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\begin{document}

\title{An External Representation for the GHC Core Language (DRAFT for GHC5.02)}
\author{Andrew Tolmach ({\tt apt@cs.pdx.edu})\\and The GHC Team}

\maketitle
\makeatactive

\abstract{
This document provides a precise definition for the GHC Core language,
so that it can be used to communicate between GHC and new stand-alone
compilation tools such as back-ends or optimizers.
The definition includes a formal grammar and an informal semantics.
An executable typechecker and interpreter (in Haskell), 
which formally embody the static and dynamic semantics,
are available separately.

Note: This is a draft document, which attempts to describe GHC's current
behavior as precisely as possible.  Working notes scattered throughout indicate
areas where further work is needed.  Constructive comments are very welcome, 
both on  the presentation, and on ways in which GHC could be improved in order
to simplify the Core story.
}

\section{Introduction}

The Glasgow Haskell Compiler (GHC) uses an intermediate language, called
``Core,''  as its internal program representation during
several key stages of compiling.
Core resembles a subset of Haskell, but with explicit type annotations
in the style of the polymorphic lambda calculus (F$_\omega$).
GHC's front end translates full Haskell 98 (plus some extensions) into
well-typed Core, which is then repeatedly rewritten by the GHC optimizer.
Ultimately, GHC translates Core into STG-machine code and then into
C or native code.  The rationale for the design of Core and its use are discussed
in existing papers~\cite{ghc-inliner,comp-by-trans-scp}, although the (two different)
idealized versions of Core described therein differ in significant ways
from the actual Core language in current GHC.

Researchers interested in writing just {\it part} of a Haskell compiler,
such as a new back-end or a new optimizer pass, might like to make
use of GHC to provide the other parts of the compiler.  For example, they
might like to use GHC's front end to parse, desugar, and type-check source Haskell,
then feeding the resulting code to their own back-end tool.
Currently, they can only do this by linking their code into the
GHC executable, which is an arduous process (and essentially requires
the new code to be written in Haskell).   It would be much easier for
external developers if GHC could be made to produce Core files in
an agreed-upon external format.  To allow the widest range of interoperability,
the external format should be text-based; pragmatically, it should
also be human-readable. (It may ultimately be desirable to use a
standard interchange base format such as ASDL or XML.)

In the past, Core has had no rigorously defined external representation, although 
by setting certain compiler flags, one can get a (rather ad-hoc) textual
representation to be printed at various points in the compilation process;
this is usually done to help debug the compiler.  To make Core fully useable
a bi-directional communication format, it will be necssary to

\begin{enumerate}
\item define precisely the external format of Core;

\item modify GHC to produce external Core files, if so requested, at one or more
useful points in the compilation sequence -- e.g., just before optimization,
or just after;

\item modify GHC to accept external Core files in place of Haskell 
source files, again at one or more useful points.

\end{enumerate}

The first two facilities will let one couple GHC's front-end (parser,
type-checker, etc.), and optionally its optimizer, with new back-end tools.
Adding the last facility will let one implement new Core-to-Core 
transformations in an external tool and integrate them into GHC. It will also
allow new front-ends to generate Core that can be fed into GHC's optimizer or 
back end; however, because there are many (undocumented)
idiosynracies in the way GHC produces Core from source Haskell, it will be hard
for an external tool to produce Core that can be integrated with GHC-produced core 
(e.g., for the Prelude), and we don't aim to support this.

This document addresses the first requirement, a formal Core definition,
by proposing  a formal grammar for an external representation of Core
(Section~\ref{sec:external}, and 
an informal semantics (Section~\ref{sec:informal}.

Beginning in GHC5.02, external Core (post-optimization) adhering to this definition
can be generated using the compiler flag @-fext-core@.

Formal static and dynamic semantics in the form of an executable typechecker and interpreter
are available separately in the GHC source tree under @fptools/ghc/utils/ext-core@.

\section{External Grammar of Core}
\label{sec:external}

In designing the external grammar, we have tried to strike a balance among
a number of competing goals, including easy parseability by machines,
easy readability by humans, and adequate structural simplicity to 
allow straightforward presentations of the semantics. This has inevitably
led to certain compromise. In particular:

\begin{itemize}
\item In order to avoid explosion of parentheses, various standard precedences
and short-cuts are supported for expressions, types, and kinds; this led to the introduction
of multiple non-terminals for each of these syntactic categories, which
makes the concrete grammar longer and more complex than the underlying abstract syntax.

\item On the other hand, the grammar has been kept simpler by avoiding special syntax for 
tuple types and terms; tuples (both boxed and unboxed) are treated 
as ordinary constructors. 

\item All type abstractions and applications are given in full, even though
some of them (e.g., for tuples) could be reconstructed; this permits Core to
be parsed without the necessity of performing any type reconstruction.

