Building Projects

Jhc does its own dependency chasing to track down source files, you need only provide it with the file containing your 'main' function on the command line.

; jhc HelloWorld.hs -o hello

Jhc searches for modules in its search path, which defaults to the current directory. Modules are searched for based on their names. For instance, import Data.Foo will search for a file as Data/Foo.hs and Data.Foo.hs. The search path may be modifed with the -i command line option or by setting the JHC_PATH environment variable.

Using Libraries

jhc libraries are distributed as files with an hl suffix, such as applicative-1.0.hl. In order to install a haskell library you simply need to place the file in a directory that jhc will search for it. For example $HOME/lib/jhc. You may set the environment variable JHC_LIBRARY_PATH to specify alternate locations to search for libraries or specify directory to search with the -L command line option. -L- will clear the search path. You can see jhc's built in search path by passing the --info option.

You can then use libraries with the '-p' command line option.

; jhc -p mylibrary MyProgram.hs -o myprogram

You can list all available libraries by passing the --list-libraries option to jhc. If you include -v for verbose output, you will get detailed information about the libraries in a YAML format suitable for processing by external tools.

Library development

It is often useful to use jhc directly on files in a library during development. In order to support this you can use --with file.yaml which will load the same environment from the yaml file as it would when building the library but allow different commands to be specified.

Environment Variables

Jhc's behavior is modified by several enviornment variables.


this is read and appended to the command line of jhc invocations.


This specifies the path to search for modules; it is equivalent to '-i' on the command line.


This specifies the path to search for libraries; it is equivalent to '-L' on the command line.


This specified the directory jhc will use to cache values. having a valid cache is essential for jhc performance. It defaults to ~/.jhc/cache.

Building Haskell Libraries

Libraries are built by passing jhc a file describing the library via the --build-hl option. The library file format is a stadard YAML file.

; jhc --build-hl mylibrary.yaml

Library File Format

The library file is a YAML document, jhc will recognize several fields and ignore unknown ones.


The name of your library


The version of your library, The version number is used to differentiate different versions of the library passed to the '-p' command line option but is not otherwise special to jhc.


A list of modules to be included in the library and exposed to users of the library as its public interface. This may include modules that are part of another library, they will be re-exported by the current library.


A list of modules that the library may use internally but that should not be exposed to the user. Jhc may optimize based on this information. If this list is not exhaustive jhc will still build your library, but it will print out a warning.


A list of extensions which should be enabled during compilation of this module. When possible, jhc will match ghc extensions to their closest jhc counterparts.


Extra command line options to jhc for this library build.


libraries to include, in the same format as passed to the '-p' command line option


Directory to search for Haskell source files in, this differs from the '-i' command line option in that the directory in this field is relative to the directory the library description .yaml file is located while the '-i' option is always relative to the current working directory.


directories to be included in the preprocessor search path as if via '-I'. The directories are interpreted relative to the directory that contains the yaml file.


C files that should be linked into programs that utilize this library.


files that should be made available for inclusion when compiling the generated C code but don't need to be linked into the executable.

example library files can be seen in lib/hasklel98/haskell98.yaml and lib/jhc/jhc.yaml

Dependency Information

Jhc can output dependency information describing how source files and libraries depend on each other while compiling code. The dependency information is generated when the --deps name.yaml option is passed to jhc. It is presented in the standard YAML format and its fields are as described below.

An example tool to processs the deps.yaml file and spit out appropriate Makefile rules is included as utils/deps_to_make.prl.


Usage Examples

./jhc [OPTION] File.hs   # compile given module
./jhc [OPTION] --build-hl libdef.yaml   # compile library described by file

Option Flags

flag description
-V --version print version info and exit
-h --help print help information and exit
--info show compiler configuration information and exit
--purge-cache clean out jhc compilation cache
-v --verbose chatty output on stderr
-z Increase verbosity of statistics
-d [no-]flag dump specified data during compilation
-f [no-]flag set or clear compilation options
-X Extension enable the given language extension
-o FILE --output FILE output to FILE
-i DIR --include DIR where to look for source files
-I DIR add to preprocessor include path
--with foo.yaml include values from yaml file in configuration
-D NAME=VALUE add new definitions to set in preprocessor
--optc option extra options to pass to c compiler
-c just compile the modules, caching the results.
-C compile to C code
-E preprocess the input and print result to stdout
-k --keepgoing keep going on errors
--cross enable cross-compilation, choose target with the -m flag
--stop parse/typecheck/c stop after the given pass, parse/typecheck/c
--width COLUMNS width of screen for debugging output
--main Main.main main entry point
-m arch --arch arch target architecture options
--entry main entry point, showable expression
--show-ho file.ho Show contents of ho or hl file
--noauto Don't automatically load base and haskell98 packages
-p package Load given haskell library package
-L path Look for haskell libraries in the given directory
--build-hl desc.yaml Build hakell library from given library description file
--annotate-source Write preprocessed and annotated source code to the directory specified
--deps Write dependency information to file specified
--interactive run interactivly ( for debugging only)
--ignore-cache Ignore existing compilation cache entries.
--readonly-cache Do not write new information to the compilation cache.
--no-cache Do not use or update the cache.
--cache-dir JHC_CACHE Use a global cache located in the directory passed as an argument.
--stale Module Treat these modules as stale, even if they exist in the cache
--list-libraries List of installed libraries
--tdir dir/ specify the directory where all intermediate files/dumps will be placed.

