# 1. Introduction¶

SPARK is a programming language and a set of verification tools designed to meet the needs of high-assurance software development. SPARK is based on Ada, both subsetting the language to remove features that defy verification and also extending the system of contracts by defining new Ada aspects to support modular, constructive, formal verification.

The new aspects support the analysis of incomplete programs, abstraction and refinement and facilitate deep static analysis to be performed including information-flow analysis and formal verification of an implementation against a specification.

Meaningful static analysis is possible on complete programs without the SPARK specific aspects and pragmas (for programs which are otherwise within the SPARK subset), in fact the formal verification of an implementation against a specification of a complete program is possible using only the Ada contracts. Without the SPARK specific aspects, however, analysis has to be performed on a completed program and cannot be applied constructively during its development.

The current version of SPARK, sometimes referred to as SPARK 2014, is a much larger and more flexible language than its predecessor SPARK 2005. The language can be configured to suit a number of application domains and standards, from server-class high-assurance systems to embedded, hard real-time, critical systems.

A major feature of SPARK is the support for a mixture of proof and other verification methods such as testing. This facilitates the use of unit proof in place of unit testing, for example as formalized in avionics certification standard DO-178C and its DO-333 formal methods supplement. Certain units may be formally proven and other units validated through testing.

Ada 2012 introduced executable contracts such as Pre and Post conditions and new types of expression, in particular conditional expressions and quantifiers. SPARK uses these contracts and expressions and extends them with new aspects and pragmas.

The new aspects defined for SPARK all have equivalent pragmas which allows a SPARK program to be compiled by and executed by any Ada implementation; for instance an Ada 95 compiler provided that the use of Ada 2005 and Ada 2012 specific features is avoided. The SPARK attributes Initialized and Loop_Entry can be used only if the Ada implementation supports them.

The direct use of the new aspects requires an Ada 2012 compiler which supports them in a way consistent with the definition given here in the SPARK reference manual. The GNAT implementation is one such compiler.

As with the Ada contracts, the new SPARK aspects and pragmas have executable semantics and may be executed at run time. An expression in an Ada contract or SPARK aspect or pragma is called an assertion expression and it is the ability to execute such expressions which facilitates the mix of proof and testing.

The run-time checking of assertion expressions may be suppressed by using the Ada pragma Assertion_Policy but the static analysis and proof tools always use the assertion expressions whatever the assertion policy.

## 1.1. Structure of Introduction¶

This introduction contains the following sections:

## 1.2. How to Read and Interpret this Manual¶

This RM (reference manual) is not a tutorial guide to SPARK. It is intended as a reference guide for users and implementors of the language. In this context, “implementors” includes those producing both compilers and verification tools.

This manual is written in the style and language of the Ada RM, so knowledge of Ada is assumed. Chapters 2 through 13 mirror the structure of the Ada RM. Chapters 14 onward cover all the annexes of the Ada RM. Moreover, this manual should be interpreted as an extension of the Ada RM (that is, SPARK is fully defined by this document taken together with the Ada RM).

The SPARK RM uses and introduces technical terms in its descriptions, those that are less well known or introduced are summarized in a Glossary following the sections covering the Ada annexes.

SPARK introduces a number of aspects. The language rules are written as if all the SPARK specific aspects are present but minimum requirements are placed on a tool which analyzes SPARK to be able to synthesize (from the source code) some of these aspects if they are not present. A tool may synthesize more aspects than the minimum required (see Synthesis of SPARK Aspects). An equivalent pragma is available for each of the new aspects but these are not covered explicitly in the language rules either. The pragmas used by SPARK are documented in Language-Defined Pragmas (Annex L).

Readers interested in how SPARK 2005 constructs and idioms map into SPARK should consult the appendix SPARK 2005 to SPARK 2014 Mapping Specification.

## 1.3. Method of Description¶

In expressing the aspects, pragmas, attributes and rules of SPARK, the following chapters of this document follow the notational conventions of the Ada RM (section 1.1.4).

The following sections are given for each new language feature introduced for SPARK, following the Ada RM (other than Verification Rules, which is specific to SPARK):

1. Syntax: this section gives the format of any SPARK specific syntax.

2. Legality Rules: these are rules that are enforced at compile time. A construct is legal if it obeys all of the Legality Rules.

3. Static Semantics: a definition of the compile-time effect of each construct.

4. Dynamic Semantics: a definition of the run-time effect of each construct.

5. Verification Rules: these rules define checks to be performed on the language feature that relate to static analysis rather than simple legality rules.