\item The syntax of identifiers is heavily restricted (essentially to just
alphanumerics); this again makes Core easier to parse but harder to read.
\end{itemize}

\workingnote{These choices are certainly debatable.  In particular, keeping 
type applications on tuples and case arms considerably increases the size of core files and
makes them less human-readable, though it allows a Core parser to be simpler.}

We use the following notational conventions for syntax:

\begin{tabular}{ll}
{\it [ pat ]} & optional \\
{\it \{ pat \}} & zero or more repetitions \\
{\it \{ pat \}$^{+}$} & one or more repetitions \\
{\it pat$_1$ \orderives\ pat$_2$} & choice \\
@fibonacci@ & terminal syntax in typewriter font \\
\end{tabular}

{\it
\begin{tabular}{lrclr}
{\rm Module} &	 module &	 \derives &	 
	\multicolumn{2}{l}{@\%module@ mident \many{tdef @;@} \many{\optional{@\%local@} vdefg @;@}} \\
\\
{\rm Type defn.} &	 tdef &	 \derives &	@%data@ qtycon \many{tbind} @=@ @{@ cdef \many{@;@ cdef} @}@ & {\rm algebraic type}\\
   		 &	 &	 \orderives &	 @%newtype@ qtycon \many{tbind} \optional{@=@ ty} &	 {\rm newtype} \\
\\
{\rm Constr. defn.} &	cdef &	 \derives &	 qdcon \many{@\at@ tbind} \many{aty} \\
\\
{\rm Value defn.}  &	vdefg &	 \derives &	 @%rec@ @{@ vdef \many{@;@ vdef} @}@ &			 {\rm recursive} \\
      		   &	&	 \orderives &	 vdef &	 						 {\rm non-recursive} \\
		   &    vdef  &  \derives & qvar @::@ ty @=@ exp & \\
\\
{\rm Atomic expr.} &     aexp &  \derives &	 qvar &	 						{\rm variable} \\
		 &	&	 \orderives &	 qdcon &	 					{\rm data constructor}\\ 
		 &	&	 \orderives &	 lit &	 						{\rm literal} \\
		 &	&	 \orderives &	 @(@ exp @)@ &						{\rm nested expr.}\\
\\
{\rm Expression} &	exp   &  \derives    &   aexp & 						{\rm atomic expresion}\\
	         &	&	\orderives  &    aexp \oneormore{arg} & 				{\rm application}\\
		 &	&	 \orderives &	 @\@ \oneormore{binder} @->@ exp &		 	{\rm abstraction}\\
		 &	&	 \orderives &	 @%let@ vdefg @%in@ exp &	 			{\rm local definition}\\
		 &	&	 \orderives &	 @%case@ exp @%of@ vbind @{@ alt \many{@;@ alt} @}@ &	{\rm case expression}\\
		 &	&	 \orderives &	 @%coerce@ aty exp &					{\rm type coercion}\\
		 &	&	 \orderives &	 @%note@  @"@ \many{char} @"@ exp &			{\rm expression note}\\
		 &	&	 \orderives &	 @%external@ @"@ \many{char} @"@ aty &			{\rm external reference}\\
\\
{\rm Argument}   &	arg & 	\derives &	 \at\ aty &						{\rm type argument}\\
		 &	&	 \orderives &	 aexp &							{\rm value argument} \\
\\
{\rm Case alt.} &	alt &	 \derives &	qdcon  \many {@\at@ tbind} \many{vbind} @->@ exp &{\rm constructor alternative}\\
		&	&	 \orderives &	 lit @->@ exp &	 			{\rm literal alternative} \\
		&	&	 \orderives &	 @%_@ @->@ exp & 				{\rm default alternative} \\
\\
{\rm Binder}	 & 	binder & \derives & \at\ tbind	&					{\rm type binder}\\
		 & 		& \orderives & 	vbind	&						{\rm value binder}\\
\\
{\rm Type binder} &	tbind & \derives   & tyvar & {\rm implicitly of  kind @*@} \\
                  &           & \orderives & @(@ tyvar @::@ kind @)@ & {\rm explicitly kinded} \\
\\
{\rm Value binder} & 	vbind & \derives &   @(@ var @::@ ty @)@ \\
\\
{\rm Literal} &	 lit &	 \derives &	 @(@ [@-@] \oneormore{digit} @::@ ty @)@ & {\rm integer} \\
	    &	&	 \orderives &	 @(@ [@-@] \oneormore{digit} @.@ \oneormore{digit} @::@ ty @)@ & {\rm rational} \\
	    &	&	 \orderives &	 @(@ @'@ char @'@ @::@ ty @)@ & {\rm character} \\
	    &	&	 \orderives &	 @(@ @"@ \many{char} @"@ @::@ ty @)@ & {\rm string} \\
\\
{\rm Character}  & char & \derives & \multicolumn{2}{l}{any ASCII character in range 0x20-0x7E except 0x22,0x27,0x5c}\\
		&	& \orderives & @\x@ hex hex  & {\rm ASCII code escape sequence} \\
		&  hex   & \derives & @0@ \orderives  \ldots \orderives  @9@ \orderives  @a@ \orderives  \ldots \orderives  @f@ \\
\end{tabular}

