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A simple, possibly correct LR parser for C11
Jacques-Henri Jourdan, Inria Paris, MPI-SWS
François Pottier, Inria Paris

The syntax of the C programming language is described in the C11 standard by an ambiguous context-freegrammar, accompanied with English prose that describes the concept of “scope” and indicates how certain
ambiguous code fragments should be interpreted. Based on these elements, the problem of implementing acompliant C11 parser is not entirely trivial. We review the main sources of difficulty and describe a relatively
simple solution to the problem. Our solution employs the well-known technique of combining an LALR(1)parser with a “lexical feedback” mechanism. It draws on folklore knowledge and adds several original aspects, including: a twist on lexical feedback that allows a smooth interaction with lookahead; a simplified andpowerful treatment of scopes; and a few amendments in the grammar. Although not formally verified, ourparser avoids several pitfalls that other implementations have fallen prey to. We believe that its simplicity,
its mostly-declarative nature, and its high similarity with the C11 grammar are strong informal arguments
in favor of its correctness. Our parser is accompanied with a small suite of “tricky” C11 programs. We hopethat it may serve as a reference or a starting point in the implementation of compilers and analysis tools.
CCS Concepts: •Software and its engineering → Parsers;
Additional Key Words and Phrases: Compilation; parsing; ambiguity; lexical feedback; C89; C99; C11
ACM Reference Format:
Jacques-Henri Jourdan and François Pottier. 2017. A simple, possibly correct LR parser for C11 ACM Trans.
Program. Lang. Syst. 39, 4, Article 14 (August 2017), 37 pages.
DOI: https://doi.org/10.1145/3064848

1. INTRODUCTION

This paper explains how to build a compliant C11 parser by combining: an LALR(1)automaton, produced out of a context-free grammar by an LALR(1) parser generator; alexical analyzer or “lexer”, also generated from a declarative description; and a “lexical
feedback” mechanism.
Naturally, this is by no means the only approach to parsing C11. Several other approaches are discussed in Section 4. However, this technique seems quite appealing, forat least two reasons. First, it requires comparatively little effort, as a large part of thecode is generated. Second, it makes it comparatively easy to convince oneself that theresulting parser complies with the C11 standard. Indeed, our lexer and parser together
are less than a thousand (nonblank, noncomment) lines of code, and are expressed ina mostly declarative style.
Instead of immediately delving into the low-level details of LALR(1) automata, lexical feedback, and so on, we give in Section 2 a high-level overview of the various sourcesof syntactic ambiguity in the C11 standard. As illustrations, we present a collection of“tricky” yet syntactically valid C11 program fragments. (Unless otherwise indicated,
every program fragment in the paper is syntactically valid.) This collection, which we
make available online [Jourdan and Pottier 2017], forms a small benchmark suite.
This work is supported by Agence Nationale de la Recherche, grant ANR-11-INSE-003.
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DOI: https://doi.org/10.1145/3064848
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J.-H. Jourdan and F. Pottier

It can be used to test whether a compiler appears to comply with the C11 standard,
especially as concerns the classification of identifiers.
In Section 3, we describe our solution to the problem of parsing C11. It involves atwist on lexical feedback that allows a smooth interaction with lookahead; a simplified
and powerful treatment of scopes; and amendments to the C11 grammar. It has been
implemented and is available online [Jourdan and Pottier 2017]. We believe that itcomplies with the C11 standard. We hope that it may serve as a reference or as astarting point in the implementation of compilers, analysis tools, and so on.
In what sense, if any, is our parser “correct”? In a formal sense, this claim cannot
easily be stated (let alone proven), as there is no mathematical specification of the
C11 language. The informal prose in the standard does not have unequivocal formal
meaning; in fact, we point out two ambiguities in it (see Sections 2.2.1 and 2.4). One
might wish to come up with a formal specification of the syntax of the C11 language
and prove (either on paper or with machine assistance) that our parser complies withthis specification. However, a simple, formal specification of the C11 syntax is elusive:
the shortest and simplest specification that we know of is precisely our parser itself.
As a result, our parser is not verified, and cannot formally be claimed correct. In an
experimental sense, we have evidence that it is working: a slightly extended versionof it is used in the CompCert C compiler [Leroy 2009; Leroy 2017]. Although it mightseem desirable to test it more extensively (both against real-world C11-compliant codebases and against examples of invalid code), we have not undertaken this effort.
2. CHALLENGES IN PARSING C11

To a first approximation, the syntax of the C11 programming language is describedby a context-free grammar, which appears in the C11 standard [ISO 2011, A.2]. This
grammar is unfortunately ambiguous. The ambiguity is in principle eliminated by aset of rules, expressed in plain English prose, and somewhat scattered through the
C11 standard.
In order to implement a correct parser for C11, one must understand why there isambiguity and how the rules eliminate it, or attempt to eliminate it. As we will see, a
few rules are worded in such a way that several interpretations are possible!
In the following, we present the sources of ambiguity, as well as the disambiguation
rules and their subtleties, via a series of illustrating examples. It forms a small suiteof tricky cases, which can be used as a test suite for a C11 parser.
2.1. Ambiguity in the meaning of identifiers

The most problematic source of ambiguity in the C11 grammar lies in the various rolesof identifiers. An identifier may belong to one of four name spaces [ISO 2011, 6.2.3],
namely “label names”, “tags”, “members”, and “ordinary identifiers”. Furthermore, anordinary identifier can play one of two roles: it can be viewed either as a “variable” oras a “typedef name” [ISO 2011, 6.2.1, §1]. (We use the word “variable” to mean an “object”, a “function”, or an “enumeration constant” paragraph 6.2.1, §1.) Unfortunately,
the distinction between these two roles requires contextual information. For example,
consider the following two valid code fragments:// typedef_star.c
typedef int T;
void f(void) {T * b;}// variable_star.c
int T, b;
void f(void) {T * b;}In the left-hand fragment, the function f contains a declaration of the local variable b
as a pointer to an object of type T (which has been declared as a synonym for int). On the
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other hand, in the right-hand fragment, the body of f does not contain any declaration:
it contains one statement, namely an expression statement, a multiplication of the
global variable T by the global variable b.
Thus, the manner in which one should interpret the body of f depends on the context
in which this declaration appears. In particular, its interpretation depends on whether
the identifier T denotes a variable or a typedef name. Some mechanism is therefore
needed in order to classify identifiers.
Before discussing how such a mechanism might be described and implemented(which we do in Section 3), let us recall the rules that this classification process mustobey. These rules are relatively simple, but exhibit a few subtleties (such as noncontiguous scopes; see Section 2.1.4) and interactions with other language features (suchas the “dangling else” ambiguity; see Section 2.2.2) which further complicate the problem.
2.1.1. Name spaces. As noted above, there are four name spaces of identifiers [ISO2011, 6.2.3]: label names, tags, members, and ordinary identifiers. An identifier may
play independent roles in independent name spaces. For instance, the following code
is valid:// namespaces.c
typedef int S, T, U;
struct S { int T; };union U { int x; };void f(void) {// The following uses of S, T, U are correct, and have no// effect on the visibility of S, T, U as typedef names.
struct S s = { .T = 1 };T: s.T = 2;
union U u = { 1 };goto T;// S, T and U are still typedef names:
S ss = 1; T tt = 1; U uu = 1;}

2.1.2. Visibility and scopes. A declaration introduces either new variables or new typedef names, depending on whether the typedef keyword appears among the declaration specifiers. A declaration may contain multiple declarators. A declarator declaresexactly one entity, and introduces one identifier [ISO 2011, 6.7.6, §2]. It is “visible”
within a certain region of the program text [ISO 2011, 6.2.1, §2]. Where the declarator
is visible, the declared entity can be referred to via its identifier.
Visibility begins where a declarator is complete. Visibility stops at the end of thescope that the declaration inhabits. The program text is organized in “scopes”, that is,regions that begin and end at well-defined points, such as the beginning and end of a
block (see Section 2.1.4). Scopes can overlap: more precisely, they can be nested [ISO2011, 6.2.1, §4]. A declaration of an identifier in an inner scope hides a declaration of
the same identifier in the same scope or in an outer scope. Thus, the region where adeclaration is visible is not necessarily contiguous:// local_scope.c
typedef int T;
void f(void) {T y = 1; // T is a typeif(1) {
int T;
T = 1; // T is a variable

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J.-H. Jourdan and F. Pottier}T x = 1; // T is a type again}

Both variable declarations and type declarations may appear in an inner scope. A
variable declaration can hide a type declaration, and vice-versa:// local_typedef.c
typedef int T1;
void f(void) {typedef int *T2;
T1 x1;
T2 x2;
x1 = 0;x2 = 0;}// Declaration of type T1 as int// Declaration of type T2 as pointer to int// Declaration of x1 of type T1// Declaration of x2 of type T2

A variable or typedef name becomes visible just after the completion of its declarator[ISO 2011, 6.2.1, §7]. In C terminology, a declarator is a fragment of a declaration thatconcerns a single identifier. The syntax for declaring pointers, functions, and arrays ispart of a declarator, whereas declaration specifiers (such as int and const) and optional
initializers are not. Thus, the following code is valid:// declarator_visibility.c
typedef int T, T1(T);// T is visible when declaring T1.
void f(void) {int (*T)(T x) = 0;// This declaration declares T as being a pointer to a// function taking one parameter, x, of type T, and// returning an integer. It initializes T to the null pointer.
// The declaration is valid, since in the declarator of the// parameter x, T is still a typedef name, as the declarator// of T has not yet ended.
int T1 = sizeof((int)T1);// In the initializer sizeof((int)T1), the declarator of T1 has// ended (it is constituted solely by the identifier T1), so T1// denotes a variable.
}

2.1.3. Enumeration specifiers modify the current scope. A somewhat counter-intuitive feature of enumeration specifiers is that they declare enumeration constants [ISO 2011,
6.7.2.2, §3], which are ordinary identifiers [ISO 2011, 6.2.3, §1]. This phenomenon
takes place regardless of the context in which the enumeration specifier occurs.
The newly declared enumeration constants remain visible (except where temporarily
hidden) until the end of the current scope, whatever that scope might be.
For instance, mentioning an enumeration specifier as an argument to the sizeof operator, or as part of a cast expression, declares new enumeration constants. Because an
expression does not form a scope, these constants remain visible past the end of the expression. In the following example, the typedef name T is hidden by a local declarationof T as an enumeration constant:// enum_shadows_typedef.c
typedef int T;
void f(void) {int x = (int)(enum {T})1;// T now denotes an enumeration constant,

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A simple, possibly correct LR parser for C11

14:5// and behaves syntactically like a variable:
x = (int)T;}

An enumeration constant becomes visible in the current scope just after the completion of its enumerator [ISO 2011, 6.2.1, §7]. Thus, the newly declared constant can bereferred to in the declaration of further enumeration constants and in the remainderof the current scope:// enum_constant_visibility.c
typedef int T;
void f(void) {int x;
x = (enum {T, U = T+1})1 + T;
int y = U - T;}