6. Name Resolution Rules: There are very few SPARK specific name resolution rules. Where they exist they are placed under this heading.

A section might not be present if there are no rules specific to SPARK associated with the language feature.

When presenting rules, additional text may be provided in square brackets [ ]. This text is redundant in terms of defining the rules themselves and simply provides explanatory detail.

In addition, examples of the use of the new features are given along with the language definition detail.

## 1.4. Formal Analysis¶

SPARK will be amenable to a range of formal analyses, including but not limited to the following static analysis techniques:

• Data-flow analysis, which considers the initialization of variables and the data dependencies of subprograms (which parameters and variables get read or written).

• Information-flow analysis, which also considers the coupling between the inputs and outputs of a subprogram (which input values of parameters and variables influence which output values). The term flow analysis is used to mean data-flow analysis and information-flow analysis taken together.

• Formal verification of robustness properties. In Ada terminology, this refers to the proof that certain predefined checks, such as the ones which could raise Constraint_Error, will never fail at run time and hence the corresponding exceptions will not be raised.

• Formal verification of functional properties, based on contracts expressed as preconditions, postconditions, type invariants and so on. The term formal verification is used to mean formal verification of robustness properties and formal verification of functional properties taken together.

Data and information-flow analysis is not valid and might not be possible if the legality rules of Ada and those presented in this document are not met. Similarly, a formal verification might not be possible if the legality rules are not met and may be unsound if data-flow errors are present.

### 1.4.1. Further Details on Formal Verification¶

Many Ada constructs have dynamic semantics which include a requirement that some error condition must or may1 be checked, and some exception must or may1 be raised, if the error is detected (see Ada RM 1.1.5(5-8)). For example, evaluating the name of an array component includes a check that each index value belongs to the corresponding index range of the array (see Ada RM 4.1.1(7)).

For every such run-time check a corresponding obligation to prove that the error condition cannot be true is introduced. In particular, this rule applies to the run-time checks associated with any assertion (see Ada RM (11.4.2)); the one exception to this rule is pragma Assume (see Proof Pragmas).

In addition, the generation of verification conditions is unaffected by the suppression of checks (e.g., via pragma Suppress) or the disabling of assertions (e.g., via pragma Assertion_Policy). In other words, suppressing or disabling a check does not prevent generation of its associated verification conditions. Similarly, the verification conditions generated to ensure the absence of numeric overflow for operations of a floating point type T are unaffected by the value of T’Machine_Overflows.

All such generated verification conditions must be discharged before the formal program verification phase may be considered to be complete.

Footnotes

1(1,2)

In the case of some bounded errors, performing a check (and raising an exception if the check fails) is permitted but not required.

A SPARK implementation has the option of treating any construct which would otherwise generate an unsatisfiable verification condition as illegal, even if the construct will never be executed. For example, a SPARK implementation might reject the declaration

X : Positive := 0;


in almost any context. [Roughly speaking, if it can be determined statically that a runtime check associated with some construct will inevitably fail whenever the construct is elaborated, then the implementation is allowed (but not required) to reject the construct just as if the construct violated a legality rule.] For purposes of this rule, the Ada rule that Program_Error is raised if a function “completes normally without executing a return statement” is treated as a check associated with the end of the function body’s sequence_of_statements. [This treatment gives SPARK implementations the option of imposing simpler (but more conservative) rules to ensure that the end of a function is not reachable. Strictly speaking, this rule gives SPARK implementations the option of rejecting many things that should not be rejected (e.g., “pragma Assert (False);” in an unreachable arm of a case statement); reasonable implementations will not misuse this freedom.]

Formal verification of a program may depend on properties of either the machine on which it is to be executed or on properties of the tools used to compile and build it. For example, a program might depend on the bounds of the type Standard.Long_Integer or on the implementation-dependent bounds chosen for the unconstrained base subtype associated with a declaration like “type T is range 1 .. 10;”. In such cases it must be possible to provide the needed information as explicit inputs to the formal verification process. The means by which this is accomplished is not specified as part of the SPARK language definition.

## 1.5. Executable Contracts and Mathematical Numbers¶

Contracts, in the form of assertion expressions, are executable in Ada and SPARK and have the same semantics in both. The new aspects and pragmas introduced by SPARK where they are assertion expressions are also executable. Executable contracts have a number of advantages but also a few drawbacks that SPARK to a large extent mitigates.