\begin{tabular}{lrclr}
{\rm Atomic type} & aty & \derives &	 tyvar &	 				{\rm type variable} \\
 	  &	&	 \orderives &	 qtycon &					{\rm type constructor}\\
	  & 	&  	 \orderives &	 @(@ ty @)@ &					{\rm nested type}\\
\\
{\rm Basic type} & bty  & \derives & 	aty  & 						{\rm atomic type}\\
	          &      & \orderives & bty aty &	 				{\rm type application}\\
\\
{\rm Type} &	 ty &	 \derives   & 	bty & 						{\rm basic type}\\
	  &	&	 \orderives &	@%forall@ \oneormore{tbind} @.@ ty  &		{\rm type abstraction}\\
	  &	&	 \orderives &	bty @->@ ty  &	 				{\rm arrow type construction} \\
\\
{\rm Atomic kind} & akind & \derives &   @*@ &				{\rm lifted kind}\\
		& 	& \orderives &	 @#@ &				{\rm unlifted kind}\\
		& 	& \orderives &   @?@ &				{\rm open kind}\\
		& 	& \orderives &   @(@ kind @)@&			{\rm nested kind}\\
\\
{\rm Kind} &	kind &	 \derives &	 akind & 			{\rm atomic kind}\\
 	   &	&	 \orderives &	 akind @->@ kind 	 &	{\rm arrow kind} \\
\\
{\rm Identifier}	&	mident & \derives &uname &	{\rm module} \\
	&	tycon &	 \derives &	 uname &	 	{\rm type constr.}  \\
	&	qtycon & \derives &	 mident @.@  tycon &	{\rm qualified type constr.} \\
	&	tyvar &	 \derives &	 lname &		{\rm type variable} \\
	&	dcon &	 \derives &	 uname &	 	{\rm data constr.} \\
	&	qdcon &	 \derives &	 mident @.@  dcon & 	{\rm qualified data constr.} \\
	&	var &	 \derives &	 lname &		{\rm variable} \\
	&	qvar &	 \derives &	 [ mident @.@ ] var &	{\rm optionally qualified variable} \\
\\
{\rm Name} 	&	lname  &  \derives & 	 lower \many{namechar} \\
 	&       uname &  \derives & 	 upper \many{namechar} & \\
	&	namechar & \derives &	 lower \orderives\  upper \orderives\  digit \orderives\  @'@ \\
	&	lower &  \derives &      @a@ \orderives\  @b@ \orderives\  \ldots \orderives\  @z@ \orderives\  @_@ \\
	&	upper &  \derives &      @A@ \orderives\  @B@ \orderives\  \ldots \orderives\  @Z@ \\
	& 	digit &  \derives & 	 @0@ \orderives\  @1@ \orderives\  \ldots \orderives\  @9@ \\
\\
\end{tabular}
}

\workingnote{Should add some provision for comments.}

\section{Informal Semantics}
\label{sec:informal}

Core resembles a explicitly-typed polymorphic lambda calculus (F$_\omega$), with the addition
of local @let@ bindings, algebraic type definitions, constructors, and @case@ expressions,
and primitive types, literals and operators.
It is hoped that this makes it easy to obtain an informal understanding of Core programs
without elaborate description.   This section therefore concentrates on the less obvious points.

\subsection{Program Organization and Modules}

Core programs are organized into {\em modules}, corresponding directly to source-level Haskell modules.
Each module has a identifying name {\it mident}.

Each module may contain the following kinds of top-level declarations:
\begin{itemize}
\item Algebraic data type declarations, each defining a type constructor and one or more data constructors;
\item Newtype declarations,  corresponding to Haskell @newtype@ declarations, each defining a type constructor; and
\item Value declarations, defining the types and values of top-level variables.
\end{itemize}
No type constructor, data constructor, or top-level value may be declared more than once within a given module.
All the type declarations are (potentially) mutually recursive. Value declarations must be
in dependency order, with explicit grouping of mutually recursive declarations.

Identifiers defined in top-level declarations may be {\it external} or {\it internal}.
External identifiers can be referenced from any other module in
the program, using conventional dot notation (e.g., @PrelBase.Bool@, @PrelBase.True@).  
Internal identifiers are visible only within the defining module.
All type and data constructors are external, and are always defined and referenced using
fully qualified names (with dots).  A top-level value is external if it is defined and referenced 
using a fully qualified name with a dot (e.g., @MyModule.foo = ...@); otherwise, it is internal
(e.g., @bar = ...@).  
Note that the notion of external identifier does not necessarily coincide with that of ``exported''
identifier in a Haskell source module: all constructors are external, even if not exported, and
non-exported values may be external if they are referenced from potentially in-lineable exported values.
Core modules have no explicit import or export lists. 
Modules may be mutually recursive.

\workingnote{But in the presence of inter-module recursion, is there much point in
keeping track of recursive groups within modules? Options: (1) don't worry about it;
(2) put all declarations in module (indeed whole program) into one huge recursive pot;
(3) abandon general module recursion, and introduce some kind of import declaration to define the 
types (only) of things from external modules that currently introduce module recursion.}

There is also an implicitly-defined module @PrelGHC@, which exports the ``built-in'' types and values
that must be provided by any implementation of Core (including GHC).   Details of this
module are in Section~\ref{sec:prims}.

A Core {\em program} is a collection of distinctly-named modules that includes a module
called @Main@ having an exported value called @main@ of type @PrelIOBase.IO a@ (for some type @a@).

Many modules of interest derive from library modules, such as @PrelBase@, which implement parts of
the Haskell basis library.  In principle, these modules have no special status.  In practice, the
requirement on the type of @Main.main@ implies that every program will contain a large subset of
the Prelude library modules.

