In this section, we describe the syntax and informal semantics of Haskell expressions, including their translations into the Haskell kernel, where appropriate. Except in the case of let expressions, these translations preserve both the static and dynamic semantics. Free variables and constructors used in these translations refer to entities defined by the Prelude. To avoid clutter, we use True instead of Prelude.True or map instead of Prelude.map. (Prelude.True is a qualified name as described in Section 5.3.)
In the syntax that follows, there are some families of nonterminals indexed by precedence levels (written as a superscript). Similarly, the nonterminals op, varop, and conop may have a double index: a letter l, r, or n for left, right or nonassociativity and a precedence level. A precedencelevel variable i ranges from 0 to 9; an associativity variable a varies over {l, r, n}. Thus, for example
aexp  >  ( exp^{i+1} qop^{(a,i)} ) 
exp  >  exp^{0} :: [context =>] type  (expression type signature) 
  exp^{0}  
exp^{i}  >  exp^{i+1} [qop^{(n,i)} exp^{i+1}]  
  lexp^{i}  
  rexp^{i}  
lexp^{i}  >  (lexp^{i}  exp^{i+1}) qop^{(l,i)} exp^{i+1}  
lexp^{6}  >   exp^{7}  
rexp^{i}  >  exp^{i+1} qop^{(r,i)} (rexp^{i}  exp^{i+1})  
exp^{10}  >  \ apat_{1} ... apat_{n} > exp  (lambda abstraction, n>=1) 
  let decls in exp  (let expression)  
  if exp then exp else exp  (conditional)  
  case exp of { alts }  (case expression)  
  do { stmts }  (do expression)  
  fexp  
fexp  >  [fexp] aexp  (function application) 
aexp  >  qvar  (variable) 
  gcon  (general constructor)  
  literal  
  ( exp )  (parenthesized expression)  
  ( exp_{1} , ... , exp_{k} )  (tuple, k>=2)  
  [ exp_{1} , ... , exp_{k} ]  (list, k>=1)  
  [ exp_{1} [, exp_{2}] .. [exp_{3}] ]  (arithmetic sequence)  
  [ exp  qual_{1} , ... , qual_{n} ]  (list comprehension, n>=1)  
  ( exp^{i+1} qop^{(a,i)} )  (left section)  
  ( qop^{(a,i)} exp^{i+1} )  (right section)  
  qcon { fbind_{1} , ... , fbind_{n} }  (labeled construction, n>=0)  
  aexp_{{qcon}} { fbind_{1} , ... , fbind_{n} }  (labeled update, n >= 1) 
As an aid to understanding this grammar, Table 1 shows the relative precedence of expressions, patterns and definitions, plus an extended associativity.  indicates that the item is nonassociative.
Item  Associativity 
simple terms, parenthesized terms   
irrefutable patterns (~)   
aspatterns (@)  right 
function application  left 
do, if, let, lambda(\), case (leftwards)  right 
case (rightwards)  right 
infix operators, prec. 9  as defined 
...  ... 
infix operators, prec. 0  as defined 
function types (>)  right 
contexts (=>)   
type constraints (::)   
do, if, let, lambda(\) (rightwards)  right 
sequences (..)   
generators (<)   
grouping (,)  nary 
guards ()   
case alternatives (>)   
definitions (=)   
separation (;)  nary 
The grammar is ambiguous regarding the extent of lambda abstractions, let expressions, and conditionals. The ambiguity is resolved by the metarule that each of these constructs extends as far to the right as possible. As a consequence, each of these constructs has two precedences, one to its left, which is the precedence used in the grammar; and one to its right, which is obtained via the metarule. See the sample parses below.
Expressions involving infix operators are disambiguated by the operator's fixity (see Section 4.4.2). Consecutive unparenthesized operators with the same precedence must both be either left or right associative to avoid a syntax error. Given an unparenthesized expression "x qop^{(a,i)} y qop^{(b,j)} z", parentheses must be added around either "x qop^{(a,i)} y" or "y qop^{(b,j)} z" when i=j unless a=b=l or a=b=r.
Negation is the only prefix operator in Haskell ; it has the same precedence as the infix  operator defined in the Prelude (see Figure 2).