The Ada pragma Assertion_Policy controls whether contracts and assertion expressions in general are executed and checked at run-time. Assertion expressions are always significant in static analysis and proof and, indeed, form the basis of the specification against which the implementation is verified.

In summary, Ada in itself enables contract-based, dynamic verification of complex properties of a program. SPARK enables contract-based static deductive verification of a large subset of Ada.

### 1.5.1. The Advantages of Executable Contracts¶

The possibility of making assertions and contracts executable benefits the programmer in a number of ways:

• it gives the programmer a gentle introduction to the use of contracts, and encourages the development of assertions and code in parallel. This is natural when both are expressed in the same programming language;

• executable assertions can be enabled and checked at run time, and this gives valuable information to the user. When an assertion fails, it means that the code failed to obey desired properties (i.e., the code is erroneous), or that the intent of the code has been incorrectly expressed (i.e., the assertion is erroneous) and experience shows that both situations arise equally often. In any case, the understanding of the code and properties of the programmer are improved. This also means that users get immediate benefits from writing additional assertions and contracts, which greatly encourages the adoption of contract-based programming;

• contracts can be written and dynamically verified even when the contracts or the program are too complex for automatic proof.

Executable contracts can be less expressive than pure mathematical ones, or more difficult to write in some situations but SPARK has features to largely mitigate these issues as described in the following subsections.

### 1.5.2. Mathematical Numbers and Arithmetic¶

In Ada numeric overflow may occur when evaluating an assertion expression this adds to the complexity of writing contracts and specifications using them, for instance, the expression

Post => X = (Y + Z) / 100


might raise a run-time exception if Y is an integer and Y + Z > Integer’Last even if the entire expression is less then Integer’Last.

SPARK requires checks that have to be proven to demonstrate that an overflow cannot occur, which would not be provable in the above example. Instead, the postcondition would would have to be rewritten, perhaps as something like:

Post => X = Integer ((Long_Integer (Y) + Long_Integer (Z)) / 100)


In general, the Ada library Ada.Numerics.Big_Numbers.Big_Integers can be used so that expressions (at least for Integer types) are treated as mathematical, with no overflow and no exception raised. Using this library, the above example can be rewritten:

Post => To_Big_Integer (X) = (To_Big_Integer (Y) + To_Big_Integer (Z)) / 100


### 1.5.3. Libraries for Specification and Proof¶

It is intended that SPARK toolchains have available libraries (as packages) of common paradigms such as sets, supported by an underlying model of the library packages with an expressive specification that makes automatic proof of (executable) contracts using these libraries practical.

## 1.6. Dynamic Semantics of SPARK Programs¶

Every valid SPARK program is also a valid Ada program. However, SPARK makes use of SPARK-defined attributes, aspects, and pragmas which an Ada compiler must process consistently with their SPARK definitions in order to compile and execute a SPARK program as an Ada program; this is possible because Ada permits implementation-defined attributes, aspects, and pragmas. The dynamic semantics of SPARK and of Ada are the same, assuming appropriate Ada support for those SPARK-defined constructs. That one sentence defines the dynamic semantics of SPARK; the only other description of dynamic semantics in the SPARK language definition is in defining these SPARK-defined attributes, aspects, and pragmas.

SPARK programs that have failed their static analysis checks can still be valid Ada programs. An incorrect SPARK program with, say, flow analysis anomalies or undischarged verification conditions can still be executed as long as the Ada compiler in question finds nothing objectionable. What one gives up in this case is the formal analysis of the program, such as proof of absence of run-time errors or the static checks performed by flow analysis such as the proof that all variables are initialized before use.

SPARK may make use of certain aspects, attributes and pragmas which are not defined in the Ada reference manual. Ada explicitly permits implementations to provide implementation-defined aspects, attributes and pragmas. If a SPARK program uses one of these aspects (e.g., Global), or attributes (e.g., Initialized) then it can only be compiled and executed by an implementation which supports the construct in a way consistent with the definition given here in the SPARK reference manual.

If the equivalent pragmas are used instead of the implementation-defined aspects and if the use of implementation-defined attributes is avoided, then a SPARK program may be compiled and executed by any Ada implementation (whether or not it recognizes the SPARK pragmas). Ada specifies that unrecognized pragmas are ignored: an Ada compiler that ignores the pragma is correctly implementing the dynamic semantics of SPARK and the SPARK tools will still be able to undertake all their static checks and proofs. If an Ada compiler defines a pragma with the same name as a SPARK specific pragma but has different semantics, then the compilation or execution of the program may fail.