\subsection{Namespaces}

There are five distinct name spaces: 
\begin{enumerate}
\item module identifiers (@mident@),
\item type constructors (@tycon@),
\item type variables (@tyvar@),
\item data constructors (@dcon@),
\item term variables (@var@).
\end{enumerate}  
Spaces (1), (2+3), and (4+5) can be distinguished from each other by context.
To distinguish (2) from (3) and (4) from (5), we require that 
(both sorts of) constructors begin with an upper-case character
and that (both sorts of) variables begin with a lower-case character (or @_@).
Primitive types and operators are not syntactically distinguished.

A given variable (type or term) may have multiple (local) definitions within a module.
However, definitions never ``shadow'' one another; that is, the scope of the definition
of a given variable never contains a redefinition of the same variable.  The only exception
to this is that (necessarily closed) types labelling @%external@ expressions may contain 
@tyvar@ bindings that shadow outer bindings.

Core generated by GHC makes heavy use of encoded names, in which the characters @Z@ and @z@ are
used to introduce escape sequences for non-alphabetic characters such as dollar sign @$@ (@zd@),
hash @#@ (@zh@), plus @+@ (@zp@), etc.  This is the same encoding used in @.hi@ files and in the
back-end of GHC itself, except that we sometimes change an initial @z@ to @Z@, or vice-versa, 
in order to maintain case distinctions.

\subsection{Types and Kinds}

In Core, all type abstractions and applications are explicit.  This make it easy to 
typecheck any (closed) fragment.  An full executable typechecker is available separately.

Types are described by type expressions, which 
are built from named type constructors and type variables
using type application and universal quantification.  
Each type constructor has a fixed arity $\geq 0$.  
Because it is so widely used, there is
special infix syntax for the fully-applied function type constructor (@->@).
(The prefix identifier for this constructor is @PrelGHC.ZLzmzgZR@; this should
only appear in unapplied or partially applied form.)
There are also a number of other primitive type constructors (e.g., @Intzh@) that
are predefined in the @PrelGHC@ module, but have no special syntax.
Additional type constructors are
introduced by @%data@ and @%newtype@ declarations, as described below.
Type constructors are distinguished solely by name.

As described in the Haskell definition, it is necessary to distinguish 
well-formed type-expressions by classifying them into different {\it kinds}.
In particular, Core explicitly records the kind of every bound type variable.
Base kinds (@*@,@#@, and @?@) represent actual types, i.e., those that can be assigned
to term variables; all the nullary type constructors have one of these kinds.
Non-nullary type constructors have higher kinds of the form $k_1 @->@ k_2$,
where $k_1$ and $k_2$ are kinds.   For example, the function type constructor
@->@ has kind @* -> (* -> *)@.  Since Haskell allows abstracting over type
constructors, it is possible for type variables to have higher kinds; however,
it is much more common for them to have kind @*@, so this is the default if
the kind is omitted in a type binder.

The three base kinds distinguish the {\it liftedness} of the types they classify:
@*@ represents lifted types; @#@ represents unlifted types; and @?@ represents
``open'' types, which may be either lifted or unlifted.  Of these, only @*@ ever
appears in Core code generated from user code; the other two are needed to describe
certain types in primitive (or otherwise specially-generated) code.
Semantically, a type is lifted if and only if it has bottom as an element. 
Operationally, lifted types may be represented by closures; hence, any unboxed
value is necessarily unlifted.  
In particular, no top-level identifier (except in @PrelGHC@) has a type of kind @#@ or @?@.
Currently, all the primitive types are unlifted 
(including a few boxed primitive types such as @ByteArrayzh@).
The ideas behind the use of unboxed and unlifted types are described in ~\cite{pj:unboxed}.

There is no mechanism for defining type synonyms (corresponding to
Haskell @type@ declarations).
Type equivalence is just syntactic equivalence on type expressions
(of base kinds) modulo:

\begin{itemize} 
\item alpha-renaming of variables bound in @%forall@ types;
\item the identity $a$ @->@ $b$ $\equiv$ @PrelGHC.ZLzmzgZR@ $a$ $b$
\item the substitution of representation types for {\it fully applied} instances of newtypes
(see Section~\ref{sec:newtypes}).
\end{itemize}

\subsection{Algebraic data types}

Each @data@ declaration introduces a new type constructor and a set of one or
more data constructors, normally corresponding directly to a source Haskell @data@ declaration.
For example, the source declaration
\begin{code}
data Bintree a =
   Fork (Bintree a) (Bintree a)
|  Leaf a
\end{code}
might induce the following Core declaration
\begin{code}
%data Bintree a = {
   Fork (Bintree a) (Bintree a);
   Leaf a)}
\end{code}
which introduces the unary type constructor @Bintree@ of kind @*->*@  and two data constructors with types
\begin{code}
Fork :: %forall a . Bintree a -> Bintree a -> Bintree a
Leaf :: %forall a . a -> Bintree a
\end{code}
We define the {\it arity} of each data constructor to be the number of value arguments it takes;
e.g. @Fork@ has arity 2 and @Leaf@ has arity 1.