2.1.4. Where scopes begin and end. According to the C11 standard [ISO 2011, 6.2.1, §2],
there are three kinds of scopes: file, block, and function prototype. (The fourth kind,function scope, does not concern ordinary identifiers. In our case, it can be ignored.) For
our purposes, though, it is not necessary to keep track of the various kinds of scopes;
it suffices to know where they are opened and closed.
A “file” scope is opened at the beginning of a translation unit, and closed at the end.
The C11 standard [ISO 2011, 6.8.2, §2] states that “a compound statement is a
block”, which means that a new “block” scope must be created at the beginning of acompound statement, and closed at the end:// block_scope.c
typedef int T;
int x;
void f(void) {{ T T;
T = 1;
typedef int x;}
x = 1; // x as a type is no longer visible
T u;// T as a variable is no longer visible}

A selection statement forms a block. Furthermore, each of its immediate substatements also forms a block [ISO 2011, 6.8.4, §3]:// if_scopes.c
typedef int T, U;
int x;
void f(void) {if(sizeof(enum {T}))// The declaration of T as an enumeration constant is// visible in both branches:
x = sizeof(enum {U}) + T;
else {// Here, the declaration of U as an enumeration constant// is no longer visible, but that of T still is.
U u = (int)T;}
switch(sizeof(enum {U})) x = U;// Here, T and U are typedef names again:

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J.-H. Jourdan and F. Pottier
T t; U u;}

The same rule applies to iteration statements [ISO 2011, 6.8.5, §5]:// loop_scopes.c
typedef int T, U;
int x;
void f(void) {for(int T = 0; sizeof(enum {U}); ) x = U+T;
for(sizeof(enum {U}); ; ) x = U + sizeof(enum {T});while(sizeof(enum {U})) x = U;// A declaration in the body of a do ... while loop// is not visible in the loop condition.
do x = sizeof(enum {U}) + U;
while((U)1 + sizeof(enum {U}));// The above declarations of T and U took place in inner scopes// and are no longer visible.
T u3; U u4;}

On the other hand, expression statements, return statements, and labelled statements do not give rise to new scopes:// no_local_scope.c
typedef int T, U, V;
int x;
int f(void) {x = sizeof(enum {T});label: x = sizeof(enum {U});return sizeof(enum {V});// T, U and V now denote enumeration constants:
x = T + U + V;}

The parameter list of a function prototype gives rise to a new “function prototype”
scope, which must be opened at the beginning of the parameter list and closed at theend of the parameter list. Thus, a name introduced somewhere in the parameter list
is visible in the remainder of the parameter list and is no longer visible after theparameter list ends. We emphasize that such a name can be either a formal parameteror an enumeration constant that appears in the type of a formal parameter. In thefollowing example, the names introduced by the parameter list of f are T, U, y, x:// function_parameter_scope.c
typedef long T, U;
enum {V} (*f(T T, enum {U} y, int x[T+U]))(T t);// The above declares a function f of type:// (long, enum{U}, ptr(int)) -> ptr (long -> enum{V})T x[(U)V+1]; // T and U again denote types; V remains visible

The parameter list of a function definition gives rise to a new “block” scope, whichmust be opened at the beginning of the parameter list and closed at the end of the function body. Indeed, the C11 standard [ISO 2011, 6.2.1, §4] prescribes: “If the declarator
or type specifier that declares the identifier appears [...] within the list of parameter
declarations in a function definition, the identifier has block scope, which terminates atthe end of the associated block.” Thus, in the following example, which begins like theprevious one, the scope of the names T, U, y, x, which are introduced in the parameter
list of f, includes the function body:
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14:7// function_parameter_scope_extends.c
typedef long T, U;
enum {V} (*f(T T, enum {U} y, int x[T+U]))(T t) {// The last T on the previous line denotes a type!
// Here, V, T, U, y, x denote variables:
long l = T+U+V+x[0]+y;
return 0;}

This example is particularly challenging. It shows that a scope need not be contiguous. Indeed, the block scope created at the beginning of the parameter list
(T T, enum {U} y, int x[T+U]) encompasses this parameter list as well as the function
body, but does not include the rest of the declarator of f. In particular, the identifier T
in the parameter list (T t) must be interpreted as a typedef name introduced by the
initial typedef declaration.
In an implementation, when reaching the end of a parameter list, one must close
the scope that was opened for this parameter list. Yet, one must not discard it entirely,
as one may have to re-open it at the beginning of the function body, if this parameter
list turns out to be part of a function definition. One cannot “fake” this by opening
a new scope at the beginning of the function body and introducing the names of theformal parameters into it, as this new scope would then be missing the enumeration
constants that may have been declared in the parameter list.
2.2. Ambiguity in if versus if-else

An if statement may or may not have an else branch. This creates an ambiguity, which
is well-known as the “dangling else” problem: an else branch that follows two nested if
constructs can be attached either to the farthest or to the nearest if construct. For example, according to the C11 grammar, the following code may give rise to two different
syntax trees, depending on which if statement the else branch is associated with:// dangling_else.c
int f(void) {if(0)if(1) return 1;
else return 0;
return 1;}

2.2.1. An arguably ambiguous disambiguating sentence. The C11 standard attempts to explicitly eliminate this ambiguity by stating: “An else is associated with the lexicallynearest preceding if that is allowed by the syntax” [ISO 2011, 6.8.4.1, §3]. Thus, in theprevious example, the else branch must be attached to the second if construct.
However, this disambiguating sentence is itself somewhat unclear, in a subtle way,
and could arguably be viewed as ambiguous or misleading. The following invalid codefragment illustrates the problem:// dangling_else_misleading.fail.c
typedef int T;
void f(void) {if(1)for(int T; ;)if(1) {}
else {T x;}}

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J.-H. Jourdan and F. PottierHere, if the else branch is attached to the second if construct, then the last occurrenceof T must denote a variable, which implies that the program is syntactically invalid.
One might therefore interpret paragraph 6.8.4.1, §3 as dictating that the else branch
be attached to the first if construct. Under this interpretation, the last occurrence of T
would denote a typedef name, and the program would be syntactically valid.
Such an interpretation seems exotic: we know of no C compiler that behaves in thismanner. Therefore, our informal interpretation of paragraph 6.8.4.1, §3 is that “anelse is associated with the lexically nearest preceding if that is allowed by the syntax, considering only what has been read so far”. In other words, the text beyond theelse keyword must not be taken into account when one commits its association with acertain if keyword.
Nevertheless, we believe it is interesting to point out that the short informal sentence in paragraph 6.8.4.1, §3 does not have clear formal meaning. We point out another such sentence in Section 2.4.
2.2.2. An interaction between the if-else ambiguity and the scoping rules. Another subtle issue caused by the fact that else branches are optional is its interaction with the scoping
rules (which we have recalled in Section 2.1.4). Consider an open-ended if statement,that is, one that does not (yet) have an else branch, such as “if(1);”. After such a statement has been read, two cases arise:— If the token that follows this if statement is the keyword else, then this if statement
is in fact not finished. Its scope must extend all the way to the end of the else branch.
— If, on the other hand, the token that follows this if statement is not else, then this if
statement is finished. Its scope ends immediately before this token.
Although this specification is clear, it may be somewhat tricky to implement correctly
in a deterministic parser, such as an LALR(1) parser with lexical feedback. Whenone reads the first token beyond an open-ended if statement, one does not know yet
whether the scope of the if statement has ended. Thus, if this token happens to be an
identifier, and if one attempts too early to classify this identifier as a variable or a typedef name, one runs a risk of classifying it incorrectly. The potential danger appears in
the following valid example:// dangling_else_lookahead.c
typedef int T;
void f(void) {for(int T; ;)if(1);// T must be resolved outside of the scope of the// "for" statement, hence denotes a typedef name:T x;
x = 0;}

This particular example is incorrectly rejected by GCC 5.3 (and older versions). We
have reported this bug to the developers of GCC [Jourdan 2015]. It has been acknowledged and fixed in the development version.
2.3. Ambiguity in declarations and struct declarations

The C11 grammar exhibits an ambiguity in the syntax of declarations. This is illustrated by the following code fragment:// declaration_ambiguity.c
typedef int T;
void f (void) {ACM Transactions on Programming Languages and Systems, Vol. 39, No. 4, Article 14, Publication date: August 2017.

A simple, possibly correct LR parser for C11
unsigned int;
const T;
T x;
unsigned T;
T = 1;

14:9// declares zero variables of type "unsigned int"// declares zero variables of type "const T"// T is still visible as a typedef name// declares a variable "T" of type "unsigned"}

In the C11 grammar [ISO 2011, 6.7, §1], the syntax of declarations is defined by
the production declaration: declaration-specifiers init-declarator-listopt ;. With thisin mind, there is only one way of reading the third line above, “unsigned int”. Indeed, unsigned and int are type specifiers, hence also declaration specifiers; the initdeclarator-list in this case must be absent. Hence, this declaration declares zero variables of type unsigned int. However, there are two ways of reading each of the two declarations “const T” and “unsigned T”. On the one hand, since T is a typedef name, it isalso a type specifier, so these declarations could be interpreted, like the previous one,as declarations of zero variables of type const T and unsigned T, respectively. On theother hand, since T is an identifier, it forms a declarator, so these declarations can beinterpreted as declarations of a variable T of type const and unsigned, respectively.
This ambiguity also appears in the syntax of parameter declarations, where it iscaused by the fact that a parameter may be named or anonymous [ISO 2011, 6.7.6, §1].
An analogous ambiguity appears in the syntax of struct declarations [ISO 2011,
6.7.2.1, §1], where it is caused by the fact that the struct-declarator-list is optional.
Struct declarations exhibit another (similar) ambiguity, which is caused by the factthat a bit-field can be anonymous, as prescribed by the production struct-declarator:
declaratoropt : constant-expression [ISO 2011, 6.7.2.1, §1]. This is illustrated by thefollowing code fragment:// bitfield_declaration_ambiguity.c
typedef signed int T;
struct S {unsigned T:3; // bit-field named T with type unsigned
const T:3;// anonymous bit-field with type const T};

This declares a structure S with two bit-fields. There are, however, two ways of interpreting each of the above two bit-field declarations. Indeed, in each of them, one may
consider T either as a type specifier (in which case an anonymous bit-field of type T is
being defined) or as a member name (in which case a bit-field named T is being defined).
All of the ambiguities discussed above are eliminated by paragraph 6.7.2, §2, which
limits the combinations of type specifiers that may be used in a declaration or structdeclaration:
At least one type specifier shall be given in the declaration specifiers in eachdeclaration, and in the specifier-qualifier list in each struct declaration andtype name. Each list of type specifiers shall be one of the following multisets[...]: – void; – char; – signed char; [...]
In light of this paragraph, the declaration “const T” in declaration_ambiguity.c must
be interpreted as follows. Because every declaration must contain at least one typespecifier, T must be interpreted in this declaration as a type specifier. Therefore, thisdeclaration does not declare any variable.
By the same reasoning, the bit-field “const T:3” in the previous example must be
interpreted as a constant anonymous bit-field of type T.
The declaration “unsigned T” in declaration_ambiguity.c must be interpreted as follows.
Among the combinations of type specifiers not permitted by paragraph 6.7.2, §2, one
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finds unsigned T, where T is a typedef name. Thus, this cannot be a declaration of zerovariables. Therefore, this must be a declaration of a variable T of type unsigned.
By the same reasoning, the bit-field “unsigned T:3” in the previous example must be
interpreted as a bit-field named T whose type is unsigned. (It is worth noting that, therefore, this occurrence of T lies in the name space of “members”. Thus, it does not hide
the earlier declaration of T as a typedef name. This declaration remains visible on thefollowing line.)
2.4. Ambiguity in parameter declarations