## 1.7. Main Program¶

There is no aspect or pragma in SPARK indicating that a subprogram is a main program. Instead it is expected that any implementation of SPARK will have its own mechanism to allow the tools to identify the main program (albeit not within the language itself).

## 1.8. SPARK Strategic Requirements¶

The following requirements give the principal goals to be met by SPARK. Some are expanded in subsequent sections within this chapter.

• The SPARK language subset shall embody the largest subset of Ada to which it is currently practical to apply automatic formal verification, in line with the goals below. However, future advances in verification research and computing power may allow for expansion of the language and the forms of verification available. See section Principal Language Restrictions for further details.

• The use of Ada preconditions, postconditions and other assertions dictates that SPARK shall have executable semantics for assertion expressions. Such expressions may be executed, proven or both. See section Executable Contracts and Mathematical Numbers for further details.

• SPARK shall provide for mixing of verification evidence generated by formal analysis [for code written in the SPARK subset] and evidence generated by testing or other traditional means [for code written outside of the core SPARK language, including legacy Ada code, or code written in the SPARK subset for which verification evidence could not be generated]. See section Combining Formal Verification and Testing for further details. Note, however, that a core goal of is to provide a language expressive enough for the whole of a program to be written in SPARK, making it potentially entirely provable largely using automatic proof tools.

• SPARK shall support constructive, modular development which allows contracts to be specified on the declaration of program units and allows analysis and verification to be performed based on these contracts as early as possible in the development lifecycle, even before the units are implemented. As units are implemented the implementation is verified against its specification given in its contract. The contracts are specified using SPARK specific aspects.

• A SPARK analysis tool is required to synthesize at least some of the SPARK specific aspects, used to specify the contract of a program unit, if a contract is not explicitly specified, for instance the Global Aspects and the Depends Aspects from the implementation of the unit if it exists. The minimum requirements are given in Synthesis of SPARK Aspects but a particular tool may provide more precise synthesis and the synthesis of more aspects. The synthesized aspect is used in the analysis of the unit if the aspect is not explicitly specified. The synthesis of SPARK specific aspects facilitates different development strategies and the analysis of pre-existing code (see section Synthesis of SPARK Aspects).

• Although a goal of SPARK is to provide a language that supports as many Ada features as practical, there is another goal which is to support good programming practice guidelines and coding standards applicable to certain domains or standards. This goal is met either by standard Ada Restrictions and Profile pragmas, or via existing tools (e.g., pragma Restriction_Warnings in GNAT, or the coding standard checker GNATcheck).

• SPARK shall allow the mixing of code written in the SPARK subset with code written in full Ada. See section In and Out of SPARK for further details.

• Many systems are not written in a single programming language. SPARK shall support the development, analysis and verification of programs which are only partly in SPARK, with other parts in another language, for instance, C. SPARK specific aspects manually specified at unit level will form the boundary interface between the SPARK and other parts of the program.

• SPARK shall support entities which do not affect the functionality of a program but may be used in the test and verification of a program. See section Adding Code for Specification and Verification.

• SPARK shall support the analysis of external communication channels, which are typically implemented using volatile variables. See section Volatile State for further details.

• The language shall offer an unambiguous semantics. In Ada terminology, this means that all erroneous and unspecified behavior shall be eliminated either by direct exclusion or by adding rules which indirectly guarantee that some implementation-dependent choice, other than the fundamental data types and constants, cannot effect the externally-visible behavior of the program. For example, Ada does not specify the order in which actual parameters are evaluated as part of a subprogram call. As a result of the SPARK rules which prevent the evaluation of an expression from having side effects, two implementations might choose different parameter evaluation orders for a given call but this difference won’t have any observable effect. [This means undefined, implementation-defined and partially-specified features may be outside of SPARK by definition, though their use could be allowed and a warning or error generated for the user. See section In and Out of SPARK for further details.] Where the possibility of ambiguity still exists it is noted, namely the reading of an invalid value from an external source and the use of Unchecked_Conversion, otherwise there are no known ambiguities in the language presented in this document.

