occurs in a context that is assertion-level-dependent on it. This ensures that disabling or enabling an assertion level won't cause the program to stop compiling. Ghost entities and assertions without a level are exempted from this check so as not to force the use of assertion levels in user code.] Two ghost entities A and B are said to have a *matching assertion level* if A is assertion-level-dependent on B and B is assertion-level-dependent on A. .. container:: heading Legality Rules 6. The Ghost aspect may only be specified [explicitly] for the declaration of a subprogram, a generic subprogram, a type (including a partial view thereof), an object (or list of objects, in the case of an ``aspect_specification`` for an ``object_declaration`` having more than one ``defining_identifier``), a package, a generic package, or a generic formal parameter. The Ghost aspect may be specified via either an ``aspect_specification`` or via a pragma. The representation pragma Ghost takes a single argument, a name denoting one or more entities whose Ghost aspect is then specified to be True. [In particular, |SPARK| does not currently include any form of ghost components of non-ghost record types, or ghost parameters of non-ghost subprograms. |SPARK| does define ghost state abstractions, but these are described elsewhere.] 7. A Ghost aspect value of False shall not be explicitly specified except in a confirming aspect specification. [For example, a non-ghost declaration cannot occur within a ghost subprogram.] The value specified for the Ghost assertion policy in an Assertion_Policy pragma shall be either Check or Ignore. [In other words, implementation-defined assertion policy values are not permitted.] The Ghost assertion policy in effect at any point of a SPARK program shall be either Check or Ignore. 8. A ghost type or object shall not be effectively volatile. A ghost object shall not be imported or exported. [In other words, no ghost objects for which reading or writing would constitute an external effect (see Ada RM 1.1.3).] 9. A ghost primitive subprogram of a non-ghost type extension shall not override an inherited non-ghost primitive subprogram. A non-ghost primitive subprogram of a type extension shall not override an inherited ghost primitive subprogram. In addition, a ghost primitive subprogram of a type extension that overrides an inherited ghost primitive subprogram shall have the same Ghost aspect value as the overridden subprogram unless the ghost type extension is assertion-level-dependent on the overridden subprogram. In this case, the overriding subprogram shall have the same Ghost aspect value as the type extension. [A ghost subprogram may be a primitive subprogram of a non-ghost tagged type. A ghost type extension may have a non-ghost parent type or progenitor; primitive subprograms of such a type may override inherited (ghost or non-ghost) subprograms.] 10. A Ghost pragma which applies to a declaration occuring in the visible part of a package shall not occur in the private part of that package. [This rule is to ensure that the ghostliness of a visible entity can be determined without having to look into the private part of the enclosing package.] 11. If ghost entity is declared inside another ghost entity or as the child of another ghost entity, then it shall be assertion-level-dependent on its enclosing or parent ghost entity unless the declared entity is a generic instance or a renaming declaration. [This avoids enabled declarations in disabled scope.] 12. A ghost entity shall only be referenced: * from within an assertion expression that is assertion-level-dependent on it; or * from within an aspect specification [(i.e., either an ``aspect_specification`` or an aspect-specifying pragma)]; or * within the declaration or completion of a ghost entity that is assertion-level-dependent on it (e.g., from within the body of a ghost subprogram); or * within a call to a ghost procedure that is assertion-level-dependent on it; or * within an assignment statement whose target is a ghost variable that is assertion-level-dependent on it; or * within a ``with_clause`` or ``use_clause``; or * within a renaming_declaration which either renames a ghost entity or occurs within a ghost subprogram or package; or * within an actual parameter in a generic instantiation when the corresponding generic formal parameter is ghost. A ghost attribute like ``Initialized`` shall only be referenced where a ghost entity would be allowed. 13. A ghost entity shall not be referenced within an aspect specification [(including an aspect-specifying pragma)] which specifies an aspect of a non-ghost entity except in the following cases: * the reference occurs within an assertion expression that is assertion-level-dependent on it and is not a predicate expression, unless the predicate is introduced by aspect Ghost_Predicate; or * the specified aspect is either Global, Depends, Refined_Global, Refined_Depends, Initializes, or Refined_State on an entity that is assertion-level-dependent on the ghost entity. [For example, the Global aspect of a non-ghost subprogram might refer to a ghost variable.] [Predicate expressions are excluded because predicates participate in membership tests; no Assertion_Policy pragma has any effect on this participation. In the case of a Static_Predicate expression, there are also other reasons (e.g., case statements).] 14. An **out** or **in out** mode actual parameter in a call to a ghost subprogram shall be a ghost variable. In addition, the variable and the subprogram shall have matching assertion levels. 