For a less conventional example illustrating the possibility of higher-order kinds, the Haskell source declaration
\begin{code}
data A f a = MkA (f a)
\end{code}
might induce the core declaration
\begin{code}
%data A (f::*->*) (a::*) = { MkA (f a) }
\end{code}
which introduces the constructor
\begin{code}
MkA :: %forall (f::*->*) (a::*) . (f a) -> (A f) a
\end{code}


GHC (like some other Haskell implementations) supports an extension to Haskell98 
for existential types such as 
\begin{code}
data T = forall a . MkT a (a -> Bool)
\end{code}
This is represented by the Core declaration
\begin{code}
%data T = {MkT @a a (a -> Bool)}
\end{code}
which introduces the nullary type constructor @T@ and the data constructor
\begin{code}
MkT :: %forall a . a -> (a -> Bool) -> T
\end{code}
In general, existentially quantified variables appear as extra univerally
quantified variables in the data contructor types.
An example of how to construct and deconstruct values of type @T@ is shown in 
Section~\ref{sec:exprs}.

\subsection{Newtypes}
\label{sec:newtypes}


Each Core @%newtype@ declaration introduces a new type constructor and (usually) an associated
representation type, corresponding to a source Haskell @newtype@
declaration.  However, unlike in source Haskell, no data constructors are introduced.
In fact, newtypes seldom appear in value types
in Core programs, because GHC usually replaces them with their representation type.
For example, the Haskell fragment
\begin{code}
newtype U = MkU Bool
u = MkU True
v = case u of
  MkU b -> not b
\end{code}
might induce the Core fragment
\begin{code}
%newtype U = Bool;
u :: Bool = True;
v :: Bool = 
   %let b :: Bool = u
   %in not b;
\end{code}
The main purpose of including @%newtype@ declarations in Core is to permit checking of
type expressions in which partially-applied newtype constructors are used to instantiate higher-kinded
type variables.  For example:
\begin{code}
newtype W a = MkW (Bool -> a)
data S k = MkS (k Bool)
a :: S W = MkS (MkW(\x -> not x))
\end{code}
might generate this Core:
\begin{code}
%newtype W a = Bool -> a;
%data S (k::(*->*)) = MkS (k Bool);
a :: S W = MkS @ W (\(x::Bool) -> not x)
\end{code}
The type application @(S W)@ cannot be checked without a definition for @W@.

Very rarely, source @newtype@ declarations may be (directly or indirectly) recursive. In such
cases, it is not possible to subsitute the representation type for the new type;
in fact, the representation type is omitted from the corresponding Core @%newtype@ declaration.
Elements of the new
type can only be created or examined by first explicitly coercing them from/to
the representation type, using a @%coerce@ expression.  For example, the silly
Haskell fragment
\begin{code}
newtype U = MkU (U -> Bool)
u = MkU (\x -> True)
v = case u of
  MkU f -> f u
\end{code}
might induce the Core fragment
\begin{code}
%newtype U; 
u :: U = %coerce U (\ (x::U) -> True);
v :: Bool = 
   %let f :: U -> Bool = %coerce (U -> Bool) u 
   %in f u;
\end{code}

\workingnote{The treatment of newtypes is still very unattractive: acres of explanation for
very rare phenomena.}

\subsection{Expression Forms}
\label{sec:exprs}

Variables and data constructors are straightforward.

Literal ({\it lit}) expressions consist of a literal value, in one of four different formats,
and a (primitive) type annotation.   Only certain combinations of format and type
are permitted; see Section~\ref{sec:prims}.  The character and string formats can describe only
8-bit ASCII characters.  Moreover, because strings are interpreted as C-style null-terminated
strings, they should not contain embedded nulls.

Both value applications and type applications are made explicit, and similarly
for value and type abstractions.  To tell them apart, type arguments in applications
and formal type arguments in abstractions are preceded by an \at\ symbol. (In abstractions,
the \at\ plays essentially the same role as the more usual $\Lambda$ symbol.)
For example, the Haskell source declaration
\begin{code}
f x = Leaf (Leaf x)
\end{code}
might induce the Core declaration
\begin{code}
f :: %forall a . a -> BinTree (BinTree a) =
  \ @a (x::a) -> Leaf @(Bintree a) (Leaf @a x)
\end{code}

Value applications may be of user-defined functions, data constructors, or primitives.
None of these sorts of applications are necessarily saturated (although previously published variants
of Core did require the latter two sorts to be).

Note that the arguments of type applications are not always of kind @*@.  For example,
given our previous definition of type @A@:
\begin{code}
data A f a = MkA (f a)
\end{code}
the source code
\begin{code}
MkA (Leaf True)
\end{code}
becomes
\begin{code}
(MkA @Bintree @Bool) (Leaf @Bool True)
\end{code}

Local bindings, of a single variable or of a set of mutually recursive variables,
are represented by @%let@ expressions in the usual way. 

By far the most complicated expression form is @%case@.
@%case@ expressions are permitted over values of any type, although they will normally
be algebraic or primitive types (with literal values).
Evaluating a @%case@ forces the evaluation of the expression being
tested (the ``scrutinee''). The value of the scrutinee is bound to the variable
following the @%of@ keyword, which is in scope in all alternatives; 
this is useful when the scrutinee is a non-atomic
expression (see next example).