In addition to the ambiguity discussed above (Section 2.3), the C11 grammar exhibitsa further ambiguity in the syntax of parameter declarations. Consider the following
code fragment:// parameter_declaration_ambiguity.c
typedef int T;
void f(int(x), int(T), int T);// First parameter: named x, of type int// Second parameter: anonymous, of type int(T) (i.e., T -> int)// Third parameter: named T, of type int

According to the C11 grammar, in this fragment, the parameter declaration int(T) canbe interpreted in two ways. One can read it as introducing a parameter whose nameis T and whose type is int. One can also read it as introducing an anonymous parameter
whose type is int(T), that is, “function of T to int”. In the first reading, the name of theparameter is parenthesized, as allowed by the syntax of declarators. The identifier T,
which happens to denote a typedef name, is re-declared as a variable. In the second
reading, because T denotes a typedef name, (T) forms a valid abstract declarator.
The C11 standard attempts to eliminate this ambiguity as follows [ISO 2011,
6.7.6.3, §11]:
If, in a parameter declaration, an identifier can be treated either as a typedef
name or as a parameter name, it shall be taken as a typedef name.
In particular, in the previous example, the second reading must be preferred. The parameter declaration int(T) introduces an anonymous parameter whose type is int(T).
Just like the sentence that pretends to eliminate the “dangling else” ambiguity (Section 2.2.1), this sentence is arguably unclear: it must be carefully interpreted. Indeed,
consider the following code fragment, which we consider invalid:
typedef int T;
int f(int(T[const*]));

Here, one might argue that the identifier T “cannot” be treated as a typedef name,because this leads (a little later) to a syntax error: indeed, [const*] is not allowed by thesyntax of abstract declarators1 . Therefore, one might conclude that T must be treatedas a parameter name. Under this interpretation, the following two declarations would
be considered equivalent:
int f(int(T[const*]));
int f(int T[const*] );1 The production direct-abstract-declarator: direct-abstract-declarator

opt [ * ] [ISO 2011, 6.7.7, §1] does notallow const to appear here. This is an asymmetry with the production direct-declarator: direct-declarator[ type-qualifier-listopt * ], which allows it. We do not have an explanation for this asymmetry. It would bepossible to relax the syntax of abstract declarators without introducing a conflict.

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As in Section 2.2.1, we argue that such an interpretation seems counter-intuitive anddifficult or costly to implement. Moreover, in practice, Clang and GCC both accept[const*] as part of an abstract declarator, and view T as a typedef name in this example. Therefore, we follow Clang and GCC: when one finds an identifier T in this ambiguous position, one should commit to the “typedef name” interpretation before one reads
further ahead. In our parser, this is done by appropriately resolving a reduce/reduce
conflict (Section 3.5).
2.5. Ambiguity in the use of _Atomic

C11 introduces the keyword _Atomic. This keyword can be used in two different syntactic fashions:— It can be used as a type qualifier, like const, restrict, and volatile [ISO 2011, 6.7.3, §1].
— It can be used as part of an atomic type specifier [ISO 2011, 6.7.2.4, §1]. More precisely, if τ is a type name, then _Atomic(τ ) is a type specifier.
At first sight, this overloading of the _Atomic keyword appears as if it might create
an ambiguity. When _Atomic is followed by an opening parenthesis, one does not knowwhether _Atomic is used as a type qualifier (in which case the declaration specifier list
is finished, and this parenthesis is the beginning of a parenthesized declarator) or
whether this is the beginning of an atomic type specifier. In order to eliminate thispotential ambiguity, the C11 standard states [ISO 2011, 6.7.2.4, §4]:
If the _Atomic keyword is immediately followed by a left parenthesis, it isinterpreted as a type specifier (with a type name), not as a type qualifier.
However, this restriction is not really necessary, as paragraph 6.7.2, §2 (quoted anddiscussed in Section 2.3) already removes this ambiguity. Indeed, upon encountering
an _Atomic keyword followed by an opening parenthesis, one may reason as follows:— If a type specifier has been read already as part of the current declaration, thenthis _Atomic keyword cannot be viewed as the beginning of another type specifier.
Indeed, according to the list of permitted combinations of type specifiers [ISO 2011,
6.7.2, §2], an atomic type specifier cannot be accompanied by another type specifier.
Thus, in this case, _Atomic must be viewed as a type qualifier. (In this case, paragraph6.7.2.4, §4 would impose rejecting the code.)— If no type specifier has been read yet, then this _Atomic keyword cannot be viewed asa type qualifier. Indeed, that would imply that the parenthesis is the beginning of aparenthesized declarator, so that the declaration specifier list is finished and contains
no type specifier. This is forbidden: a declaration specifier list must contain at least
one type specifier. Thus, in this case, _Atomic must be viewed as the beginning of a
type specifier.
This may seem a somewhat complicated and informal proof of unambiguity. Fortunately, the absence of ambiguity is automatically proved by LR parser generators (seeSection 3.5).
3. AN LALR(1) PARSER FOR C11

Our C11 parser [Jourdan and Pottier 2017] is produced by an LALR(1) parser generator out of a grammar which we strive to keep as close as possible to the C11 grammar
and as simple as possible. We assume that its input is preprocessed source code.
3.1. In search of a suitable grammar

What grammar should be provided as an input to an LALR(1) parser generator? Itseems natural to first examine the C11 grammar [ISO 2011, A.2]. Let us refer to it as
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G0 . As explained earlier (Section 2.1), it is an ambiguous context-free grammar, whose
most problematic source of ambiguity has to do with the various roles of identifiers.
An identifier may belong to one of four name spaces [ISO 2011, 6.2.3], namely “labelnames”, “tags”, “members”, and “ordinary identifiers”. Furthermore, an ordinary identifier can play one of two roles: it can be viewed either as a “variable” or as a “typedef
name” [ISO 2011, 6.2.1, §1]. In G0 , identifier is a terminal symbol, whereas typedefname is a nonterminal symbol, defined by the production typedef-name: identifier [ISO2011, 6.7.8, §1]. This creates an ambiguity: G0 does not indicate when this production
should be used, that is, when an identifier should be viewed as a typedef name andwhen (on the contrary) it should be viewed as a variable (or a label name, or a tag, or amember). This is done in the most part by a set of informal “scoping rules” [ISO 2011,
6.2.1] and in a lesser part by informal restrictions enunciated in other places, such as
paragraph 6.7.2, §2, paragraph 6.7.6.3, §11, and paragraph 6.9.1, §6.
In order to eliminate this source of ambiguity, it is customary2 to remove from G0 the
production typedef-name: identifier and view identifier and typedef-name as two distinct terminal symbols. By doing so, one ostensibly assumes that ordinary identifiers
are somehow classified prior to parsing as variables or typedef names. Let us refer tothis new grammar as G1 [Degener 2012].
The grammar G1 seems remarkably well-behaved. It is “almost” LALR(1). More precisely, the automaton built for G1 by an LALR(1) parser generator exhibits only two
conflicts: a shift/reduce conflict caused by the “dangling else” ambiguity (Section 2.2)
and a shift/reduce conflict caused by the “_Atomic(” ambiguity (Section 2.5). In bothcases, the desired behavior can be obtained by instructing the parser generator to always prefer shifting.
Unfortunately, the grammar G1 is too restrictive: there are valid C11 programs thatit rejects. Indeed, whereas in G0 the terminal symbol identifier means “an arbitrary
identifier”, in G1 it has more restricted conventional meaning: it represents “an identifier that has been classified as a variable” (as opposed to a typedef name). In twoplaces, namely primary-expression [ISO 2011, 6.5.1, §2] and identifier-list [ISO 2011,
6.9.1, §6], this restricted meaning is in fact desired. Therefore, in these two places, it
is fine to use identifier. Everywhere else, the unrestricted meaning of “an arbitrary
identifier” is desired. In those places, G1 is too restrictive and must be amended by replacing identifier with a choice between identifier and typedef-name. This yields a newgrammar, which we refer to as G2 .
The grammar G2 is slightly less well-behaved than G1 . In addition to the two shift/reduce conflicts mentioned above, it exhibits a reduce/reduce conflict caused by the “parameter declaration” ambiguity (Section 2.4) and a shift/reduce conflict caused by the“declaration” ambiguity (Section 2.3). The former conflict can be solved by instructing
the parser generator to always prefer a certain production (Section 3.5). Unfortunately,
the latter conflict cannot be statically solved: neither “always shift” nor “always reduce”
is the correct behavior (Section 3.4).
In summary, the grammar G2 is our starting point. At least two problems remain
to be solved. First, one must implement a mechanism by which ordinary identifiersare (correctly) classified as variables or typedef names. Although it is well-known thatsuch a classification must be performed on the fly via a form of “lexical feedback”, theproblem is trickier than it may at first seem, as we have argued earlier (Section 2).
2 This idea probably goes back to the early days of the B and C programming languages, circa 1969–

70 [Ritchie 1993]. In any case, it explicitly appears in Kernighan and Ritchie’s 1988 book [Kernighan andRitchie 1988, §A.13], which describes “K&R C”. They write: “With one further change, namely deleting the
production typedef-name: identifier and making typedef-name a terminal symbol, this grammar is acceptable
to the YACC parser-generator. It has only one conflict, generated by the if-else ambiguity.”