Code Options

Various options affecting how jhc interprets and compiles code can be controlled with the '-f' flag, the following options are availible, you can negate any particular one by prepending 'no-' to it.

Code options
bang-patterns - bang patterns
cpp pass haskell source through c preprocessor
exists exists keyword for existential types recognized
ffi support foreign function declarations
forall forall keyword for rank-n types and explicit quantification
m4 pass haskell source through m4 preprocessor
prelude implicitly import Prelude
sugar disable all desugarings, only unboxed literals allowed.
type-families type/data family support
unboxed-tuples allow unboxed tuple syntax to be recognized
unboxed-values allow unboxed value syntax
user-kinds user defined kinds
defaulting perform defaulting of ambiguous types
monomorphism-restriction enforce monomorphism restriction
lint perform lots of extra type checks
Optimization Options
global-optimize perform whole program E optimization
inline-pragmas use inline pragmas
rules use rules
type-analysis perform a basic points-to analysis on types right after method generation
Code Generation
boehm use Boehm garbage collector
debug enable debugging code in generated executable
full-int extend Int and Word to 32 bits on a 32 bit machine (rather than 30)
jgc use the jgc garbage collector
profile enable profiling code in generated executable
raw just evaluate main to WHNF and nothing else.
standalone compile to a standalone executable
wrapper wrap main in exception handler
Default settings
default inline-pragmas rules wrapper defaulting type-analysis monomorphism-restriction global-optimize full-int prelude sugar
glasgow-exts forall ffi unboxed-tuples

Dumping Debugging Information

You can have jhc print out a variety of things while running as Controlled by the '-d' flag. The following is a list of possible parameters you can pass to '-d'.

Front End
decls processed declarations before typechecking
defs Show all defined names in a module
derived show generated derived instances
exports show which names are exported from each module
fixity show fixity map
imports show in scope names for each module
ini all ini configuration options
parsed parsed code
preprocessed code after preprocessing/deliting
renamed code after uniqueness renaming
scc-modules show strongly connected modules in dependency order
tokens raw token stream before parsing
Type Checker
all-types show unified type table, after everything has been typechecked
aspats show as patterns
bindgroups show bindgroups
boxy-steps show step by step what the type inferencer is doing
class detailed information on each class
class-summary summary of all classes
dcons data constructors
instance show instances
kind show results of kind inference for each module
kind-steps show steps of kind inference
program impl expls, the whole shebang.
sigenv initial signature environment
srcsigs processed signatures from source code
types display unified type table containing all defined names
Intermediate code
core show intermediate core code
core-afterlift show final core before writing ho file
core-beforelift show core before lambda lifting
core-initial show core right after E.FromHs conversion
core-mangled de-typed core right before it is converted to grin
core-mini show details even when optimizing individual functions
core-pass show each iteration of code while transforming
core-steps show what happens in each pass
datatable show data table of constructors
datatable-builtin show data table entries for some built in types
e-alias show expanded aliases
e-info show info tags on all bound variables
e-size print the size of E after each pass
e-verbose print very verbose version of E code always
optimization-stats show combined stats of optimization passes
rules show all user rules and catalysts
rules-spec show specialization rules
Grin code
grin dump all grin to the screen
grin-datalog print out grin information in a format suitable for loading into a database
grin-final final grin before conversion to C
grin-graph print dot file of final grin code to
grin-initial grin right after conversion from core
grin-normalized grin right after first normalization
grin-posteval show grin code just before eval/apply inlining
grin-preeval show grin code just before eval/apply inlining
steps show interpreter go
tags list of all tags and their types
Backend code
c don't delete C source file after compilation
atom dump atom table on exit
progress show basic progress indicators
stats show extra information about stuff
verbose progress
veryverbose progress stats