• SPARK shall support provision of “formal analysis” as defined by the DO-333 formal methods supplement of the avionics certification standard DO-178C, which states “an analysis method can only be regarded as formal analysis if its determination of a property is sound. Sound analysis means that the method never asserts a property to be true when it is not true.” A language with unambiguous semantics is required to achieve this and additionally any other language feature that for which sound analysis is difficult or impractical will be eliminated or its use constrained to meet this goal. See section Principal Language Restrictions for further details.

## 1.9. Explaining the Strategic Requirements¶

The following sections provide expanded detail on the main strategic requirements.

### 1.9.1. Principal Language Restrictions¶

To facilitate formal analyses and verification, SPARK enforces a number of global restrictions to Ada. While these are covered in more detail in the remaining chapters of this document, the most notable restrictions are:

• Restrictions on the use of access types and values, similar in some ways to the ownership model of the programming language Rust.

• All expressions (including function calls) are free of side-effects.

• Aliasing of names is not permitted in general but the renaming of entities is permitted as there is a static relationship between the two names. In analysis all names introduced by a renaming declaration are replaced by the name of the renamed entity. This replacement is applied recursively when there are multiple renames of an entity.

• Backward goto statements are not permitted.

• The use of controlled types is not currently permitted.

• Tasks and protected objects are permitted only if the Ravenscar profile (or the Jorvik profile) is specified.

• Raising and handling of exceptions is not currently permitted (exceptions can be included in a program but proof must be used to show that they cannot be raised).

### 1.9.2. Combining Formal Verification and Testing¶

There are common reasons for combining formal verification on some part of a codebase and testing on the rest of the codebase:

1. Formal verification is only applicable to a part of the codebase. For example, it might not be possible to apply the necessary formal verification to Ada code that is not in SPARK.

2. Formal verification only gives strong enough results on a part of the codebase. This might be because the desired properties cannot be expressed formally, or because proof of these desired properties cannot be sufficiently automated.

3. Formal verification might be only cost-effective on a part of the codebase. (And it may be more cost-effective than testing on this part of the codebase.)

Since the combination of formal verification and testing cannot guarantee the same level of assurance as when formal verification alone is used, the goal when combining formal verification and testing is to reach a level of confidence at least as good as the level reached by testing alone.

Mixing of formal verification and testing requires consideration of at least the following three issues.

#### 1.9.2.1. Demarcating the Boundary between Formally Verified and Tested Code¶

Contracts on subprograms provide a natural boundary for this combination. If a subprogram is proved to respect its contract, it should be possible to call it from a tested subprogram. Conversely, formal verification of a subprogram (including absence of run-time errors and contract checking) depends on called subprograms respecting their own contracts, whether these are verified by formal verification or testing.

In cases where the code to be tested is not SPARK, then additional information may be provided in the code – possibly at the boundary – to indicate this (see section In and Out of SPARK for further details).

#### 1.9.2.2. Checks to be Performed at the Boundary¶

When a tested subprogram T calls a proved subprogram P, then the precondition of P must hold. Assurance that this is true is generated by executing the assertion that P’s precondition holds during the testing of T.

Similarly, when a proved subprogram P calls a tested subprogram T, formal verification will have shown that the precondition of T holds. Hence, testing of T must show that the postcondition of T holds by executing the corresponding assertion. This is a necessary but not necessarily sufficient condition. Dynamically, there is no check that the subprogram has not updated entities not included in the postcondition.

In general, formal verification works by imposing requirements on the callers of proved code, and these requirements should be shown to hold even when formal verification and testing are combined. Any tool set that proposes a combination of formal verification and testing for SPARK should provide a detailed process for doing so, including any necessary additional testing of proof assumptions.

#### 1.9.2.3. Conditions that Apply to the Tested Code¶

The unit of test and formal verification is a subprogram (the sequence of statements of a package body is regarded as a subprogram). There are several sources of conditions that apply to a tested subprogram:

• The need to validate a partial proof of a subprogram that calls a subprogram that is not itself proven but is only tested.

• The need to validate the assumptions on which a proof of a subprogram is based when a tested subprogram calls it.

• A tested subprogram may be flow analyzed if it is in SPARK even if it is not formally proven.

• A tested subprogram may have properties that are formally proven.