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Our solution, which requires several changes in the grammar, is described in Section 3.3. Second, one must further modify the grammar so as to eliminate the problematic shift/reduce conflict described above. Our solution is described in Section 3.4.
3.2. Tools

We build our lexer and parser with the programming language OCaml, the lexer generator ocamllex, and the parser generator Menhir [Pottier and Régis-Gianas 2016].
The latter two can be described as the OCaml analogues of lex and yacc. Minsky etal. [Minsky et al. 2013, Chapter 16] give a good tutorial introduction to these tools.
The implementation of the lexer does not present any significant difficulty, except in
its interaction with the parser, which is described in detail in the following.
Menhir supports several parser construction methods, including LALR(1), Pager’s
method [Pager 1977] and Knuth’s canonical method [Knuth 1965]. For our purposes,
LALR(1) is sufficient. We exploit two specific features of Menhir that improve conciseness and readability, namely parameterized nonterminal symbols [Pottier and RégisGianas 2016, §5.2] and inlined nonterminal symbols [Pottier and Régis-Gianas 2016,§5.3]. Both features can be expanded away (by Menhir itself), producing a version of
the grammar that does not exploit these features.
This expanded grammar, with empty semantic actions, forms a valid .y file, whichyacc and Bison [Donnelly and Stallman 2015] can read and process, and which we
distribute [Jourdan and Pottier 2017]. The LALR(1) automata produced by Bison andMenhir appear to be identical. (We have checked that they have the same number ofstates.)3.3. Lexical feedback

As explained in Section 3.1, we follow an approach where variables and typedef names
must give rise to distinct tokens (or, in our case, distinct sequences of tokens). In an
ideal world, this distinction would be made prior to parsing, in a logically separate
phase. It would take the form of extra logic inserted into the lexer (or between thelexer and parser). Unfortunately, in reality, this is impossible. Indeed, as explained in
Section 2, in order to tell whether an identifier is a variable or a typedef name, onemust know which declarations are visible in the current scope. This in turn requires
being aware of where scopes are opened and closed and where declarations take effect.
To obtain this information requires parsing. Thus, a form of feedback is required: theparser must provide information to the lexer. To this end, some form of global state,
which the lexer reads and the parser updates, is required. This is known elegantly as“lexical feedback”, or, rather more prosaically, as “the lexer hack”.
In all implementations of lexical feedback known to us, including ours, the lexer
has read access to some global state, which the parser is in charge of updating. The
updates take place in the semantic actions associated with certain productions. They
are executed when these productions are reduced.
In all previous implementations of lexical feedback known to us, upon encountering
an identifier in the source code, the lexer immediately consults the global state so as
to determine whether (in the current scope) this identifier represents a variable or a
typedef name, and, depending on the outcome of this test, emits distinct tokens: say,
VARIABLE versus TYPE. In our approach, in contrast, upon encountering an identifier inthe source code, the lexer immediately produces the token NAME, followed with either
VARIABLE or TYPE. This delays the access by the lexer to the global state, thus eliminating
the risk of incorrect classification that was illustrated in Section 2.2.2.
In the following, we first describe what global state is shared between our lexer andparser, and through which API this global state is updated and read (Section 3.3.1).
Then, we explain when this global state is updated by the parser. This involves savACM Transactions on Programming Languages and Systems, Vol. 39, No. 4, Article 14, Publication date: August 2017.

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ing and restoring contexts (Section 3.3.2) and declaring new identifiers in the current
context (Section 3.3.3). Finally, we explain when the lexer accesses the global state(Section 3.3.4).
3.3.1. Context API. Let us use the word “context”, in a precise technical sense, to meana “set of identifiers”. A context represents a set of identifiers that should be viewed as
typedef names (whereas all other identifiers should be viewed as variables). It is an
immutable set.
In Our OCaml implementation, the management of contexts is encapsulated in asingle module, baptized Context. This module is extremely simple: it is implemented
in 8 lines of code. It contains one mutable global variable, namely current, which holds
a pointer to an immutable set of identifiers. The set !current is “the current context”3 .
This module is used by the lexer (which consults the global state) and by the parser(which updates the global state), thus allowing information to flow from the parser tothe lexer. It offers the following API:val declare_typedefname : string -> unit
val declare_varname: string -> unit
val is_typedefname: string -> bool
type context
val save_context: unit -> context
val restore_context: context -> unit

The functions declare_typedefname and declare_varname are invoked by the parser whena new variable or typedef name is introduced: they change the current context.
More precisely, the call declare_typedefname id adds the identifier id to the current context, whereas declare_varname id removes id from the current context. The function
is_typedefname is invoked by the lexer when it needs to decide whether to emit VARIABLE
or TYPE; it consults the current context. These three functions have logarithmic timecomplexity: OCaml’s persistent set library exploits balanced binary search trees.
The function save_context is invoked by the parser when opening a new scope. Thisfunction returns !current, an immutable set of identifiers: in other words, a snapshotof the current context. This snapshot can be later re-installed (if and when desired) byinvoking restore_context. This function simply writes its argument into current. These
two functions have constant time complexity.
The module Context does not internally maintain a stack. Nor does its API impose
a stack discipline: calls to save_context and restore_context need not be balanced. Thus,
the API is very simple and powerful.
3.3.2. Where contexts are saved and restored. For convenience, we define a nonterminal
symbol, save_context, which generates the empty sentence, as follows:
save_context: (* empty *) { save_context() }When this production is reduced, its semantic action is executed and returns a snapshot of the current context. We use this nonterminal symbol at any point in the grammar where we need to save the current context in order to prepare for a possible later
re-installation. We may do so quite freely, for the following reasons:— Because save_context generates the empty sentence, its use has no effect on the language that is accepted by the parser.
— As noted earlier, the runtime cost of saving the context is very low.
3 In OCaml, ! dereferences a mutable variable.

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14:15— Since calls to save_context and restore_context need not be balanced, we may
use save_context wherever we please, without worrying about matching calls to
restore_context.
One possible adverse effect of inserting occurrences of save_context in the grammar
is that this can create new shift/reduce conflicts. Such a conflict is typically between
reducing the production save_context: (*empty *) (which means: take a snapshot now!)and shifting (which means: make progress in some other productions p1 , p2 , . . .). We
avoid all such conflicts by adding redundant occurrences of save_context in the productions p1 , p2 , . . . By doing so, we instruct the parser to always take a snapshot now, evenin situations where it is not known yet whether this snapshot will be useful in the
future.
Most calls to save_context and restore_context come in matching pairs. In that case, fordocumentation and for conciseness, it is desirable to phrase the grammar in terms ofa high-level notion of “scope”, instead of low-level function calls. To this end, we definea parameterized nonterminal symbol, scoped(X):scoped(X):ctx = save_context
x = X{ restore_context ctx; x }The parameter X stands for a (terminal or nonterminal) symbol. By definition, scoped(X)generates the same language as save_context X, which itself generates the same language as X. The difference between scoped(X) and X is in the semantic actions: when one
uses scoped(X), the current context is saved initially and restored at the end4 . More precisely, when the production scoped(X): save_context X is reduced, the top two cells of theparser’s stack respectively contain a saved context ctx and an abstract syntax tree x forthe symbol X. The semantic action restore_context ctx; x re-installs the context ctx andreturns x. This explains why we do not need to explicitly maintain a stack of contexts:
saved contexts are naturally stored in the parser’s stack. An analogous idea appears
in Bison’s manual [Donnelly and Stallman 2015, 3.4.8.1]. It is unfortunately expressedin a much lower-level style that makes it more difficult to understand and notationallyheavier.
We use this construction, among other places, in the syntax of statements:
statement:labeled_statement| scoped(compound_statement)| expression_statement| scoped(selection_statement)| scoped(iteration_statement)| jump_statement{}

This elegantly reflects the fact that compound statements, selection statements, anditeration statements form a “block” (Section 2.1.4) and therefore require opening andclosing a new scope.
Function definitions are more difficult to deal with, in part because one cannot distinguish a declaration and a function definition until one reaches a function body, andin part because in a function definition the scope where the parameters are visible isnoncontiguous. (Both phenomena have been illustrated in Section 2.1.4.)
4 Again, ctx and x are OCaml variables: they are bound to the semantic values returned by save_context
and X, respectively. One could replace them in the semantic action with $1 and $2.

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To deal with these difficulties, we build (simplified) abstract syntax trees for declarators. An abstract syntax tree of OCaml type declarator stores the identifier that is declared and (if this is a function declarator) a snapshot of the context at the end of theparameter list. The API offered by these abstract syntax trees is as follows:
type declarator(* Constructors. *)val identifier_declarator: string -> declarator
val function_declarator: declarator -> context -> declarator
val other_declarator: declarator -> declarator(* Accessors. *)val identifier: declarator -> string
val reinstall_function_context: declarator -> unit

The three constructors above are used in the semantic actions associated with thenonterminal symbols declarator and direct_declarator. For instance, the following production recognizes a function declarator and builds an abstract syntax tree for it:
direct_declarator:...
| d = direct_declarator LPAREN ctx = scoped(parameter_type_list) RPAREN{ function_declarator d ctx }| ...

The variable ctx above represents a snapshot of the context at the end of the parameter
list. This stems from the following definition:
parameter_type_list:
parameter_list option(COMMA ELLIPSIS {}) ctx = save_context { ctx }The accessor function identifier retrieves the identifier that is declared by a declarator. It is used in the definition of the nonterminal symbols declarator_varname anddeclarator_typedefname, which recognize the same language as declarator and have theadded side effect of declaring this identifier (as a variable or as a typedef name, respectively) in the current scope:declarator_varname:d = declarator { declare_varname(identifier d); d }declarator_typedefname:d = declarator { declare_typedefname (identifier d); d }The accessor function reinstall_function_context expects its argument d to be a function declarator. It retrieves the context that was saved at the end of the parameter list
and re-installs it (by invoking restore_context). On top of that, it declares the function’sname as a variable, by calling declare_varname (identifier d).
Putting the pieces together, a function definition is described as follows:
function_definition1:
declaration_specifiers d = declarator_varname{ let ctx = save_context () inreinstall_function_context d;
ctx }function_definition:
ctx = function_definition1 declaration_list? compound_statement{ restore_context ctx }Assume, for the sake of simplicity, that the parser is reading a function definition
whose declaration_list? is empty. Then, the nonterminal symbol function_definition1 is
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reduced when the parser looks ahead at the opening brace that forms the beginning of
the coumpound_statement. At this point, the current context is saved under the name ctx.
(This context includes the function’s name, declared as a variable, because we haveused declarator_varname.) Then, the call reinstall_function_context d restores the context
that existed at the end of the parameter list (which has been saved as part of theabstract syntax tree d) and, on top of it, declares the function’s name. The function
body is parsed in this scope. Upon completion, this scope is closed by restoring thecontext ctx.
3.3.3. Where declarations take effect. In the C11 grammar, “variable” declarations and“type” declarations are described by a single nonterminal symbol, declaration [ISO2011, 6.7]. In our parser, however, we must know, at the end of each declarator, whether
this declarator introduces a new variable or a new typedef name. Indeed, we must
make the lexer aware of this new name, by updating the current context.
For this reason, we distinguish between two kinds of declarations: those that contain one occurrence of the typedef keyword, and those that do not. (The C11 standard
forbids multiple occurrences of typedef.) A list of declaration specifiers that does notcontain typedef is described by the nonterminal symbol declaration_specifiers, whereas
a list that contains one occurrence of typedef is described by the nonterminal symbol
declaration_specifiers_typedef. (The definitions of these symbols are given and explainedin Section 3.4.)
This allows us to distinguish between “variable” declarations and “type” declarations, as follows:declaration:
declaration_specifiers
init_declarator_list(declarator_varname)?
SEMICOLON| declaration_specifiers_typedef
init_declarator_list(declarator_typedefname)? SEMICOLON| static_assert_declaration{}