In an algebraic @%case@, all the case alternatives must be
labeled with distinct data constructors from the algebraic type, followed by
any existential type variable bindings (see below), and 
typed term variable bindings corresponding to the data constructor's
arguments. The number of variables must match the data constructor's arity.

For example, the following Haskell source expression
\begin{code}
case g x of
  Fork l r -> Fork r l
  t@(Leaf v) -> Fork t t
\end{code}
might induce the Core expression
\begin{code}
%case g x %of (t::Bintree a)
   Fork (l::Bintree a) (r::Bintree a) ->
      Fork @a r l
   Leaf (v::a) ->
      Fork @a t t
\end{code}

When performing a @%case@ over a value of an existentially-quantified algebraic
type, the alternative must include extra local type bindings 
for the existentially-quantified variables.  For example, given 
\begin{code}
data T = forall a . MkT a (a -> Bool)
\end{code}
the source
\begin{code}
case x of
  MkT w g -> g w
\end{code}
becomes
\begin{code}
%case x %of (x'::T) 
  MkT @b (w::b) (g::b->Bool) -> g w
\end{code}

In a @%case@ over literal alternatives,
all the case alternatives must be distinct literals of the same primitive type.

The list of alternatives may begin with a 
default alternative labeled with an underscore (@%_@), which will be chosen if
none of the other alternative match.  The default is optional except for a case
over a primitive type, or when there are no other alternatives.
If the case is over neither an
algebraic type nor a primitive type, the default alternative is the {\it only}
one that can appear.
For algebraic cases, the set of alternatives
need not be exhaustive, even if no default is given; if alternatives are missing,
this implies that GHC has deduced that they cannot occur. 

The @%coerce@ expression is primarily used in conjunction with manipulation of
newtypes, as described in Section~\ref{sec:newtypes}. 
However, @%coerce@ is sometimes used for
other purposes, e.g. to coerce the return type of a function (such as @error@)
that is guaranteed never to return.  By their natures, uses of @%coerce@ cannot
be independently justified, and must be taken on faith by a type-checker for Core.

A @%note@ expression is used to carry arbitrary internal information of interest to
GHC.  The information must be encoded as a string.  Expression notes currently generated by GHC
include the inlining pragma (@InlineMe@) and cost-center labels for profiling.

A @%external@ expression denotes an external identifier, which has
the indicated type (always expressed in terms of Haskell primitive types).
\workingnote{The present syntax is sufficient for describing C functions and labels.
Interfacing to other languages may require additional information or a different interpretation
of the name string.}


\subsection{Expression Evaluation}  

The dynamic semantics of Core are defined on the type-erasure of the program;
ie. we ignore all type abstractions and applications.  The denotational semantics
the resulting type-free program are just the conventional ones for a call-by-name
language, in which expressions are only evaluated on demand.
But Core is intended to be a call-by-{\it{need}} language, in which
expressions are only evaluated {\it once}.  To express the sharing behavior
of call-by-need, we give an operational model in the style of Launchbury.
This section describes the model informally; a more formal semantics is
separately available in the form of an executable interpreter.

To simplify the semantics, we consider only ``well-behaved'' Core programs in which
constructor and primitive applications are fully saturated, and in which
non-trivial expresssions of unlifted kind (@#@) appear only as scrutinees
in @%case@ expressions.  Any program can easily be put into this form;
a separately available executable preprocessor illustrates how.
In the remainder of this section, we use ``Core'' to mean ``well-behaved'' Core.

Evaluating a Core expression means reducing it to {\it weak-head normal form (WHNF)},
i.e., a primitive value, lambda abstraction, or fully-applied data constructor.
Evaluation of a program is evaluation of the expression @Main.main@.

To make sure that expression evaluation is shared, we
make use of a {\it heap}, which can contain
\begin{itemize}
\item {\em Thunks} representing suspended (i.e., as yet unevaluated) expressions.

\item {\em WHNF}s representing the result of evaluating such thunks. Computations over
primitive types are never suspended, so these results are always closures (representing
lambda abstractions) or data constructions.
\end{itemize}
Thunks are allocated when it
is necessary to suspend a computation whose result may be shared.
This occurs when evaluating three different kinds of expressions:
\begin{itemize}
\item Value definitions at top-level or within a local @let@ expression.
Here, the defining expressions are suspended and the defined names
are bound to heap pointers to the suspensions.

\item User function applications.  Here, the actual argument expression is
suspended and the formal argument is bound to a heap pointer to the suspension.

\item Constructor applications. Here, the actual argument expression is
suspended and a heap pointer to the suspension is embedded in the constructed value.
\end{itemize}

As computation proceeds, copies of the heap pointer propagate. 
When the computation is eventually forced, the heap entry is overwritten with the resulting
WHNF, so all copies of the pointer now point to this WHNF.   Forcing occurs
only in the context of
\begin{itemize}
\item evaluating the operator expression of an application; 

\item evaluating the ``scrutinee'' of a @case@ expression; or 

\item evaluating an argument to a primitive or external function application
\end{itemize}

Ultimately, if there are no remaining pointers to the heap entry (whether suspended or evaluated),
the entry can be garbage-collected; this is assumed to happen implicitly.