##### 1.9.2.3.1. Flow analysis of a non-proven subprogram¶

If a subprogram is in SPARK but is too complex or difficult to prove formally then it still may be flow analyzed which is a fast and efficient process. Flow analysis in the absence of proof has a number of significant benefits as the subprogram implementation is

• checked that it is in SPARK;

• checked that there are no uses of uninitialized variables;

• checked that there are no ineffective statements; and

• checked against its specified Global and Depends aspects if they exist or alternatively facilitating their synthesis. This is important because this automatically checks one of the conditions on tested subprograms which are called from proven code (see Conditions on a tested subprogram which is called from a partially proven subprogram).

##### 1.9.2.3.2. Proving properties of a tested subprogram¶

A tested subprogram which is in SPARK may have properties, such as the absence of run-time exceptions proven even though the full functionality of the subprogram is tested rather than proven. The extent to which proof is performed is controlled using pragma Assume (see Proof Pragmas).

To perform proof of absence of run-time exceptions but not the postcondition of a subprogram a pragma Assume stating the postcondition is placed immediately prior to each exit point from the subprogram (each return statement or the end of the body). Parts of the postcondition may be proved using a similar scheme.

If the proof of absence of one or more run-time exceptions is not proven automatically or takes too long to prove then pragma Assume may be used to suppress the proof of a particular check.

Pragma Assume informs the proof system that the assumed expression is always True and so the prover does not attempt to prove it. In general pragma Assume should be used with caution but it acts as a pragma Assert when the subprogram code is run. Therefore, in a subprogram that is tested it acts as an extra test.

##### 1.9.2.3.3. Conditions on a tested subprogram which is called from a partially proven subprogram¶

When a subprogram which is to be partially proven calls a tested (but not proven subprogram) then the following conditions must be met by the called subprogram:

• if it is in SPARK then it should be flow analyzed to demonstrate that the implementation satisfies the Global aspect and Depends aspects pf the subprogram if they are given, otherwise conservative approximations will be synthesized from the implementation of the subprogram;

• if it is not in SPARK then at least a Global aspect shall be specified for the subprogram. The Global aspect must truthfully represent the global variables and state abstractions known to the SPARK program (not just the calling subprogram) and specify whether each of the global items are an Input, an Output or is In_Out. The onus is on the user to show that the Global (and Depends) aspect is correct as the SPARK tools do not check this because the subprogram is not in SPARK;

• it shall not update any variable or state abstraction known to the SPARK program, directly or indirectly, apart from through an actual parameter of the subprogram or a global item listed in its Global aspect. Updating a variable or state abstraction through an object of an access type or through a subprogram call is an indirect update. Here again, if the subprogram is not in SPARK and cannot be flow analyzed, the onus is on the user to show this condition is met; and

• if it has a postcondition sufficient testing to demonstrate to a high-level of confidence that the postcondition is always True must be performed.

A tool set may provide further tools to demonstrate that the Global aspects are satisfied by a non-SPARK subprogram and possibly partially check the postcondition.

##### 1.9.2.3.4. Conditions on a tested subprogram which is calls a proven subprogram¶

A tested (but not proven) subprogram which calls a proven subprogram must satisfy the following conditions:

• if it is in SPARK then flow analysis of the tested subprogram should be performed. This demonstrates that all variables and state abstractions which are inputs to the called subprogram are initialized and that the outputs of the called subprogram are used;

• if it is not in SPARK the user must ensure that all variables and state abstractions that are inputs to the called subprogram are initialized prior to calling the subprogram. This is the responsibility of the user as the SPARK tools cannot check this as the subprogram is not in SPARK; and

• if it is in SPARK it may be possible to prove that the precondition of the called subprogram is always satisfied even if no other proof is undertaken, otherwise sufficient testing must be performed by the user to demonstrate to a high-level of confidence that the precondition of the subprogram will always be True when the subprogram is called. The proof of the called subprogram relies on its precondition evaluating to True.

### 1.9.3. Adding Code for Specification and Verification¶

Often extra entities, such as types, variables and functions may be required only for test and verification purposes. Such entities are termed ghost entities and their use is restricted so that they do not affect the functionality of the program. Complete removal of ghost entities has no functional impact on the program.

SPARK supports ghost subprograms, types, objects, and packages. Ghost subprograms may be executable or non-executable. Non-executable ghost subprograms have no implementation and can be used for the purposes of formal verification only. Such functions may have their specification defined within an external proof tool to facilitate formal verification. This specification is outside of the SPARK language and toolset and therefore cannot be checked by the tools. An incorrect definition of function may lead to an unsound proof which is of no use. Ideally any definition will be checked for soundness by the external proof tools.