15. In a generic declaration: * the default expression (if any) for a ghost generic formal object [both of mode **in** and] of access-to-variable type shall be a ghost object with a matching assertion level [otherwise writing to a reachable part (see :ref:`Access Types`) of the ghost formal object would have an effect on a non-ghost variable]; and * the default subprogram (if any) for a ghost generic formal procedure shall be a ghost procedure with a matching assertion level [otherwise a call to the ghost formal procedure could have effects on non-ghost variables, if the default non-ghost procedure is writing to non-ghost variables]. 16. In a generic instantiation: * the actual parameter for a ghost generic formal object of mode **in out** or both of mode **in** and of access-to-variable type, shall be a ghost object with a matching assertion level [otherwise writing to a reachable part (see :ref:`Access Types`) of the ghost formal object would have an effect on a non-ghost variable]; * the actual parameter for a ghost generic formal procedure shall be a ghost procedure with a matching assertion level [otherwise a call to the ghost formal procedure could have effects on non-ghost variables, if the actual non-ghost procedure is writing to non-ghost variables]; and * the actual parameter for a ghost generic formal package shall be a ghost package with a matching assertion level [otherwise an object or a procedure in the package could lead to the problems mentions in the two previous cases]. 17. If the assertion policy applicable to the declaration of a Ghost entity is Ignore, then the assertion policy applicable to any reference to that entity shall be Ignore except if the reference occurs in an aspect specification for the aspects Global, Depends, Refined_Global, Refined_Depends, Initializes, or Refined_State. If the Ghost assertion policy in effect at the point of the declaration of a ghost variable is Check, then the assertion policy applicable to any assignment to a part of that variable shall be Check. [This includes both assignment statements and passing a ghost variable as an **out** or **in out** mode actual parameter.] 18. An Assertion_Policy pragma specifying a Ghost policy shall not occur within a ghost subprogram or package. Similarly, an Assertion_Policy pragma specifying an Assertion_Level policy shall not occur within a ghost subprogram or package associated to an assertion level which depends on this level. If a ghost entity has a completion then the assertion policies applicable to the declaration and to the completion of the entity shall be the same. [This rule applies to subprograms, packages, types, and deferred constants.] The assertion policies applicable to the declaration of an entity and to an aspect specification which applies to that entity shall be the same. 19. If the assertion policy applicable to the declaration of a Ghost entity state abstraction is Ignore, then the assertion policy applicable to the declaration of each constituent of that abstraction shall be Ignore. In addition, constituents of a ghost state abstraction shall be assertion-level-dependent of it. 20. If a tagged type is not a disabled ghost type, and if a primitive operation of the tagged type overrides an inherited operation, then the corresponding operation of the ancestor type shall be a disabled ghost subprogram if and only if the overriding subprogram is a disabled ghost subprogram. 21. A ghost type shall not have a task or protected part. A ghost object shall not be of a type which yields synchronized objects (see section :ref:`Tasks and Synchronization`). A ghost object shall not have a volatile part. A synchronized state abstraction shall not be a ghost state abstraction (see :ref:`Abstract_State Aspects`). 22. A user-defined primitive equality operation on a non-ghost record type shall not be ghost, unless the record type has only limited views (see :ref:`Overloading of Operators`). In addition, a user-defined primitive equality operation on a ghost record type shall have a matching assertion level. [This avoids the case where such a record type is a component of another non-ghost composite type, whose predefined non-ghost equality operation now calls a ghost function through the primitive equality operation on its component.] .. container:: heading Verification Rules 23. A ghost subprogram with side effects shall not have a non-ghost [global] output. In addition, [global] outputs of a ghost subprogram shall be assertion-level-dependent on the subprogram. [This ensures that a disabled ghost subprogram never modifies an enabled (ghost) state]. 24. An output of a non-ghost subprogram other than a state abstraction or a ghost global shall not depend on a ghost input. In addition, if a ghost output of a subprogram depends on one of its ghost inputs, then the output should be assertion-level-dependent on the input. [It is intended that this follows as a consequence of other rules. Although a non-ghost state abstraction output which depends on a ghost input may have a non-ghost constituent, other rules prevent such a non-ghost constituent from depending on the ghost input.] 25. A global input of a ghost subprogram with side effects shall not be effectively volatile for reading. [This rule says, in effect, that ghost procedural subprograms are subject to the same restrictions as non-ghost nonvolatile functions with respect to reading volatile objects.] A name occurring within a ghost statement shall not denote an object that is effectively volatile for reading. [In other words, a ghost statement is subject to effectively the same restrictions as a ghost subprogram with side effects.] 