With the exception of functions, arrays, and mutable variables, the intention is that values of all primitive types
should be held {\it unboxed}, i.e., not heap-allocated.  This causes no problems for laziness because all
primitive types are {\it unlifted}.  Unboxed tuple types are not heap-allocated either.

Certain primitives and @%external@ functions cause side-effects to state threads or to the real world.
Where the ordering of these side-effects matters, Core already forces this order
by means of data dependencies on the psuedo-values representing the threads.

The @raisezh@ and @handlezh@ primitives requires special support in an implementation, such as a handler stack; 
again, real-world threading guarantees that they will execute in the correct order.

\section{Primitive Module}
\label{sec:prims}

This section describes the contents and informal semantics of the primitive module @PrimGHC@.
Nearly all the primitives are required in order to cover GHC's implementation of the Haskell98
standard prelude; the only operators that can be completely omitted are those supporting the byte-code interpreter, 
parallelism, and foreign objects.  Some of the concurrency primitives are needed, but can be
given degenerate implementations if it desired to target a purely sequential backend; see Section~\ref{sec:sequential}.

In addition to these primitives, a large number of C library functions are required to implement
the full standard Prelude, particularly to handle I/O and arithmetic on less usual types.
% We list these separately in section~\ref{sec:ccalls}.

\subsection{Types}

\begin{tabular}{|l|l|l|}
\hline
Type & Kind & Description \\
\hline
@ZLzmzgZR@ & @* -> * -> *@ & functions (@->@) \\
@Z1H@ & @? -> #@    & unboxed 1-tuple \\
@Z2H@	   & @? -> ? -> #@ & unboxed 2-tuple \\
\ldots   & \ldots & \ldots \\
@Z100H@	   & @? -> ? -> ? -> ... -> ? -> #@ & unboxed 100-tuple \\
@Addrzh@    & @#@	   & machine address (pointer) \\
@Charzh@	   & @#@	   & unicode character (31 bits) \\
@Doublezh@  & @#@	   & double-precision float \\
@Floatzh@   & @#@	   & float \\
@Intzh@	   & @#@	   & int (30+ bits) \\
@Int32zh@   & @#@	   & int (32 bits) \\
@Int64zh@   & @#@	   & int (64 bits) \\
@Wordzh@	   & @#@	   & unsigned word (30+ bits) \\
@Word32zh@   & @#@	   & unsigned word (32 bits) \\
@Word64zh@   & @#@	   & unsigned word (64 bits) \\
@RealWorld@ & @*@          & pseudo-type for real world state \\
@Statezh@    & @* -> #@     & mutable state \\
@Arrayzh@   & @* -> #@     & immutable arrays \\
@ByteArrayzh@   & @#@     & immutable byte arrays \\
@MutableArrayzh@   & @* -> * -> #@     & mutable arrays \\
@MutableByteArrayzh@   & @* -> #@     & mutable byte arrays \\
@MutVarzh@ & @* -> * -> #@  & mutable variables \\
@MVarzh@  & @* -> * -> #@  & synchronized mutable variables \\
@Weakzh@  & @* -> #@      & weak pointers \\
@StablePtrzh@ & @* -> #@  & stable pointers \\
@ForeignObjzh@ & @#@	& foreign object \\
@ThreadIdzh@ & @#@	 & thread id \\
@ZCTCCallable@ & @? -> *@ & dictionaries for CCallable pseudo-class \\
@ZCTCReturnable@ & @? -> *@ & dictionaries for CReturnable pseudo-class \\
\hline
\end{tabular}

In addition, the types @PrelBase.Bool@ and @PrelBase.Unit@, which are non-primitive
and are defined as ordinary algebraic types in module @PrelBase@, are used in
the types of some operators in @PrelGHC@.

The unboxed tuple types are quite special: they hold sets of values in an unlifted
context, i.e., to be manipulated directly rather than being stored in the heap.  They can only
appear in limited contexts in programs; in particular, they cannot be bound by a
lambda abstraction or case alternative pattern. Note that they can hold either lifted
or unlifted values.  The limitation to 100-tuples is an arbitrary one set by GHC.

The type of arbitrary precision integers (@Integer@) is not primitive; it is made
up of an ordinary primitive integer (@Intzh@) and a byte array (@ByteArrzh@).
The components of an @Integer@ are passed to primitive operators as two separate
arguments and returned as an unboxed pair.

The @Statezh@ type constructor takes a dummy type argument that is used only 
to distinguish different state {\it threads}~\cite{Launchbury94}.
The @RealWorld@ type is used only as an argument to @Statezh@, and represents
the thread of real-world state; it contains just the single value @realWorldzh@.
The mutable data types @MutableArrayzh@,@MutableByteArrayzh@,@MutVarzh@
take an initial type argument of the form @(Statezh@ $t$@)@ for some thread $t$.
The synchronized mutable variable type constructor @MVarzh@ always takes an argument of type
@Statezh RealWorld@.

@Weakzh@ is the type of weak pointers.

@StablePtrzh@ is the type of stable pointers, which are guaranteed not to move
during garbage collections; these are useful in connection with foreign functions.

@ForeignPtrzh@ is the type of foreign pointers.