If the postcondition of a function, F, can be specified in SPARK as F’Result = E, then the postcondition may be recast as the expression of an expression_function_declaration as shown below:

function F (V : T) return T1 is (E);


The default postcondition of an expression function is F’Result = E making E both the implementation and the expression defining the postcondition of the function. This is useful, particularly for ghost functions, as the expression which acts as the postcondition might not give the most efficient implementation but if the function is a ghost function this might not matter.

### 1.9.4. Synthesis of SPARK Aspects¶

SPARK supports a constructive analysis style where all program units require contracts specified by SPARK specific aspects to be provided on their declarations. Under this constructive analysis style, these contracts have to be designed and added at an early stage to assist modular analysis and verification, and then maintained by the user as a program evolves. When the body of a unit is implemented (or modified) it is checked that it conforms to its contract. However, it is mandated that a SPARK analysis tool shall be able to synthesize a conservative approximation of at least a minimum of SPARK specific aspects from the source code of a unit.

Synthesis of SPARK aspects is fundamental to the analysis of pre-existing code where no SPARK specific aspects are provided.

A SPARK analysis tool is required to be capable of synthesizing at least a basic, conservative Global Aspects, Depends Aspects, Refined_Global Aspects, Refined_Depends Aspects, Abstract_State Aspects, Refined_State Aspects, Initializes Aspects and Default_Initial_Condition Aspects from either the implementation code or from other SPARK aspects as follows:

• if a subprogram has no Depends aspect but has a Global aspect, an approximation of the Depends aspect is obtained by constructing a dependency_relation by assuming that each output is dependent on every input, where outputs are all of the parameters of mode out and in-out, plus all the global_items that have a mode_selector of Output or In_Out, and inputs are all the parameters of mode in and in-out, plus all the global_items that have a mode_selector of Input or In_Out. This is a conservative approximation;

• if a subprogram has a Depends aspect but no Global aspect then the Global aspect is determined by taking each input of the dependency_relation which is not also an output and adding this to the Global aspect with a mode_selector of Input. Each output of the dependency_relation which is not also an input is added to the Global aspect with a mode_selector of Output. Finally, any other input and output of the dependency_relation which has not been added to the Global aspect is added with a mode_selector of In_Out;

• if neither a Global or Depends aspect is present, then first the globals of a subprogram are determined from an analysis of the entire program code. This is achieved in some tool dependent way. The globals of each subprogram determined from this analysis is used to synthesize the Global aspects and then from these the Depends aspects are synthesized as described above;

• if an Abstract_State is specified on a package and a Refined_State aspect is specified in its body, then Refined_Global and Refined_Depends aspects shall be synthesized in the same way as described above. From the Refined_Global, Refined_Depends and Refined_State aspects the abstract Global and Depends shall be synthesized if they are not present.

• if no abstract state aspect is specified on a package but it contains hidden state, then each variable that makes up the hidden state has a Abstract_State synthesized to represent it. At least a crude approximation of a single state abstraction for every variable shall be provided. A Refined_State aspect shall be synthesized which shows the constituents of each state.

• if no Default_Initial_Condition is specified for a private type declaration, then the synthesized value of this aspect of the type is determined by whether the full view of the private type defines full default initialization (see SPARK RM 3.1). If it does, then the synthesized aspect value is a static Boolean_expression having the value True; if it does not, then the synthesized aspect value is a null literal.

The syntheses described above do not include all of the SPARK aspects and nor do the syntheses cover all facets of the aspects. In complex programs where extra or more precise aspects are required they might have to be specified manually.

An analysis tool may provide the synthesis of more aspects and more precise synthesis of the mandatory ones.

Some use cases where the synthesis of aspects is likely to be required are:

• Code has been developed as SPARK but not all the aspects are included on all subprograms by the developer. This is regarded as generative analysis, where the code was written with the intention that it would be analyzed.

• Code is in maintenance phase, it might or might not have all of the SPARK specific aspects. If there are aspects missing they are automatically for analysis purposes when possible. This is also regarded as generative analysis.

• Legacy code is analyzed which has no or incomplete SPARK specific aspects This is regarded as retrospective analysis, where code is being analyzed that was not originally written with analysis in mind. Legacy code will typically have a mix of SPARK and non-SPARK code (and so there is an interaction with the detail presented in section In and Out of SPARK). This leads to two additional process steps that might be necessary:

• An automatic identification of what code is in SPARK and what is not.