The symbols init_declarator_list and init_declarator are defined as in the C11 grammar, except they are parameterized over declarator. This parameter can be instantiated, as desired, with declarator_varname or declarator_typedefname (whose definitions havebeen shown in Section 3.3.2). Thus, we obtain the desired effect: the absence or presence of typedef among the declaration specifiers influences the manner in which thedeclarators update the current context.
3.3.4. Token sequences for identifiers. The lexer uses the current context in order to classify identifiers and emit appropriate tokens. However, an LALR(1) parser may request
one token from the lexer, known as a “lookahead” token, before it decides whether aproduction should be reduced and which production should be reduced. As noted earlier (Section 2.2.2), this introduces a danger of mis-classification of an identifier by thelexer. Indeed, the lexer classifies this identifier in the current scope, whereas perhaps
the parser is just about to perform a reduction that affects the current scope (by declaring a new identifier in this scope, or by closing this scope). This is not just a theoreticalpossibility: it is the root of the bug that we have identified in GCC [Jourdan 2015].
Some parser generators, such as Bison, guarantee that, in a “defaulted state”,
the parser will not request a lookahead token from the lexer5 . By relying on
this feature, one might hope to cleverly avoid the danger. We have no such luck,
5 The Bison manual [Donnelly and Stallman 2015, §5.8.2] notes: “The presence of defaulted states is an im-

portant consideration [...]. That is, if the behavior of yylex can influence or be influenced by the semantic
actions [...], then the delay of the next yylex invocation until after those reductions is significant. For exam-

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14:18J.-H. Jourdan and F. Pottierthough: in the example of Section 2.2.2, the problem arises in a state where theparser will either shift the token ELSE or reduce the production selection_statement:
IF LPAREN expression RPAREN scoped(statement). (This is the very state where the “danglingelse” shift-reduce conflict arises.) This is not a defaulted state: hence, the guarantee
offered by Bison does not help. Furthermore, Menhir does not at present offer thisguarantee, so we would rather not rely on it.
To work around this danger, we introduce an original idea. Upon encountering an
identifier, our lexer emits a sequence of two tokens. The first token is always NAME.
It is produced by the lexer without consulting the global state. The second token iseither VARIABLE or TYPE, depending on the current status of this identifier. Because thedistinction is delayed until the second token is demanded by the parser, the dangerof mis-classification disappears. By the time the second token is demanded, the global
state must have been updated already (if necessary) and cannot be outdated. Indeed,
one can check6 that no production with a side effect can be reduced when the lookahead
token is “fragile”, that is, when it is VARIABLE or TYPE.
Our grammar has three nonterminal symbols that correspond to an identifier7 :typedef_name:i = NAME TYPE
{ i }var_name:
i = NAME VARIABLE{ i }general_identifier: i = typedef_name | i = var_name { i }Where the C11 grammar uses typedef-name, we use typedef_name. Where the C11 grammar uses identifier, we use var_name or general_identifier. More precisely, var_name isused when referring to a variable in an expression (primary_expression: var_name [ISO2011, 6.5.1, §2]) or in the identifier list of a K&R function declarator8(identifier_list: var_name | identifier_list COMMA var_name), whereas general_identifier isused everywhere else.
3.4. Controlling type specifiers in declarations and struct declarations

As explained in Section 2.3, the C11 grammar exhibits an ambiguity in the syntax
of declarations. This ambiguity gives rise in the grammar G2 to a shift/reduce conflict(Section 3.1). In short, this conflict can be explained as follows: when the parser has
read a list of declaration specifiers and finds that the next input symbol is a typedef
name, it must choose between shifting (which means that the list of declaration specifiers is not finished, and this typedef name is a type specifier) and reducing (whichmeans that the list of declaration specifiers is finished, and this typedef name is the
beginning of a declarator). This conflict cannot be solved via a precedence declaration.
Indeed, neither “always shift” nor “always reduce” is the correct behavior.
As explained in Section 2.3, in order to eliminate the ambiguity, the C11 standard imposes a well-formedness constraint on lists of declaration specifiers [ISO 2011,
ple, the semantic actions might pop a scope stack that yylex uses to determine what token to return. Thus,
the delay might be necessary to ensure that yylex does not look up the next token in a scope that should
already be considered closed.”
6 In our grammar, VARIABLE and TYPE always follow NAME. In other words, they never follow a nonterminal
symbol, and they are never the first symbol in a right-hand side. Therefore, no reduction can possibly takeplace when VARIABLE or TYPE is the lookahead symbol. This reasoning holds even in the presence of default
reductions.
7 In Menhir, the syntax “i =” introduces an OCaml variable i and binds it to the semantic value of the symbolthat follows. (An analogous feature in Bison is known as a “named reference” [Donnelly and Stallman 2015,§3.6].) Here, one could also remove all occurrences of “i =” and write “$1” instead of “i” in the semantic
actions.
8 The C11 standard [ISO 2011, 6.9.1, §6] does not allow a typedef name to occur in the identifier list of a K&R
function declarator. Indeed, it prescribes: “An identifier declared as a typedef name shall not be redeclared
as a parameter”.

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6.7.2, §2]. Similarly, in order to eliminate the shift/reduce conflict, we must encode thisconstraint into our grammar. Fortunately, we need not enforce this constraint exactly.
We may enforce a weaker constraint, provided it is still strong enough to eliminate theconflict. Checking that the C11 standard is respected is deferred to a later semantic
analysis. Our aim is to keep our grammar as simple as possible.
We split type specifiers in two disjoint categories:— “Unique” type specifiers cannot occur together with any other type specifiers in a
declaration. They are void, _Bool, atomic type specifiers, struct or union specifiers,
enumeration specifiers, and typedef names.
— “Nonunique” type specifiers can occur together with other (nonunique) type specifiers in a declaration. They are char, short, int, long, float, double, signed, unsigned and_Complex.
It follows from paragraph 6.7.2, §2 that a list of declaration specifiers either contains
exactly one unique type specifier or contains one or more nonunique type specifiers.
Fortunately, lists restricted by simple numeric constraints can be described in theformalism of LR(1) grammars. For instance, the parameterized nonterminal symbol
list_eq1(A, B) describes a list whose elements are A’s or B’s and which contains exactly
one element of type A:
list_eq1(A, B):
A B* | B list_eq1(A, B) {}This definition states that such a list either begins with A, in which case the remainderof the list must match B*, or begins with B, in which case the remainder of the list mustmatch list_eq1(A, B) again. Similarly, we define list_ge1(A, B), which describes a list
whose elements are A’s or B’s and which contains at least one element of type A:
list_ge1(A, B):
A B* | A list_ge1(A, B) | B list_ge1(A, B) {}Equipped with these tools, we can easily require every list of declaration specifiers
to either contain exactly one unique type specifier or contain at least one nonuniquetype specifier:declaration_specifiers:
list_eq1(type_specifier_unique,declaration_specifier)| list_ge1(type_specifier_nonunique, declaration_specifier){}The nonterminal symbols type_specifier_unique and type_specifier_nonunique are as described above. The nonterminal symbol declaration_specifier corresponds to a declaration specifier that is neither a type specifier nor the typedef keyword. (Our handling of
typedef is discussed below.)This grammar fragment is amenable to LR(1) parsing. As long as it finds
declaration_specifiers, the LR automaton accumulates them on its stack, exploring inparallel the possibility that this could be a list_eq1(type_specifier_unique, ...) and thepossibility that this could be a list_ge1(type_specifier_nonunique, ...). As soon as it finds
a type specifier (which must be either unique or nonunique, but cannot be both), oneof these possibilities is discarded.
The nonterminal symbol declaration_specifiers_typedef, which was mentioned earlier(Section 3.3.3), is defined in an analogous manner. Like declaration_specifiers, it requires the list to either contain exactly one unique type specifier or contain at least
one nonunique type specifier. In addition, it requires the list to exhibit exactly one
occurrence of typedef.
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14:20J.-H. Jourdan and F. Pottierdeclaration_specifiers_typedef:
list_eq1_eq1(TYPEDEF,
type_specifier_unique,declaration_specifier)| list_eq1_ge1(TYPEDEF,
type_specifier_nonunique, declaration_specifier){}The parameterized nonterminal symbol list_eq1_eq1(A, B, C) describes a list of A’s, B’s,
and C’s that contains exactly one A and exactly one B. Similarly, list_eq1_ge1(A, B, C)
describes a list of A’s, B’s, and C’s that contains exactly one A and at least one B. Theirdefinitions are omitted.
3.5. Wrapping up

We have presented the main two ingredients of our approach, namely the originalmanner in which we set up lexical feedback (Section 3.3) and the manner in which we
avoid the conflict caused by the “declaration” ambiguity (Section 3.4). There remain
two conflicts in the grammar. They are statically solved, as follows.
The “dangling else” ambiguity (Section 2.2) gives rise to a well-known shift-reduce
conflict. This conflict is solved via a suitable precedence declaration [Aho et al. 1986,
Chapter 4], which causes shifting to be preferred to reduction when the lookahead
symbol is ELSE:
selection_statement:
IF LPAREN expression RPAREN scoped(statement) ELSE scoped(statement)| IF LPAREN expression RPAREN scoped(statement) %prec below_ELSE| SWITCH LPAREN expression RPAREN scoped(statement)

The “parameter declaration” ambiguity (Section 2.4) gives rise in our grammar to a reduce/reduce conflict. Initially, this conflict is between the productions
general_identifier: typedef_name (Section 3.3.4) and type_specifier_unique: typedef_name(Section 3.4). It appears in only one state of the automaton, and only when the lookahead symbol is ’(’, ’)’, or ’[’. By studying how one may reach this situation, one findsthat it is reachable only via a parameter declaration. Thus, paragraph 6.7.6.3, §11
applies, and prescribes that the typedef name on top of the parser’s stack should
be viewed as a type specifier. Thus, the parser generator must be instructed to always reduce the second of the above two productions. Menhir, like Bison [Donnelly
and Stallman 2015, §5.6], always favors the production that appears first in thegrammar. In our grammar, the production general_identifier: typedef_name happens tocome first, and we do not wish to change that, as we want to keep the rules inthe same order as they appear in the C11 grammar [ISO 2011, A.2]. So, we replace
type_specifier_unique: typedef_name with type_specifier_unique: typedef_name_spec and add
the production typedef_name_spec: typedef_name at the beginning of the grammar. Thishas the desired effect.
The “_Atomic(” ambiguity (Section 2.5) gives rise to a shift/reduce conflict in the grammars G1 and G2 (Section 3.1). Fortunately, in our grammar, this conflict is gone. As
explained in Section 2.5, the restriction imposed by paragraph 6.7.2, §2 eliminates theambiguity; and we are fortunate enough that our implementation of this restriction(Section 3.4) eliminates the conflict.
Because the restriction of paragraph 6.7.2.4, §4 is not necessary, our parser does
not, by default, implement it. Therefore, it accepts a slightly larger language thanprescribed by the C11 standard. For instance, it accepts the following noncompliantcode:// atomic_parenthesis.c
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In case strict compliance is needed, our parser can be configured to enforce the restriction of paragraph 6.7.2.4, §4 and reject the above code. To do this, we let thelexer emit the special token ATOMIC_LPAREN, instead of LPAREN, when it encounters an
opening parenthesis that immediately follows an _Atomic keyword. Furthermore, we
add the production atomic_type_specifier: ATOMIC ATOMIC_LPAREN type_name RPAREN. Thus, aparenthesis that follows _Atomic must be part of an atomic type specifier; it cannot beinterpreted in any other way.
4. RELATED WORK

Our approach to parsing C11 combines a deterministic parser (produced by an
LALR(1) parser generator, based on a slightly modified version of the C11 grammar)
and a deterministic “lexical feedback” mechanism, which distinguishes between variables and typedef names. This approach follows a well-established tradition, which we
discuss in Section 4.1. However, there are other approaches to parsing C (and, moregenerally, C++), which we discuss in Section 4.2.
4.1. LR parsers and lexical feedback