26. If the assertion policy applicable to the declaration of a ghost variable or ghost state abstraction is Check, then the assertion policy applicable to any call to a procedural subprogram for which that variable or state abstraction is a global output shall be Check. .. container:: heading Examples .. code-block:: ada function A_Ghost_Expr_Function (Lo, Hi : Natural) return Natural is (if Lo > Integer'Last - Hi then Lo else ((Lo + Hi) / 2)) with Pre => Lo <= Hi, Post => A_Ghost_Expr_Function'Result in Lo .. Hi, Ghost; function A_Ghost_Function (Lo, Hi : Natural) return Natural with Pre => Lo <= Hi, Post => A_Ghost_Function'Result in Lo .. Hi, Ghost; -- The body of the function is declared elsewhere. function A_Nonexecutable_Ghost_Function (Lo, Hi : Natural) return Natural with Pre => Lo <= Hi, Post => A_Nonexecutable_Ghost_Function'Result in Lo .. Hi, Ghost, Import; -- The body of the function is not declared elsewhere. .. index:: Relaxed_Initialization Initialized initialization; by proof Relaxed Initialization ---------------------- |SPARK| defines the Boolean-valued aspect Relaxed_Initialization and the related Boolean-valued ghost attribute, Initialized. Without the Relaxed_Initialization aspect, the rules that statically prevent reading an uninitialized scalar object are defined with "whole object" granularity. For example, all inputs of a subprogram are required to be fully initialized at the point of a call to the subprogram and all outputs of a subprogram are required to be fully initialized at the point of a return from the subprogram. The Relaxed_Initialization aspect, together with the Initialized attribute, provides a mechanism for safely (i.e., without introducing the possibility of improperly reading an uninitialized scalar) referencing partially initialized Inputs and Outputs. The Relaxed_Initialization aspect may be specified for a type or for a subprogram or entry, where it effectively applies to one or more of its formal parameters and the return object of a function. The prefix of an Initialized attribute reference shall denote an object. .. container:: heading Static Semantics 1. An object is said to *have relaxed initialization* if and only if * its Relaxed_Initialization aspect is True; or * the Relaxed_Initialization aspect of its type is True; or * it is a subcomponent of an object that has relaxed initialization; or * it is the return object of a function call and the Relaxed_Initialization aspect of the function's result is True; or * it is the return object of a call to a predefined concatenation operator and at least one of the operands is a name denoting an object having relaxed initialization; or * it is the result object of an aggregate having a least one component whose value is that of an object that has relaxed initialization; or * it is the result of evaluating a value conversion whose operand has relaxed initialization; or * it is the associated object of an expression (e.g., a view conversion, a qualified expression, or a conditional expression) which has at least one operative constituent (see Ada RM 4.4) which is not the expression itself and whose associated object has relaxed initialization. A type has relaxed initialization if its Relaxed_Initialization aspect is True. An expression has relaxed initialization if its evaluation yields an object that has relaxed initialization. 2. A Relaxed_Initialization aspect specification for a formal parameter of a subprogram or entry or for a function's result is expressed syntactically as an aspect_specification of the declaration of the enclosing callable entity. [This is expressed this way because Ada does not provide syntax for specifying aspects for subprogram/entry parameters, or for the result of a function.] In the following example, the parameter X1 and the result of F are specified as having relaxed initialization; the parameters X2 and X3 are not: .. code-block:: ada function F (X1 : T1; X2 : T2; X3 : T3) return T4 with Relaxed_Initialization => (X1 => True, F'Result); .. More precisely, the Relaxed_Initialization aspect for a subprogram or entry (or a generic subprogram) is specified by an ``aspect_specification`` where the ``aspect_mark`` is Relaxed_Initialization and the ``aspect_definition`` has the following grammar for ``profile_aspect_spec``: :: profile_aspect_spec ::= ( profile_spec_item {, profile_spec_item} ) profile_spec_item ::= parameter_name [=> aspect_definition] | function_name'Result [=> aspect_definition] 3. Relaxed_Initialization aspect specifications are inherited by a derived type (if the aspect is specified for the ancestor type) and by an inherited subprogram (if the aspect is specified for the corresponding primitive subprogram of the ancestor type). 