The dictionary types @ZCTCCallable@ and @ZCTCReturnable@ are just placeholders
which can be represented by a void type;
any code they appear in should be unreachable.

\subsubsection{Non-concurrent Back End}
\label{sec:sequential}

The Haskell98 standard prelude doesn't include any concurrency support, but GHC's
implementation of it relies on the existence of some concurrency primitives.  However,
it never actually forks multiple threads.  Hence, the concurrency primitives can
be given degenerate implementations that will work in a non-concurrent setting,
as follows:
\begin{itemize}
\item  @ThreadIdzh@ can be represented
by a singleton type, whose (unique) value is returned by @myThreadIdzh@.

\item @forkzh@ can just die with an ``unimplemented'' message.

\item @killThreadzh@ and @yieldzh@ can also just die ``unimplemented'' since
in a one-thread world, the only thread a thread can kill is itself, and
if a thread yields the program hangs.

\item @MVarzh a@ can be represented by @MutVarzh (Maybe a)@;
where a concurrent implementation would block, the sequential implementation can
just die with a suitable message (since no other thread exists to unblock it).

\item @waitReadzh@ and @waitWritezh@ can be implemented using a @select@ with no timeout. 
\end{itemize}

\subsection{Literals}

Only the following combination of literal forms and types are permitted:

\begin{tabular}{|l|l|l|}
\hline
Literal form & Type & Description \\
\hline 
integer	&  @Intzh@ & Int \\
%	&  @Int32zh@ & Int32 \\
%	&  @Int64zh@ & Int64 \\
	&  @Wordzh@ & Word \\
%	&  @Word32zh@ & Word32 \\
%	&  @Word64zh@ & Word64 \\
	&  @Addrzh@ & Address \\
	&  @Charzh@ & Unicode character code \\
rational & @Floatzh@ & Float \\
	 & @Doublezh@ & Double \\
character & @Charzh@ & Unicode character specified by ASCII character\\
string &  @Addrzh@  & Address of specified C-format string \\
\hline
\end{tabular}

\subsection{Data Constructors}

The only primitive data constructors are for unboxed tuples:

\begin{tabular}{|l|l|l|}
\hline
Constructor & Type & Description \\
\hline
@ZdwZ1H@ & @%forall (a::?).a -> Z1H a@ & unboxed 1-tuple \\
@ZdwZ2H@ & @%forall (a1::?) (a2::?).a1 -> a2 -> Z2H a1 a2@ & unboxed 2-tuple \\
\ldots & \ldots & \ldots \\
@ZdwZ100H@ & @%forall (a1::?) (a2::?)... (a100::?) .@ & \\
& \ \ \ @a1 -> a2 -> ... -> a100 -> Z100H a1 a2 ... a100@ & unboxed 100-tuple \\
\hline
\end{tabular}

\subsection{Values}

Operators are (roughly) divided into collections according to the primary
type on which they operate.

\workingnote{How do primitives fail, e.g., on division by zero or
attempting an invalid narrowing coercion?}

\workingnote{The following primop descriptions are automatically generated.
The exact set of primops and their types presented here 
depends on the underlying word size at the time of generation; these
were done for 32 bit words.  This is a bit stupid.
More importantly, the word size has a big impact on just what gets produced
in a Core file, but this isn't documented anywhere in the file itself.
Perhaps there should be a global flag in the file?}

\newcommand{\primoptions}[7]{{#1} {#2} {#3} {#4} {#5}}

\newcommand{\primopsection}[2]{\subsubsection{#1}{#2}\vspace*{0.1in}}
\newcommand{\primopdefaults}[1]{Unless otherwise noted, each primop has the following default characteristics: {#1}}

\newcommand{\primopdesc}[8]{
\par\noindent{\texttt{{{#3} :: {#6}}}}
\\{#7} {#8}\\} 

\input{prims.tex}

\subsubsection{RealWorld}

There is just one value of type @RealWorld@, namely @realWorldzh@. It is used
only for dependency threading of side-effecting operations.

\begin{thebibliography}{}

\bibitem[Launchbury and {Peyton~Jones}, 1994]{Launchbury94}
Launchbury, J. and {Peyton~Jones}, S. (1994).
\newblock Lazy functional state threads.
\newblock Technical report FP-94-05, Department of Computing Science,
  University of Glasgow.

\bibitem[{Peyton~Jones} and Launchbury, 1991]{pj:unboxed}
{Peyton~Jones}, S. and Launchbury, J. (1991).
\newblock Unboxed values as first class citizens.
\newblock In {\em ACM Conference on Functional Programming and Computer
  Architecture (FPCA'91)}, pages 636--666, Boston. ACM.

\bibitem[{Peyton~Jones} and Marlow, 1999]{ghc-inliner}
{Peyton~Jones}, S. and Marlow, S. (1999).
\newblock Secrets of the {Glasgow Haskell Compiler} inliner.
\newblock In {\em Workshop on Implementing Declarative Languages}, Paris,
  France.

\bibitem[Peyton~Jones and Santos, 1998]{comp-by-trans-scp}
Peyton~Jones, S. and Santos, A. (1998).
\newblock A transformation-based optimiser for {Haskell}.
\newblock {\em Science of Computer Programming}, 32(1-3):3--47.

\end{thebibliography}

\end{document}