Lexical feedback in an LR parser is a well-known technique, and has been in use fora long time. Mason, Brown, and Levine’s book [Brown et al. 1992, Chapter 7] offers abrief description of it. It is however a rather subtle and fragile technique, due in particular to a possible adverse interaction between lexical feedback and lookahead. Thereis a danger that the lexer reads one token ahead, before the parser has updated theglobal state that informs the lexer. This would cause the lexer to deliver an incorrect
token. The issue is complicated by the fact that, in the presence of default reductions,
it can be hard to understand exactly when the parser requests a new token from thelexer.
This issue, as well as the problem of classifying identifiers in a C parser, is discussed
at length in a very interesting thread on the newsgroup comp.compilers [lex 1992].
Deep in this thread, Jim Roskind explains how to prove the absence of adverse interaction between lexical feedback and lookahead: “[one] must show that [no] reductions
involved with annotation of [the] symbol table take place while [a fragile token] is waiting in the lookahead buffer”. We have used this argument in Section 3.3.4, where (inour case) no reduction at all can take place when the lookahead token is a fragile token(that is, VARIABLE or TYPE). Roskind also asserts that “the typedef-ness of an identifier
can change only after a declarator is complete”. Technically, this is false: it can change
also when a scope is closed and when defining a new enumeration constant. In ANSI C,
at the end of a scope, the lookahead token must be ‘}’ or ‘)’, neither of which is fragile,
so all is well. In C99, however, a selection statement forms a block, so a scope is closed
at the end of such a statement. Due to the “if-else” ambiguity, determining whether
an if statement is finished requires looking ahead at the next token, which could befragile. Therefore, there is a danger of misclassification, which we have discussed in
Section 2.2.2, identifying a bug in GCC [Jourdan 2015].
In the same thread, Dale R. Worley puts forth the idea that, in order to eliminate theambiguity in declarations, “the grammar must keep track of whether a type-specifier
has been seen in the declaration-specifiers”. His changes to the grammar are analogous
in spirit to those we present in Section 3.4. We keep track of more information (namely,
the distinction between unique and nonunique type specifiers, and the absence or presence of typedef) and we use parameterized nonterminal symbols to preserve readability.
Roskind is the author of an LALR(1) grammar for ANSI C and for C++. These grammars are available online [Roskind 1990], together with detailed explanations, which
unfortunately seem to concern mostly C++. Roskind goes to great lengths to eliminate ambiguity: his ANSI C grammar exhibits only one shift/reduce conflict, namely
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J.-H. Jourdan and F. Pottier

the benign “dangling else” conflict, and no reduce/reduce conflict. The subgrammars ofdeclarations, parameter declarations, and declarators appear to have been quite deeply
re-worked. Unfortunately, Roskind’s published grammar does not contain semantic actions; it would take some work to reconstruct the lexical feedback mechanism.
Up until version 3.4.4, GCC used an LALR(1) parser [The GNU project 2004]. Like
Roskind’s [Roskind 1990] and Worley’s (cited above), this parser has (deeply) re-worked
subgrammars of declarations, declarators, declaration specifiers, etc. It uses explicit
auxiliary stacks to keep track of which scopes have been opened and (in a declaration)
which declaration specifiers have been seen. It also stores information on the parser’s
stack, in the same way as we store saved contexts on the parser’s stack (Section 3.3.2).
We are perhaps the first to point out that no auxiliary stack is needed. Since version
4.0.0, GCC uses a hand-written recursive descent parser, which today is about 16Kloc.
This parser accepts a much larger language than C11: it accepts Objective C as wellas many GNU extensions.
Clang, too, uses a hand-written recursive descent parser. Even though the recursive
descent parsers in GCC and Clang are hand-written, they use a lexical feedback mechanism, or “lexer hack”. Some claim that Clang’s approach does not use a “hack” [Bendersky 2012]. In our eyes, whether the global state resides in the lexer itself, or in a
separate “symbol table” module (such as our Context module, presented in Section 3.3.1)
makes relatively little difference: the on-the-fly classification of identifiers remains difficult to get right, as evidenced by the bug that we found in GCC [Jourdan 2015].
The CompCert C compiler [Leroy 2009; Leroy 2017] contains two parsers. The CompCert “pre-parser” (in cparser/pre_parser.mly) is an LALR(1) parser equipped with alexical feedback mechanism. The C11 parser presented in this paper is based on it.
The pre-parser is in charge of detecting and reporting syntax errors, following a technique proposed by Jeffery [Jeffery 2003] and implemented in Menhir by the second author [Pottier 2016]. The CompCert “parser” (in cparser/Parser.vy) is also an LALR(1)parser, but does not need lexical feedback: it parses the input again, exploiting theclassification of identifiers that has been performed already by the pre-parser. As aresult, it is very simple. Its grammar is very close to the C11 grammar. It is LALR(1):it has no conflicts whatsoever. In particular, the “dangling else” conflict is resolved by
distinguishing “open-ended” and “non-open-ended” if statements (Section 2.2.2). Thisis done without actually duplicating the subgrammar of statements, thanks to parameterized terminal symbols. Out of this grammar, Menhir produces an executable parser,
written in the Coq programming language, whose correctness can be verified by theCoq proof assistant [Jourdan et al. 2012].
Van Wyk and Schwerdfeger [Van Wyk and Schwerdfeger 2007] propose a “contextaware” variant of the LR algorithm where the parser passes to the lexer a “valid
lookahead set”, that is, a set of valid symbols that the lexer is permitted to returnat this point. However, this does not solve the “typedef name” ambiguity, so, whenparsing C, lexical feedback is still required [Van Wyk and Schwerdfeger 2007, §6.1].
Furthermore, because the computation of the lookahead symbol depends on the current control state of the parser, the lookahead symbol must be re-computed after eachreduction [Van Wyk and Schwerdfeger 2007, §6.2.1]. Van Wyk and Schwerdfeger use
this technique to develop an extensible variant of ANSI C.
A short paper by Scarpazza [Scarpazza 2007] presents an approach to parsing ANSI
C using flex, Bison, and lexical feedback. When parsing a declaration, Scarpazza insists that the identifier that is being declared should be classified by the lexer as avariable. (In contrast, we let the lexer randomly classify this identifier, and compensate by accepting general_identifier in our grammar.) This leads Scarpazza to set up anelaborate form of lexical feedback, whereby the parser keeps track of “type stacks” anduses them to inform the lexer.
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4.2. Other approaches

Nondeterministic parsing algorithms support general (possibly ambiguous) contextfree grammars. Examples of such algorithms include various forms of backtracking
LR, as implemented for instance in BtYacc [Dodd and Maslov 1999]; GLR [Grune andJacobs 2008, §11.1]; Earley’s algorithm [Grune and Jacobs 2008, §7.2]; and many more.
These algorithms explore several potential parses (either one after the other or inparallel), discarding those that lead to a syntax error.
Because they support ambiguous grammars, nondeterministic parsing algorithms
can be applied, without lexical feedback, to the C11 grammar, as it appears in the
C11 standard. In the newsgroup thread cited earlier [lex 1992], Jan Rekers argues
in favor of using GLR, without lexical feedback, for parsing C. Baxter et al. [Baxter
et al. 2004] also report using GLR to parse many languages, including C and C++.
McPeak and Necula present a hybrid GLR/LR parsing algorithm, and use it in a C++
parser [McPeak and Necula 2004]. However, this approach does not magically eliminate the difficulty of parsing C11. Because the C11 grammar is ambiguous, a nondeterministic parsing algorithm produces an exponential number of potential parse trees.
Well-formedness filters (applied either a posteriori or on the fly) are necessary so as todiscard those trees that do not respect the informal prose in the C11 standard. Thesefilters must implement the scoping rules as well as several paragraphs of the standard
that have been cited in Section 2. They could be just as difficult to implement correctly
as lexical feedback.
A nondeterministic parsing algorithm can also be used with lexical feedback. In thatcase, the side effects of the semantic actions must be undone when backtracking. For
instance, Thurston and Cordy develop a backtracking LR algorithm and apply it toC++ [Thurston and Cordy 2006]. Their paper contains a good survey of the related
work in this area.
A way of avoiding lexical feedback, which may be used in a deterministic or nondeterministic parser, is to modify the grammar so that it does not require a distinction
between variables and typedef names, yet is not ambiguous. This may require unifying several syntactic categories that are considered distinct in the official grammar.
For instance, a parser might recognize “T * b” as a “declaration-or-expression”, letting
a later semantic analysis determine whether (in the context where it occurs) it should
be interpreted as a declaration or as an expression. Willink [Willink 2001, Chapter 5]
adopts this approach, which he calls the “superset grammar” approach, in a nondeterministic parser for C++. This approach may well be applicable to C11. Unfortunately, it
imposes pervasive changes on the grammar and requires implementing an ad hoc semantic analysis. It may be difficult to argue that the modified grammar, in conjunction
with the semantic analysis, complies exactly with the C11 standard.
Grimm [Grimm 2006] describes Rats!, a parser generator based on parsing expression grammars (PEGs), as opposed to context-free grammars. Instead of symmetric choice, PEGs offer an ordered choice operator, therefore eliminating all ambiguity by construction. They also support syntactic predicates, which match the input without consuming it. PEG parsers are backtracking parsers. They achieve linear time and space complexity via memoization. Grimm discusses the use of Rats! toparse C [Grimm 2006, §5]. He notes that the added power of PEGs makes it easier todeal with certain aspects of C. For instance, there is no need to alter the grammar so as
to track the presence of type specifiers in a sequence of declaration specifiers, as we didin Section 3.4. To classify identifiers, Grimm uses a standard lexical feedback mechanism. In the presence of backtracking, the side effects required by this mechanism
must be performed within (nested) transactions.