Jhc comes with a few custom libraries in lib/ and various packaged external libraries specified in lib/ext

Primitive Libraries

jhc-prim is the only library that must be linked with all programs though this is done behind the scenes. It contains no code, only definitions the compiler internals expect to exist, so it will not increase the size of executables. For creating a specific environment that substantially differs from standard haskell, you would build on this layer.

jhc contains definitions useful for building the standards based libraries.

haskell98 provides a haskell 98 compatible environment.

haskell2010 provides a haskell 2010 compatible environment. It may be combined with haskell98 to have both.

flat-foreign provides non hierarchical versions of the libraries specified in the FFI addendum to the standard. They existed briefly before hierarchical modules were standard.


Pragmas are special compiler directives that change its behavior in certain ways. In general, each compiler is free to define its own pragmas however jhc does try to implement the same ones as other compilers when it makes sense. pragmas appear in source code as {-# PRAGMANAME ... #-}

All of these pragmas may be prefixed with JHC_ or the bareword JHC in order to trigger only with JHC. -fignore-pragmas will not ignore these.

Function Properties

These must appear in the same file as the definition of a function. To apply one to a instance or class method, you must place it in the where clause of the instance or class declaration.

Function Pragmas
NOINLINE Do not inline the given function during core transformations. The function may be inlined during grin transformations.
INLINE Inline this function whenever possible
SUPERINLINE Always inline no matter what, even if it means making a local copy of the functions body.
VCONSTRUCTOR Treat the function as a virtual constructor. CPR analysis and the worker/wrapper transforms will treat the function application as if it were a constructor. This implies 'NOINLINE'.

Other Pragmas

Class Method Pragmas
NOETA By default, jhc eta-expands all class methods to help enable optimizations. This disables this behavior.
RULES rewrite rules. These have the same syntax and behave similarly to GHC's rewrite rules, except 'phase' information is not allowed.
CATALYST A special type of rewrite rule that only fires if it enables the use of another RULE, so a CATALYST may allow optimizations that require passing through a non-optimal intermediate stage.
SPECIALIZE create a version of a function that is specialized for a given type
SUPERSPECIALIZE has the same effect as SPECIALIZE, but also places a run-time check in the generic version of the function to determine whether to call the specialized version.

Type Pragmas


Specify the external type that a data or newtype should use for foreign function interfaces. The type must be a newtype or unary data constructor of a type that is already foreignable. By not including a string, the type is made unFFIable. This can be used to preserve abstraction.

data {-# CTYPE "unsigned short" #-} CUShort = CUShort Word16  -- use unsigned short calling convention
newtype {-# CTYPE #-} Opaque = Opaque Int    -- disable FFI ability for this type

Header Pragmas

These pragmas are only valid in the 'head' of a file, meaning they must come before the initial 'module' definition and in the first 4096 bytes of the file and must be preceded by and contain only characters in the ASCII character set.


Specify extra options to use when processing this file. The options available are equivalent to the command line options, though, not all may have meaning when applied to a single file.

{-# OPTIONS_JHC -fno-sugar #-}

Specify various language options, options that are not understood are ignored. Specifying something here is equivalent to passing it as '-X' on the command line.

{-# LANGUAGE NoMonomorphismRestriction, CPP #-}

Special Pragmas

LINE pragmas change the logical name of the file that is being parsed, several preprocessors output these to ensure error messages refer to the original file. Jhc understands a few variants.

In addition, for compatibility with cpp and m4, the following form is also accepted if it appears at the beginning of a line.

#line linenumber "filename"?


Module Search Path

Modules in jhc are searched for based on their name as in other Haskell compilers. However in addition to searching for 'Data/Foo.hs' for the module 'Data.Foo', jhc will also search for 'Data.Foo.hs'.

extensions to the FFI

foreign imports with multiple return values.

foreign C imports may return multiple values. To indicate this is the case, use an unboxed tuple as the return value. The first return value will be the value the function directly returns, the rest will be passed as pointers at the end of the functions argument list. Only pure (non IO) functions may return multiple values.

-- frexp has C prototype
-- double frexp(double x, int *exp);
-- so it would normally have an import like so, requiring the IO module and
-- Storable to call what is otherwise a pure function.

foreign import ccall "math.h frexp"  c_frexp :: Double -> Ptr CInt -> IO Double

-- This extension allows it to be declared as so
foreign import ccall "math.h frexp"  c_frexp2 :: Double -> (# Double, CInt #)

-- The second return value is added as the last 'exp' parameter then read out
-- of the allocated memory. The contents of the memory passed into the function
-- is undefined.