• Manual definition of the boundary between the SPARK and non-SPARK code by explicitly specifying accurate and truthful contracts using SPARK specific aspects on the declarations of non-SPARK program units.

### 1.9.5. In and Out of SPARK¶

There are various reasons why it may be necessary to combine SPARK and non-SPARK in the same program, such as (though not limited to):

• Use of language features that are not amenable to formal verification (and hence where formal verification will be mixed with testing).

• Use of libraries that are not written in SPARK.

• Need to analyze legacy code that was not developed as SPARK.

Hence, it must be possible within the language to indicate what parts are (intended to be) in and what parts are (intended to be) out, of SPARK.

The default is to assume none of the program text is in SPARK, although this can be overridden. A new aspect SPARK_Mode is provided, which may be applied to a unit declaration or a unit body, to indicate when a unit declaration or just its body is in SPARK and should be analyzed. If just the body is not in SPARK a SPARK compatible contract may be supplied on the declaration which facilitates the analysis of units which use the declaration. The tools cannot check that the the given contract is met by the body as it is not analyzed. The burden falls on the user to ensure that the contract represents the behavior of the body as seen by the SPARK parts of the program and – if this is not the case – the assumptions on which the analysis of the SPARK code relies may be invalidated.

In general a definition may be in SPARK but its completion need not be.

A finer grain of mixing SPARK and Ada code is also possible by justifying certain warnings and errors. Warnings may be justified at a project, library unit, unit, and individual warning level. Errors may be justifiable at the individual error level or be unsuppressible errors.

Examples of this are:

• A declaration occurring immediately within a unit might not be in, or might depend on features not in, the SPARK subset. The declaration might generate a warning or an error which may be justifiable. This does not necessarily render the whole of the program unit not in SPARK. If the declaration generates a warning, or if the error is justified, then the unit is considered to be in SPARK except for the errant declaration.

• It is the use of the entity declared by the errant declaration, for instance a call of a subprogram or the denoting of an object in an expression (generally within the statements of a body) that will result in an unsupressible error. The body of a unit causing the unsuppressible message (or declaration if this is the cause) will need to be marked as not in SPARK to prevent its future analysis.

Hence, SPARK and non-SPARK code may mix at a fine level of granularity. The following combinations may be typical:

• Package (or generic package) specification in SPARK. Package body entirely not in SPARK.

• Visible part of package (or generic package) specification in SPARK. Private part and body not in SPARK.

• Package specification in SPARK. Package body almost entirely in SPARK, with a small number of subprogram bodies not in SPARK.

• Package specification in SPARK, with all bodies imported from another language.

• Package specification contains a mixture of declarations which are in SPARK and not in SPARK. A client of the package may be in SPARK if it only references SPARK declarations; the presence of non-SPARK constructs in a referenced package specification does not by itself mean that a client is not in SPARK.

Such patterns are intended to allow for mixed-language programming, mixed-verification using different analysis tools, and mixed-verification between formal verification and more traditional testing. A condition for safely combining the results of formal verification with other verification results is that formal verification tools explicitly list the assumptions that were made to produce their results. The proof of a property may depend on the assumption of other user-specified properties (for example, preconditions and postconditions) or implicit assumptions associated with the foundation and hypothesis on which the formal verification relies (for example, initialization of inputs and outputs, or non-aliasing between parameters). When a complete program is formally verified, these assumptions are discharged by the proof tools, based on the global guarantees provided by the strict adherence to a given language subset. No such guarantees are available when only part of a program is formally verified. Thus, combining these results with other verification results depends on the verification of global and local assumptions made during formal verification.

Full details on the SPARK_Mode aspect are given in the SPARK Toolset User’s Guide (Identifying SPARK Code).

### 1.9.6. Volatile State¶

A variable or a state abstraction may be specified as external state to indicate that it represents an external communication channel, for instance, to a device or another subsystem. An external variable may be specified as volatile. A volatile state need not have the same value between two reads without an intervening update. Similarly an update of a volatile variable might not have any effect on the internal operation of a program, its only effects are external to the program. These properties require special treatment of volatile variables during flow analysis and formal verification.

SPARK follows the Ada convention that a read of a volatile variable may have an external effect as well as reading the value of the variable. SPARK extends this notion to cover updates of a volatile variable such that an update of a volatile variable may also have some other observable effect. SPARK further extends these principles to apply to state abstractions (see section External State).