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14:24J.-H. Jourdan and F. Pottier

Semantic predicates makes it possible to invalidate a production based on an arbitrary predicate evaluated at parse time. They are available in several parser generators, including Rats!, ANTLR and in the GLR mode of Bison. They could, in principle,
lift the need for a lexical feedback mechanism by disabling the reductions containing
an identifier token when this identifier does not have the right status in the current
environment. However, to the best of our knowledge, we are not aware of any C11parser that would use semantic predicates.
We have assumed that the C source code has been preprocessed and therefore contains no preprocessor directives. In contrast, some authors attempt to parse without
expanding macros, without reading #included files, and/or without resolving static conditionals.
Padioleau [Padioleau 2009], for instance, performs neither of these three tasks. He
extends the grammar of C with new terminal symbols, including #include, #ifdef, etc.,
as well as several classes of identifiers. Indeed, in addition to typedef names and variables, he wishes to recognize identifiers that denote macros. Furthermore, he wishes todistinguish between several typical families of macros, such as macros that expand tostatements, macros that expand to loop headers, and so on. This classification involves
heuristic aspects (for instance, it exploits indentation). It takes the form of a transformation of the token stream, which is inserted between the lexer and the parser.
Padioleau’s work is used in Coccinelle [Padioleau et al. 2008], a tool that helps analyze
and evolve C code.
Gazzillo and Grimm [Gazzillo and Grimm 2012] expand macros and read #included
files, but do not resolve static conditionals, as they wish to parse all possible “configurations” of the software simultaneously. They introduce a new LR engine, Fork-MergeLR, which relies on standard LALR(1) parse tables. Like GLR, it is a nondeterministic
parsing algorithm. However, the need for nondeterminism does not stem from ambiguity in the grammar; it stems from the desire to parse all possible configurations
simultaneously. Gazzillo and Grimm’s use Roskind’s grammar, extended with support
for common gcc extensions. Their parser uses a form of lexical feedback [Gazzillo andGrimm 2012, §5.2]. When it encounters an identifier that denotes a typedef name in
one configuration and a variable in another configuration, it forks two subparsers.
5. CONCLUSION

In this paper, we have reviewed several of the difficulties that arise in writing a C11
parser, and we have presented such a parser. It is a slightly simplified version of the“pre-parser” found in the CompCert C compiler.
It is very concise: the grammar, including (just) the semantic actions necessary to
perform lexical feedback, is under 500 (nonblank, noncomment) lines of code; the lexer
and the support code are less than 400 lines.
To the best of our knowledge, this parser complies with the C11 standard. However,it has not been extensively tested. (Running it on large existing code bases would require extending it with support for the most commonly used extensions of C, such as
the GNU extensions.) We offer only a small suite of “tricky” C11 programs that can beused as a “torture test”.
There exist many commercial and academic tools that can parse C. Some of them
have been discussed in Section 4. Unfortunately, these parsers are often either designed for an older version of the language (such as C89) or plain incorrect. The C11parsers found in popular compilers, such as GCC and Clang, are very likely correct,
but their size is in the tens of thousands of lines. Therefore, we believe that there is aneed for a simple reference implementation that is easy to adopt and extend. We hopethat our parser can play this role.
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Although we discuss only C11 in this paper, our parser can also parse C99, which is asubset of C11. C89, on the other hand, is not a subset of C11. There are differences concerning the scoping rules and, more importantly, the “implicit int” rule, which allows
declarations without a type specifier, in which case the default type int is used [ANSI
1989, 3.5.2]. This makes C89 more difficult to parse. Our distribution [Jourdan andPottier 2017] includes a C89 parser, which is separate from our C11 parser. (It is basedon a different grammar.) It supports the “implicit int” rule, handles all C11 constructs,
and supports either set of scoping rules, depending on its configuration. Therefore,
when configured to use the C89 scoping rules, this parser accepts every C89 program;and, when configured to use the C99/C11 scoping rules, it accepts every C99 or C11
program. For the sake of brevity, it is not discussed in the paper.
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ANSI. 1989. ANSI X3.159-1989 Programming Language C. (1989).
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Eli Bendersky. 2012. How Clang handles the type / variable name ambiguity of C/C++. (July 2012). http://eli.thegreenplace.net/2012/07/05/how-clang-handles-the-type-variable-name-ambiguity-of-cc/.
Doug Brown, John Levine, and Tony Mason. 1992. Lex & Yacc, 2nd Edition. O’Reilly Media.
Jutta Degener. 2012. C11 Yacc grammar. http://www.quut.com/c/ANSI-C-grammar-y.html. (Dec. 2012).
Chris Dodd and Vadim Maslov. 1999. BtYacc.
Charles Donnelly and Richard Stallman. 2015. Bison.
Paul Gazzillo and Robert Grimm. 2012. SuperC: Parsing All of C by Taming the Preprocessor. In ACM
SIGPLAN Conference on Programming Language Design and Implementation (PLDI). 323–334.
Robert Grimm. 2006. Better extensibility through modular syntax. In ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI). 38–51.
Dick Grune and Ceriel J. H. Jacobs. 2008. Parsing techniques: a practical guide, second edition. Springer.
ISO. 2011. ISO/IEC 9899:2011 – Programming languages – C. (2011).
Clinton L. Jeffery. 2003. Generating LR syntax error messages from examples. ACM Transactions on Programming Languages and Systems 25, 5 (2003), 631–640.
Jacques-Henri Jourdan. 2015. GCC bug #67784: Incorrect parsing when using declarations in for loops andtypedefs. (Sept. 2015).
Jacques-Henri Jourdan and François Pottier. 2017. A simple, possibly correct LR parser for C11 – implementation and test suite. https://github.com/jhjourdan/C11parser. (Feb. 2017).
Jacques-Henri Jourdan, François Pottier, and Xavier Leroy. 2012. Validating LR(1) Parsers. In European
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Brian W. Kernighan and Dennis Ritchie. 1988. The C Programming Language, Second Edition. PrenticeHall.
Donald E. Knuth. 1965. On the translation of languages from left to right. Information & Control 8, 6 (1965),
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Xavier Leroy. 2009. Formal verification of a realistic compiler. Commun. ACM 52, 7 (2009), 107–115.
Xavier Leroy. 2017. The CompCert C verified compiler. https://github.com/AbsInt/CompCert. (2017).
Scott McPeak and George C. Necula. 2004. Elkhound: a Fast, Practical GLR Parser Generator. In International Conference on Compiler Construction (CC) (Lecture Notes in Computer Science), Vol. 2985.
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Yaron Minsky, Anil Madhavapeddy, and Jason Hickey. 2013. Real World OCaml: Functional programming
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Yoann Padioleau. 2009. Parsing C/C++ Code Without Pre-processing. In International Conference on Compiler Construction (CC) (Lecture Notes in Computer Science), Vol. 5501. Springer, 109–125.

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A. GRAMMAR%{
open Context
open Declarator%}%token<string> NAME
%token VARIABLE TYPE
%token CONSTANT STRING_LITERAL%tokenALIGNAS ALIGNOF ATOMIC BOOL COMPLEX IMAGINARY GENERIC NORETURN STATIC_ASSERTTHREAD_LOCAL AUTO BREAK CASE CHAR CONST CONTINUE DEFAULT DO DOUBLE ELSE ENUM
EXTERN FLOAT FOR GOTO IF INLINE INT LONG REGISTER RESTRICT RETURN SHORTSIGNED SIZEOF STATIC STRUCT SWITCH TYPEDEF UNION UNSIGNED VOID VOLATILE WHILE%tokenPTR INC DEC LEFT RIGHT LEQ GEQ EQEQ EQ NEQ LT GT ANDAND BARBAR PLUS MINUSSTAR TILDE BANG SLASH PERCENT HAT BAR QUESTION COLON AND MUL_ASSIGN
DIV_ASSIGN MOD_ASSIGN ADD_ASSIGN SUB_ASSIGN LEFT_ASSIGN RIGHT_ASSIGN
AND_ASSIGN XOR_ASSIGN OR_ASSIGN LPAREN ATOMIC_LPAREN RPAREN LBRACK RBRACKLBRACE RBRACE DOT COMMA SEMICOLON ELLIPSIS%token EOF%type<context> save_context parameter_type_list function_definition1%type<string> typedef_name var_name general_identifier enumeration_constant%type<declarator> declarator direct_declarator(* There is a reduce/reduce conflict in the grammar. It corresponds to theconflict in the second declaration in the following snippet:
typedef int T;
int f(int(T));
It is specified by 6.7.6.3 11: ’T’ should be taken as the type of theparameter of the anonymous function taken as a parameter by f (thus,
f has type (T -> int) -> int).
The reduce/reduce conflict is solved by letting menhir reduce the production
appearing first in this file. This is the reason why we have the[typedef_name_spec] proxy: it is here just to make sure the conflicting
production appears before the other (which concerns [general_identifier]). *)(* These precedence declarations solve the dangling else conflict. *)%nonassoc below_ELSE%nonassoc ELSE
%start<unit> translation_unit_file%%(* Helpers *)(* [option(X)] represents a choice between nothing and [X].
[ioption(X)] is the same thing, but is inlined at its use site,which in some cases is necessary in order to avoid a conflict.
By convention, [X?] is syntactic sugar for [option(X)]. *)%inline ioption(X):| /* nothing */| X{}

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option(X):| o = ioption(X){ o }(* By convention, [X*] is syntactic sugar for [list(X)]. *)list(X):| /* nothing */| X list(X){}(* A list of A’s and B’s that contains exactly one A: *)list_eq1(A, B):| A B*| B list_eq1(A, B){}(* A list of A’s and B’s that contains at least one A: *)list_ge1(A, B):| A B*| A list_ge1(A, B)| B list_ge1(A, B){}(* A list of A’s, B’s and C’s that contains exactly one A and exactly one B: *)list_eq1_eq1(A, B, C):| A list_eq1(B, C)| B list_eq1(A, C)| C list_eq1_eq1(A, B, C){}(* A list of A’s, B’s and C’s that contains exactly one A and at least one B: *)list_eq1_ge1(A, B, C):| A list_ge1(B, C)| B list_eq1(A, C)| B list_eq1_ge1(A, B, C)| C list_eq1_ge1(A, B, C){}(* Upon finding an identifier, the lexer emits two tokens. The first token,[NAME], indicates that a name has been found; the second token, either [TYPE]
or [VARIABLE], tells what kind of name this is. The classification is
performed only when the second token is demanded by the parser. *)typedef_name:| i = NAME TYPE
{ i }var_name:| i = NAME VARIABLE{ i }(* [typedef_name_spec] must be declared before [general_identifier], so that the
reduce/reduce conflict is solved the right way. *)typedef_name_spec:| typedef_name{}

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general_identifier:| i = typedef_name| i = var_name{ i }save_context:| (* empty *){ save_context () }scoped(X):| ctx = save_context x = X{ restore_context ctx; x }(* [declarator_varname] and [declarator_typedefname] are like [declarator]. In
addition, they have the side effect of introducing the declared identifier asa new variable or typedef name in the current context. *)declarator_varname:| d = declarator{ declare_varname (identifier d); d }declarator_typedefname:| d = declarator{ declare_typedefname (identifier d); d }(* End of the helpers, and beginning of the grammar proper: *)primary_expression:| var_name| CONSTANT| STRING_LITERAL| LPAREN expression RPAREN| generic_selection{}
generic_selection:| GENERIC LPAREN assignment_expression COMMA generic_assoc_list RPAREN{}
generic_assoc_list:| generic_association| generic_assoc_list COMMA generic_association{}
generic_association:| type_name COLON assignment_expression| DEFAULT COLON assignment_expression{}
postfix_expression:| primary_expression| postfix_expression LBRACK expression RBRACK| postfix_expression LPAREN argument_expression_list? RPAREN| postfix_expression DOT general_identifier| postfix_expression PTR general_identifier| postfix_expression INC| postfix_expression DEC| LPAREN type_name RPAREN LBRACE initializer_list COMMA? RBRACE{}ACM Transactions on Programming Languages and Systems, Vol. 39, No. 4, Article 14, Publication date: August 2017.