Sample parses are shown below.
This  Parses as 
f x + g y  (f x) + (g y) 
 f x + y  ( (f x)) + y 
let { ... } in x + y  let { ... } in (x + y) 
z + let { ... } in x + y  z + (let { ... } in (x + y)) 
f x y :: Int  (f x y) :: Int 
\ x > a+b :: Int  \ x > ((a+b) :: Int) 
For the sake of clarity, the rest of this section shows the syntax of expressions without their precedences.
Translations of Haskell expressions use error and undefined to explicitly indicate where execution time errors may occur. The actual program behavior when an error occurs is up to the implementation. The messages passed to the error function in these translations are only suggestions; implementations may choose to display more or less information when an error occurs.
aexp  >  qvar  (variable) 
  gcon  (general constructor)  
  literal 
gcon  >  ()  
  []  
  (,{,})  
  qcon  
var  >  varid  ( varsym )  (variable) 
qvar  >  qvarid  ( qvarsym )  (qualified variable) 
con  >  conid  ( consym )  (constructor) 
qcon  >  qconid  ( gconsym )  (qualified constructor) 
varop  >  varsym  `varid `  (variable operator) 
qvarop  >  qvarsym  `qvarid `  (qualified variable operator) 
conop  >  consym  `conid `  (constructor operator) 
qconop  >  gconsym  `qconid `  (qualified constructor operator) 
op  >  varop  conop  (operator) 
qop  >  qvarop  qconop  (qualified operator) 
gconsym  >  :  qconsym 
Alphanumeric operators are formed by enclosing an identifier between grave accents (backquotes). Any variable or constructor may be used as an operator in this way. If fun is an identifier (either variable or constructor), then an expression of the form fun x y is equivalent to x `fun`y. If no fixity declaration is given for `fun` then it defaults to highest precedence and left associativity (see Section 4.4.2).
Similarly, any symbolic operator may be used as a (curried) variable or constructor by enclosing it in parentheses. If op is an infix operator, then an expression or pattern of the form x op y is equivalent to (op) x y.
Qualified names may only be used to reference an imported variable or
constructor (see Section 5.3)
but not in the definition of a new variable or constructor. Thus
let F.x = 1 in F.x  invalid
incorrectly uses a qualifier in the definition of x, regardless of
the module containing this definition. Qualification does not affect
the nature of an operator: F.+ is an infix operator just as + is.
Special syntax is used to name some constructors for some of the builtin types, as found in the production for gcon and literal. These are described in Section 6.1.
An integer literal represents the application of the function fromInteger to the appropriate value of type Integer. Similarly, a floating point literal stands for an application of fromRational to a value of type Rational (that is, Ratio Integer).
Translation:The integer literal i is equivalent to fromInteger i, where fromInteger is a method in class Num (see Section 6.4.1).The floating point literal f is equivalent to fromRational (n Ratio.% d), where fromRational is a method in class Fractional and Ratio.% constructs a rational from two integers, as defined in the Ratio library. The integers n and d are chosen so that n/d = f. 
fexp  >  [fexp] aexp  (function application) 
exp  >  \ apat_{1} ... apat_{n} > exp 
Function application is written e_{1} e_{2}. Application associates to the left, so the parentheses may be omitted in (f x) y. Because e_{1} could be a data constructor, partial applications of data constructors are allowed.
Lambda abstractions are written \ p_{1} ... p_{n} > e, where the p_{i} are patterns. An expression such as \x:xs>x is syntactically incorrect; it may legally be written as \(x:xs)>x.
The set of patterns must be linearno variable may appear more than once in the set.
Translation:The following identity holds:

exp  >  exp_{1} qop exp_{2}  
   exp  (prefix negation)  
qop  >  qvarop  qconop  (qualified operator) 
The form e_{1} qop e_{2} is the infix application of binary operator qop to expressions e_{1} and e_{2}.
The special form e denotes prefix negation, the only prefix operator in Haskell , and is syntax for negate (e). The binary  operator does not necessarily refer to the definition of  in the Prelude; it may be rebound by the module system. However, unary  will always refer to the negate function defined in the Prelude. There is no link between the local meaning of the  operator and unary negation.
Prefix negation has the same precedence as the infix operator  defined in the Prelude (see Table 2). Because e1e2 parses as an infix application of the binary operator , one must write e1(e2) for the alternative parsing. Similarly, () is syntax for (\ x y > xy), as with any infix operator, and does not denote (\ x > x)one must use negate for that.
Translation:The following identities hold:

aexp  >  ( exp qop ) 
  ( qop exp ) 
Sections are written as ( op e ) or ( e op ), where op is a binary operator and e is an expression. Sections are a convenient syntax for partial application of binary operators.
Syntactic precedence rules apply to sections as follows. (op e) is legal if and only if (x op e) parses in the same way as (x op (e)); and similarly for (e op). For example, (*a+b) is syntactically invalid, but (+a*b) and (*(a+b)) are valid. Because (+) is left associative, (a+b+) is syntactically correct, but (+a+b) is not; the latter may legally be written as (+(a+b)).
Because  is treated specially in the grammar, ( exp) is not a section, but an application of prefix negation, as described in the preceding section. However, there is a subtract function defined in the Prelude such that (subtract exp) is equivalent to the disallowed section. The expression (+ ( exp)) can serve the same purpose.
Translation:The following identities hold:

exp  >  if exp_{1} then exp_{2} else exp_{3} 
A conditional expression has the form if e_{1} then e_{2} else e_{3} and returns the value of e_{2} if the value of e_{1} is True, e_{3} if e_{1} is False, and __ otherwise.
Translation:The following identity holds:

exp  >  exp_{1} qop exp_{2}  
aexp  >  [ exp_{1} , ... , exp_{k} ]  (k>=1) 
  gcon  
gcon  >  []  
  qcon  
qcon  >  ( gconsym )  
qop  >  qconop  
qconop  >  gconsym  
gconsym  >  : 
Lists are written [e_{1}, ..., e_{k}], where k>=1. The list constructor is :, and the empty list is denoted []. Standard operations on lists are given in the Prelude (see Section 6.1.3, and Appendix A notably Section A.1).
Translation:The following identity holds:

aexp  >  ( exp_{1} , ... , exp_{k} )  (k>=2) 
  qcon  
qcon  >  (,{,}) 
Tuples are written (e_{1}, ..., e_{k}), and may be of arbitrary length k>=2. The constructor for an ntuple is denoted by (,...,), where there are n1 commas. Thus (a,b,c) and (,,) a b c denote the same value. Standard operations on tuples are given in the Prelude (see Section 6.1.4 and Appendix A).
Translation:(e_{1}, ..., e_{k}) for k>=2 is an instance of a ktuple as defined in the Prelude, and requires no translation. If t_{1} through t_{k} are the types of e_{1} through e_{k}, respectively, then the type of the resulting tuple is (t_{1}, ..., t_{k}) (see Section 4.1.2). 
aexp  >  gcon 
  ( exp )  
gcon  >  () 
The form (e) is simply a parenthesized expression, and is equivalent to e. The unit expression () has type () (see Section 4.1.2); it is the only member of that type apart from __ (it can be thought of as the "nullary tuple")see Section 6.1.5.
Translation:(e) is equivalent to e. 
aexp  >  [ exp_{1} [, exp_{2}] .. [exp_{3}] ] 
The arithmetic sequence [e_{1}, e_{2} .. e_{3}] denotes a list of values of type t, where each of the e_{i} has type t, and t is an instance of class Enum.
Translation:Arithmetic sequences satisfy these identities:

The semantics of arithmetic sequences therefore depends entirely on the instance declaration for the type t. We give here the semantics for Prelude types, and indications of the expected semantics for other, userdefined, types.
For the type Integer, arithmetic sequences have the following meaning:
Where the type is also an instance of class Bounded and e_{3} is omitted, an implied e_{3} is added of maxBound (if the increment is positive) or minBound (resp. negative). For example, ['a'..'z'] denotes the list of lowercase letters in alphabetical order, and [LT..] is the list [LT,EQ,GT].
For continuous Prelude types that are instances of Enum, namely Float and Double, the semantics is given by the rules for Int, except that the list terminates when the elements become greater than e_{3}+i/2 for positive increment i, or when they become less than e_{3}+i/2 for negative i.
See Figure 5 and Section 4.3.3 for more details of which Prelude type are in Enum.
aexp  >  [ exp  qual_{1} , ... , qual_{n} ]  (list comprehension, n>=0) 
qual  >  pat < exp  (generator) 
  let decls  (local declaration)  
  exp  (guard)  
  (empty qualifier) 
A list comprehension has the form [ e  q_{1}, ..., q_{n} ], n>=1, where the q_{i} qualifiers are either
Such a list comprehension returns the list of elements
produced by evaluating e in the successive environments
created by the nested, depthfirst evaluation of the generators in the
qualifier list. Binding of variables occurs according to the normal
pattern matching rules (see Section 3.17), and if a
match fails then that element of the list is simply skipped over. Thus:
[ x  xs < [ [(1,2),(3,4)], [(5,4),(3,2)] ],
(3,x) < xs ]
yields the list [4,2]. If a qualifier is a guard, it must evaluate
to True for the previous pattern match to succeed.
As usual, bindings in list comprehensions can shadow those in outer
scopes; for example:
[ x  x < x, x < x ]  =  [ z  y < x, z < y] 
Translation:List comprehensions satisfy these identities, which may be used as a translation into the kernel:

As indicated by the translation of list comprehensions, variables bound by let have fully polymorphic types while those defined by < are lambda bound and are thus monomorphic (see Section 4.5.4).
exp  >  let decls in exp 
Let expressions have the general form
let { d_{1} ; ... ; d_{n} } in e,
and introduce a
nested, lexicallyscoped,
mutuallyrecursive list of declarations (let is often called letrec in
other languages). The scope of the declarations is the expression e
and the right hand side of the declarations. Declarations are
described in Section 4. Pattern bindings are matched
lazily; an implicit ~ makes these patterns
irrefutable.
For example,
let (x,y) = undefined in e
does not cause an executiontime error until x or y is evaluated.
Translation:The dynamic semantics of the expression let { d_{1} ; ... ; d_{n} } in e_{0} are captured by this translation: After removing all type signatures, each declaration d_{i} is translated into an equation of the form p_{i} = e_{i}, where p_{i} and e_{i} are patterns and expressions respectively, using the translation in Section 4.4.3. Once done, these identities hold, which may be used as a translation into the kernel:

exp  >  case exp of { alts }  
alts  >  alt_{1} ; ... ; alt_{n}  (n>=0) 
alt  >  pat > exp [where decls]  
  pat gdpat [where decls]  
  (empty alternative)  
gdpat  >  gd > exp [ gdpat ]  
gd  >   exp^{0} 
A case expression has the general form
case e of { p_{1} match_{1} ; ... ; p_{n} match_{n} }
where each match_{i} is of the general form
 g_{i1}  > e_{i1}  
...  
 g_{imi}  > e_{imi}  
where decls_{i} 
Each alternative p_{i} match_{i} consists of a pattern p_{i} and its matches, match_{i}, which consists of pairs of guards g_{ij} and bodies e_{ij} (expressions), as well as optional bindings (decls_{i}) that scope over all of the guards and expressions of the alternative. An alternative of the form
pat > exp where decls
is treated as shorthand for:
pat  True  > exp  
where decls 
A case expression must have at least one alternative and each alternative must have at least one body. Each body must have the same type, and the type of the whole expression is that type.
A case expression is evaluated by pattern matching the expression e against the individual alternatives. The matches are tried sequentially, from top to bottom. The first successful match causes evaluation of the corresponding alternative body, in the environment of the case expression extended by the bindings created during the matching of that alternative and by the decls_{i} associated with that alternative. If no match succeeds, the result is __. Pattern matching is described in Section 3.17, with the formal semantics of case expressions in Section 3.17.3.
exp  >  do { stmts }  (do expression) 
stmts  >  stmt_{1} ; ... ; stmt_{n}  (n>=0) 
stmt  >  exp  
  pat < exp  
  let decls  
  (empty statment) 
A do expression provides a more conventional syntax for monadic programming.
It allows an expression such as
putStr "x: " >>
getLine >>= \l >
return (words l)
to be written in a more traditional way as:
do putStr "x: "
l < getLine
return (words l)
Translation:Do expressions satisfy these identities, which may be used as a translation into the kernel, after eliminating empty stmts:

Different datatypes cannot share common field labels in the same scope. A field label can be used at most once in a constructor. Within a datatype, however, a field name can be used in more than one constructor provided the field has the same typing in all constructors.
aexp  >  qvar 
Field names are used as selector functions. When used as a variable, a field name serves as a function that extracts the field from an object. Selectors are top level bindings and so they may be shadowed by local variables but cannot conflict with other top level bindings of the same name. This shadowing only affects selector functions; in other record constructs, field labels cannot be confused with ordinary variables.
Translation:A field label f introduces a selector function defined as:

aexp  >  qcon { fbind_{1} , ... , fbind_{n} }  (labeled construction, n>=0) 
fbind  >  qvar = exp 
A constructor with labeled fields may be used to construct a value in which the components are specified by name rather than by position. Unlike the braces used in declaration lists, these are not subject to layout; the { and } characters must be explicit. (This is also true of field updates and field patterns.) Construction using field names is subject to the following constraints:
Translation:In the binding f = v, the field f labels v.
The auxiliary function pick^{C}_{i} bs d is defined as follows: If the ith component of a constructor C has the field name f, and if f=v appears in the binding list bs, then pick^{C}_{i} bs d is v. Otherwise, pick^{C}_{i} bs d is the default value d. 
aexp  >  aexp_{<qcon>} { fbind_{1} , ... , fbind_{n} }  (labeled update, n>=1) 
Values belonging to a datatype with field names may be nondestructively updated. This creates a new value in which the specified field values replace those in the existing value. Updates are restricted in the following ways:
Translation:Using the prior definition of pick,

Expression  Translation 
C1 {f1 = 3}  C1 3 undefined 
C2 {f1 = 1, f4 = 'A', f3 = 'B'}  C2 1 'B' 'A' 
x {f1 = 1}  case x of C1 _ f2 > C1 1 f2 
C2 _ f3 f4 > C2 1 f3 f4 
The field f1 is common to both constructors in T. This example translates expressions using constructors in fieldlabel notation into equivalent expressions using the same constructors without field labels. A compiletime error will result if no single constructor defines the set of field names used in an update, such as x {f2 = 1, f3 = 'x'}.
exp  >  exp :: [context =>] type 
Expression typesignatures have the form e :: t, where e is an expression and t is a type (Section 4.1.2); they are used to type an expression explicitly and may be used to resolve ambiguous typings due to overloading (see Section 4.3.4). The value of the expression is just that of exp. As with normal type signatures (see Section 4.4.1), the declared type may be more specific than the principal type derivable from exp, but it is an error to give a type that is more general than, or not comparable to, the principal type.
Translation:

Patterns appear in lambda abstractions, function definitions, pattern bindings, list comprehensions, do expressions, and case expressions. However, the first five of these ultimately translate into case expressions, so defining the semantics of pattern matching for case expressions is sufficient.
Patterns have this syntax:
pat  >  var + integer  (successor pattern) 
  pat^{0}  
pat^{i}  >  pat^{i+1} [qconop^{(n,i)} pat^{i+1}]  
  lpat^{i}  
  rpat^{i}  
lpat^{i}  >  (lpat^{i}  pat^{i+1}) qconop^{(l,i)} pat^{i+1}  
lpat^{6}  >   (integer  float)  (negative literal) 
rpat^{i}  >  pat^{i+1} qconop^{(r,i)} (rpat^{i}  pat^{i+1})  
pat^{10}>  apat  
  gcon apat_{1} ... apat_{k}  (arity gcon = k, k>=1)  
apat  >  var [@ apat]  (as pattern) 
  gcon  (arity gcon = 0)  
  qcon { fpat_{1} , ... , fpat_{k} }  (labeled pattern, k>=0)  
  literal  
  _  (wildcard)  
  ( pat )  (parenthesized pattern)  
  ( pat_{1} , ... , pat_{k} )  (tuple pattern, k>=2)  
  [ pat_{1} , ... , pat_{k} ]  (list pattern, k>=1)  
  ~ apat  (irrefutable pattern)  
fpat  >  qvar = pat 
The arity of a constructor must match the number of subpatterns associated with it; one cannot match against a partiallyapplied constructor.
All patterns must be linear no variable may appear more than once.
Patterns of the form var@pat are called aspatterns,
and allow one to use var
as a name for the value being matched by pat. For example,
case e of { xs@(x:rest) > if x==0 then rest else xs }
is equivalent to:
let { xs = e } in
case xs of { (x:rest) > if x==0 then rest else xs }
Patterns of the form _ are
wildcards and are useful when some part of a pattern
is not referenced on the righthandside. It is as if an
identifier not used elsewhere were put in its place. For example,
case e of { [x,_,_] > if x==0 then True else False }
is equivalent to:
case e of { [x,y,z] > if x==0 then True else False }
In the pattern matching rules given below we distinguish two kinds of patterns: an irrefutable pattern is: a variable, a wildcard, N apat where N is a constructor defined by newtype and apat is irrefutable (see Section 4.2.3), var@apat where apat is irrefutable, or of the form ~apat (whether or not apat is irrefutable). All other patterns are refutable.
Patterns are matched against values. Attempting to match a pattern can have one of three results: it may fail; it may succeed, returning a binding for each variable in the pattern; or it may diverge (i.e. return __). Pattern matching proceeds from left to right, and outside to inside, according to these rules:
Matching any value against the wildcard pattern _ always succeeds and no binding is done.
Operationally, this means that no matching is done on an irrefutable pattern until one of the variables in the pattern is used. At that point the entire pattern is matched against the value, and if the match fails or diverges, so does the overall computation.
Aside from the obvious static type constraints (for example, it is a static error to match a character against a boolean), these static class constraints hold: an integer literal pattern can only be matched against a value in the class Num and a floating literal pattern can only be matched against a value in the class Fractional. A n+k pattern can only be matched against a value in the class Integral.
Many people feel that n+k patterns should not be used. These patterns may be removed or changed in future versions of Haskell .
Here are some examples:
Top level patterns in case expressions and the set of top level patterns in function or pattern bindings may have zero or more associated guards. A guard is a boolean expression that is evaluated only after all of the arguments have been successfully matched, and it must be true for the overall pattern match to succeed. The environment of the guard is the same as the righthandside of the caseexpression alternative, function definition, or pattern binding to which it is attached.
The guard semantics have an obvious influence on the
strictness characteristics of a function or case expression. In
particular, an otherwise irrefutable pattern
may be evaluated because of a guard. For example, in
f ~(x,y,z) [a]  a && y = 1
both a and y will be evaluated by && in the guard.
The semantics of all pattern matching constructs other than case expressions are defined by giving identities that relate those constructs to case expressions. The semantics of case expressions themselves are in turn given as a series of identities, in Figures 34. Any implementation should behave so that these identities hold; it is not expected that it will use them directly, since that would generate rather inefficient code.
Figure 4Semantics of Case Expressions, Part 2 
In Figures 34: e, e' and e_{i} are expressions; g and g_{i} are booleanvalued expressions; p and p_{i} are patterns; v, x, and x_{i} are variables; K and K' are algebraic datatype (data) constructors (including tuple constructors); N is a newtype constructor; and k is a character, string, or numeric literal.
Rule (b) matches a general sourcelanguage case expression, regardless of whether it actually includes guardsif no guards are written, then True is substituted for the guards g_{i,j} in the match_{i} forms. Subsequent identities manipulate the resulting case expression into simpler and simpler forms.
Rule (h) in Figure 4 involves the overloaded operator ==; it is this rule that defines the meaning of pattern matching against overloaded constants.
These identities all preserve the static semantics. Rules (d), (e), and (j) use a lambda rather than a let; this indicates that variables bound by case are monomorphically typed (Section 4.1.4).