4. For a prefix *X* that denotes an object which has relaxed initialization, the following attribute is defined: :: X'Initialized [It follows as a consequence of the other rules of |SPARK| that if X'Initialized is True, then for every reachable part Y of X whose type is not annotated with the Relaxed_Initialization aspect, Y belongs to its subtype.] An Initialized attribute reference is never a static expression. .. container:: heading Legality Rules 5. The following rules apply to the profile_aspect_spec of a Relaxed_Initialization aspect specification for a subprogram, a generic subprogram, or an entry. * Each parameter_name shall name a parameter of the given subprogram or entry and no parameter shall be named more than once. It is not required that every parameter be named. * Each aspect_definition within a profile_aspect_spec shall be as for a Boolean aspect. * The form of profile_spec_item that includes a Result attribute reference shall only be provided if the given subprogram or entry is a function or generic function; in that case, the prefix of the attribute reference shall denote that function or generic function. Such a Result attribute reference is allowed, other language restrictions on the use of Result attribute references notwithstanding (i.e., despite the fact that such a Result attribute reference does not occur within a postcondition expression). * A parameter or function result named in the aspect_specification shall not be of an elementary type. [It is a bounded error to pass an uninitialized scalar parameter as input for an input parameter or as output for an output parameter or function result, so there is no benefit of marking such a parameter or result as having relaxed initialization. An object of access type is always initialized.] * A Boolean value of True is implicitly specified if no aspect_definition is provided, as per Ada RM 13.1.1's rules for Boolean-valued aspects. A Boolean value of False is implicitly specified if a given parameter (or, in the case of a function or generic function, the result) is not mentioned in any profile_spec_item. 6. No part of a tagged type, or of a tagged object, shall have relaxed initialization. 7. No part of an effectively volatile type, or of an effectively volatile object, shall have relaxed initialization. 8. No part of an Unchecked_Union type shall have relaxed initialization. No part of the type of the prefix of an Initialized attribute reference shall be of an Unchecked_Union type. 9. A Relaxed_Initialization aspect specification which applies to a declaration occuring in the visible part of a package [(e.g., the declaration of a private type or of a deferred constant)] shall not occur in the private part of that package. 10. A formal parameter of a dispatching operation shall not have relaxed initialization; the result of a dispatching function shall not have relaxed initialization. 11. [Ghost attribute ``Initialized`` shall only be referenced where a ghost entity would be allowed; see :ref:`Ghost Entities` for the statement of this rule.] .. container:: heading Verification Rules 12. At the point of a read of an elementary object X that has relaxed initialization, a verification condition is introduced to ensure that X is initialized. This includes the case where X is a subcomponent of a composite object that is passed as an argument in a call to a predefined relational operator (e.g., "=" or "<"). Such a verification condition is also introduced in the case where X is a reachable part (see :ref:`Access Types`) of the [source] expression of an assignment operation and the target of the assignment does not have relaxed initialization, where X is a reachable part of an actual parameter in a call where the corresponding formal parameter is of mode **in** or **in out** and does not have relaxed initialization, upon a call whose precondition implies X'Initialized, and upon return from a call whose postcondition implies X'Initialized. [For updates to X that do not involve calls, this check that X is initialized is implemented via flow analysis and no additional annotations are required. Preconditions and postconditions that mention X'Initialized may also be used to communicate information about the initialization status of X across subprogram boundaries. These rules statically prevent any of the bounded-error or erroneous execution scenarios associated with reading an uninitialized scalar object described in Ada RM 13.9.1. It may provide useful intuition to think of a subprogram as having (roughly speaking) an implicit precondition of X'Initialized for each of its inputs X that does not have relaxed initialization and an implicit postcondition of Y'Initialized for each of its outputs Y that does not have relaxed initialization; this imprecise description ignores things like volatile objects and state abstractions. For a particular call, this notional precondition is also in effect for a given formal parameter if the corresponding actual parameter does not have relaxed initialization (even if the formal parameter does). The verification conditions described here are not needed if X does not have relaxed initialization because the more conservative whole-object-granularity rules that govern that case will ensure that X is initialized whenever it is read.] 13. For any object X, evaluation of X'Initialized includes the evaluation of any subtype predicate applying to X. In addition: * if X has a composite type, evaluation of X'Initialized includes the evaluation of Y'Initialized for every component Y of X whose type is not annotated with the Relaxed_Initialization aspect, * if X has unconstrained discriminants, evaluation of X'Initialized includes the evaluation of Y'Initialized for every discriminant Y of X, * if X has an access-to-object type, evaluation of X'Initialized includes the evaluation X.all'Initialized if X is not null and the designated type of the type of X is not annotated with the Relaxed_Initialization aspect, * if X has an elementary type, its value must have been written either explicitly or implicitly through default initialization. Discriminants of out-mode parameters and Output globals of a subprogram are considered to be initialized at the beginning of the subprogram. Other reachable parts are not.