14:30J.-H. Jourdan and F. Pottierargument_expression_list:| assignment_expression| argument_expression_list COMMA assignment_expression{}
unary_expression:| postfix_expression| INC unary_expression| DEC unary_expression| unary_operator cast_expression| SIZEOF unary_expression| SIZEOF LPAREN type_name RPAREN| ALIGNOF LPAREN type_name RPAREN{}
unary_operator:| AND| STAR| PLUS| MINUS| TILDE| BANG{}
cast_expression:| unary_expression| LPAREN type_name RPAREN cast_expression{}
multiplicative_operator:
STAR | SLASH | PERCENT {}multiplicative_expression:| cast_expression| multiplicative_expression multiplicative_operator cast_expression{}
additive_operator:
PLUS | MINUS {}additive_expression:| multiplicative_expression| additive_expression additive_operator multiplicative_expression{}
shift_operator:
LEFT | RIGHT {}shift_expression:| additive_expression| shift_expression shift_operator additive_expression{}
relational_operator:
LT | GT | LEQ | GEQ {}relational_expression:| shift_expression| relational_expression relational_operator shift_expression{}

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equality_operator:
EQEQ | NEQ {}equality_expression:| relational_expression| equality_expression equality_operator relational_expression{}
and_expression:| equality_expression| and_expression AND equality_expression{}
exclusive_or_expression:| and_expression| exclusive_or_expression HAT and_expression{}
inclusive_or_expression:| exclusive_or_expression| inclusive_or_expression BAR exclusive_or_expression{}
logical_and_expression:| inclusive_or_expression| logical_and_expression ANDAND inclusive_or_expression{}
logical_or_expression:| logical_and_expression| logical_or_expression BARBAR logical_and_expression{}
conditional_expression:| logical_or_expression| logical_or_expression QUESTION expression COLON conditional_expression{}
assignment_expression:| conditional_expression| unary_expression assignment_operator assignment_expression{}
assignment_operator:| EQ| MUL_ASSIGN| DIV_ASSIGN| MOD_ASSIGN| ADD_ASSIGN| SUB_ASSIGN| LEFT_ASSIGN| RIGHT_ASSIGN| AND_ASSIGN| XOR_ASSIGN| OR_ASSIGN{}
expression:| assignment_expression| expression COMMA assignment_expression{}

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J.-H. Jourdan and F. Pottier

constant_expression:| conditional_expression{}(* We separate type declarations, which contain an occurrence of [TYPEDEF], andnormal declarations, which do not. This makes it possible to distinguish /inthe grammar/ whether a declaration introduces typedef names or variables in
the context. *)declaration:| declaration_specifiers
init_declarator_list(declarator_varname)?
SEMICOLON| declaration_specifiers_typedef init_declarator_list(declarator_typedefname)? SEMICOLON| static_assert_declaration{}(* [declaration_specifier] corresponds to one declaration specifier in the C11
standard, deprived of TYPEDEF and of type specifiers. *)declaration_specifier:| storage_class_specifier (* deprived of TYPEDEF *)| type_qualifier| function_specifier| alignment_specifier{}(* [declaration_specifiers] requires that at least one type specifier bepresent, and, if a unique type specifier is present, then no other typespecifier be present. In other words, one should have either at least one
nonunique type specifier, or exactly one unique type specifier.
This is a weaker condition than 6.7.2 2. Encoding this condition in thegrammar is necessary to disambiguate the example in 6.7.7 6:
typedef signed int t;
struct tag {unsigned t:4;
const t:5;};
The first field is a named t, while the second is unnamed of type t.
[declaration_specifiers] forbids the [TYPEDEF] keyword. *)declaration_specifiers:| list_eq1(type_specifier_unique,declaration_specifier)| list_ge1(type_specifier_nonunique, declaration_specifier){}(* [declaration_specifiers_typedef] is analogous to [declaration_specifiers],
but requires the [TYPEDEF] keyword to be present (exactly once). *)declaration_specifiers_typedef:| list_eq1_eq1(TYPEDEF, type_specifier_unique,declaration_specifier)| list_eq1_ge1(TYPEDEF, type_specifier_nonunique, declaration_specifier){}(* The parameter [declarator] in [init_declarator_list] and [init_declarator]
is instantiated with [declarator_varname] or [declarator_typedefname]. *)init_declarator_list(declarator):| init_declarator(declarator)| init_declarator_list(declarator) COMMA init_declarator(declarator){}

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init_declarator(declarator):| declarator| declarator EQ c_initializer{}(* [storage_class_specifier] corresponds to storage-class-specifier in the
C11 standard, deprived of [TYPEDEF] (which receives special treatment). *)storage_class_specifier:| EXTERN| STATIC| THREAD_LOCAL| AUTO| REGISTER{}(* A type specifier which can appear together with other type specifiers. *)type_specifier_nonunique:| CHAR| SHORT| INT| LONG| FLOAT| DOUBLE| SIGNED| UNSIGNED| COMPLEX{}(* A type specifier which cannot appear together with other type specifiers. *)type_specifier_unique:| VOID| BOOL| atomic_type_specifier| struct_or_union_specifier| enum_specifier| typedef_name_spec{}
struct_or_union_specifier:| struct_or_union general_identifier? LBRACE struct_declaration_list RBRACE| struct_or_union general_identifier{}
struct_or_union:| STRUCT| UNION{}
struct_declaration_list:| struct_declaration| struct_declaration_list struct_declaration{}
struct_declaration:| specifier_qualifier_list struct_declarator_list? SEMICOLON| static_assert_declaration{}

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14:34J.-H. Jourdan and F. Pottier(* [specifier_qualifier_list] is as in the standard, except it also encodes thesame constraint as [declaration_specifiers] (see above). *)specifier_qualifier_list:| list_eq1(type_specifier_unique,type_qualifier)| list_ge1(type_specifier_nonunique, type_qualifier){}struct_declarator_list:| struct_declarator| struct_declarator_list COMMA struct_declarator{}
struct_declarator:| declarator| declarator? COLON constant_expression{}
enum_specifier:| ENUM general_identifier? LBRACE enumerator_list COMMA? RBRACE| ENUM general_identifier{}
enumerator_list:| enumerator| enumerator_list COMMA enumerator{}
enumerator:| i = enumeration_constant| i = enumeration_constant EQ constant_expression{ declare_varname i }enumeration_constant:| i = general_identifier{ i }atomic_type_specifier:| ATOMIC LPAREN type_name RPAREN| ATOMIC ATOMIC_LPAREN type_name RPAREN{}
type_qualifier:| CONST| RESTRICT| VOLATILE| ATOMIC{}
function_specifier:
INLINE | NORETURN{}
alignment_specifier:| ALIGNAS LPAREN type_name RPAREN| ALIGNAS LPAREN constant_expression RPAREN{}
declarator:| d = direct_declarator{ d }| pointer d = direct_declarator{ other_declarator d }ACM Transactions on Programming Languages and Systems, Vol. 39, No. 4, Article 14, Publication date: August 2017.

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14:35(* The occurrences of [save_context] inside [direct_declarator] and[direct_abstract_declarator] seem to serve no purpose. In fact, they are
required in order to avoid certain conflicts. In other words, we must savethe context at this point because the LR automaton is exploring multiple
avenues in parallel and some of them do require saving the context. *)direct_declarator:| i = general_identifier{ identifier_declarator i }| LPAREN save_context d = declarator RPAREN{ d }| d = direct_declarator LBRACK type_qualifier_list? assignment_expression? RBRACK| d = direct_declarator LBRACK STATIC type_qualifier_list? assignment_expression RBRACK| d = direct_declarator LBRACK type_qualifier_list STATIC assignment_expression RBRACK| d = direct_declarator LBRACK type_qualifier_list? STAR RBRACK{ other_declarator d }| d = direct_declarator LPAREN ctx = scoped(parameter_type_list) RPAREN{ function_declarator d ctx }| d = direct_declarator LPAREN save_context identifier_list? RPAREN{ other_declarator d }pointer:| STAR type_qualifier_list? pointer?
{}type_qualifier_list:| type_qualifier_list? type_qualifier{}parameter_type_list:| parameter_list option(COMMA ELLIPSIS {}) ctx = save_context{ ctx }
parameter_list:| parameter_declaration| parameter_list COMMA parameter_declaration{}
parameter_declaration:| declaration_specifiers declarator_varname| declaration_specifiers abstract_declarator?
{}
identifier_list:| var_name| identifier_list COMMA var_name{}type_name:| specifier_qualifier_list abstract_declarator?
{}
abstract_declarator:| pointer| ioption(pointer) direct_abstract_declarator{}

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J.-H. Jourdan and F. Pottier

direct_abstract_declarator:| LPAREN save_context abstract_declarator RPAREN| direct_abstract_declarator? LBRACK ioption(type_qualifier_list) assignment_expression? RBRACK| direct_abstract_declarator? LBRACK STATIC type_qualifier_list? assignment_expression RBRACK| direct_abstract_declarator? LBRACK type_qualifier_list STATIC assignment_expression RBRACK| direct_abstract_declarator? LBRACK STAR RBRACK| ioption(direct_abstract_declarator) LPAREN scoped(parameter_type_list)? RPAREN{}
c_initializer:| assignment_expression| LBRACE initializer_list COMMA? RBRACE{}
initializer_list:| designation? c_initializer| initializer_list COMMA designation? c_initializer{}
designation:| designator_list EQ{}
designator_list:| designator_list? designator{}
designator:| LBRACK constant_expression RBRACK| DOT general_identifier{}
static_assert_declaration:| STATIC_ASSERT LPAREN constant_expression COMMA STRING_LITERAL RPAREN SEMICOLON{}
statement:| labeled_statement| scoped(compound_statement)| expression_statement| scoped(selection_statement)| scoped(iteration_statement)| jump_statement{}
labeled_statement:| general_identifier COLON statement| CASE constant_expression COLON statement| DEFAULT COLON statement{}
compound_statement:| LBRACE block_item_list? RBRACE{}
block_item_list:| block_item_list? block_item{}
block_item:| declaration| statement{}

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expression_statement:| expression? SEMICOLON{}
selection_statement:| IF LPAREN expression RPAREN scoped(statement) ELSE scoped(statement)| IF LPAREN expression RPAREN scoped(statement) %prec below_ELSE| SWITCH LPAREN expression RPAREN scoped(statement){}
iteration_statement:| WHILE LPAREN expression RPAREN scoped(statement)| DO scoped(statement) WHILE LPAREN expression RPAREN SEMICOLON| FOR LPAREN expression? SEMICOLON expression? SEMICOLON expression? RPAREN scoped(statement)| FOR LPAREN declaration expression? SEMICOLON expression? RPAREN scoped(statement){}
jump_statement:| GOTO general_identifier SEMICOLON| CONTINUE SEMICOLON| BREAK SEMICOLON| RETURN expression? SEMICOLON{}
translation_unit_file:| external_declaration translation_unit_file| external_declaration EOF{}
external_declaration:| function_definition| declaration{}
function_definition1:| declaration_specifiers d = declarator_varname{ let ctx = save_context () inreinstall_function_context d;
ctx }function_definition:| ctx = function_definition1 declaration_list? compound_statement{ restore_context ctx }declaration_list:| declaration| declaration_list declaration{}

ACM Transactions on Programming Languages and Systems, Vol. 39, No. 4, Article 14, Publication date: August 2017.