'capi' calling convention

The 'capi' calling convention may be used instead of 'ccall' for static imports. The convention means that the foreign function may not be addressable as an address, but rather may be implemnted as a macro, builtin, or other compiler specific feature. jhc will ensure that the routine is never used as a pointer and the headers specified in the dependency string are included anywhere the imported function appears. This differs from 'ccall' in that ccall makes no guarentees the given header file will be in scope and that a linker symbol of the exact name is exported.

private package C code.

dependecies in a foreign import may be written as p:foo.c or p:foo.h, this means that the file should be interpreted as part of the internal implementation of the package. jhc willl ensure the files do not clash with those of other packages that may have the same name. The files should be listed in the c-files and c-headers sections of the library config file.

Explicit namespaces in import/export lists

jhc allows explicit namespaces in import and export lists. These may be used to restrict or modiy what is imported/exported by a declaration.

* 'type' - The name is a type, as in something defined by 'type', 'newtype',
   or 'data', or the constructors of a kind declaration.
* 'class' - Specifies that the name is that of a class.
* 'data'  - Specifies that the name is a data constructor.
* 'kind'  - specifies that the name is a user defined kind.

In addition, another extension is that classes and types are in independent namespaces, so a type and a class of the same name may be in scope and not conflict.

Standalone deriving

Jhc supports standalone deriving for a few built in classes that have especially efficient implementations that cannot be hand written. Eq, Ord, Enum, and Bounded for enumerations.

deriving instance Eq Ordering

Rank-N Polymorphism

Jhc supports higher ranked polymorphism. jhc will never infer types of higher rank, however when the context unambiguously specifies a higher ranked type, it will be used. For instance, user supplied type annotations and arguments to data constructors defined to by polymorphic will get the correct polymorphic type.

Existential types

Jhc supports first class existential types, using the 'exists' keyword. It also supports existential data types in a similar fashion to ghc.

Unboxed Values

Unboxed values in jhc are specified in a similar fashion to GHC however the lexical syntax is not changed to allow # in identifiers. # is still used in the syntax for various unboxed constructs, but normal Haskell rules apply to haskell identifiers. The convention is to suffix such types with '_' to indicate their status as unboxed. All unboxed values other than unboxed tuples are enabled by the -funboxed-value flag. For compatibility with GHC, the MagicHash extension name also turns on unboxed-values.

Unboxed Tuples

Jhc supports unboxed tuples with the same syntax as GHC, (# 2, 4 #) is an unboxed tuple of two numbers. Unboxed tuples are enabled with -funboxed-tuples. Unboxed tuples are kind-polymorphic, able to hold both boxed and unboxed values. (but not another unboxed tuple)

Unboxed Strings

Unboxed strings are enabled with the -funboxed-values flag. They are specified like a normal string but have a '#' at the end. Unboxed strings have types 'BitsPtr_'.

Unboxed Characters

Unboxed characters can be expressed by putting a hash after a normal character literal. Unboxed characters are of type Char_ which is a newtype of Bits32_ and defined in Jhc.Prim.Bits

Unboxed Numbers

Unboxed numbers are enabled with the -funboxed-values flag. They are postpended with a '#' such as in 3# or 4#. Jhc supports a limited form of type inference for unboxed numbers, if the type is fully specified by the environment and it is a suitable unboxed numeric type then that type is used. Otherwise it defaults to Int__. Whether the type is fully specifed follows the same rules as rank-n types. Unboxed numbers do the right thing for enumerations, so 0# can be used for the unboxed False value and the appropriate type will be infered.

Operations on unboxed values

To operate on unboxed vaules you need to bring the appropriate primitive operators into scope. You can do this via the special form of FFI declaration for importing primitives. Any C-- primitive may be imported as well as a variety of utility routines. the primitive import mechanism is 'smart' in that it will dig through newtypes and take care of boxing/unboxing values as needed. So you can import a primitive on Char and it will take care of boxing the value up in the 'Char' constructor as well as the Char_ newtype for Bits32_, ultimately choosing the right Bits32_ primitive. imported primitives are normal haskell declarations so may be exported/imported from modules or passed as higher order functions like normal.

Foreign Primitives

In addition to foreign imports of external functions as described in the FFI spec. Jhc supports 'primitive' imports that let you communicate primitives directly to the compiler. In general, these should not be used other than in the implementation of the standard libraries. They generally do little error checking as it is assumed you know what you are doing if you use them. All haskell visible entities are introduced via foreign declarations in jhc.

They all have the form

foreign import primitive "specification" haskell_name :: type

where the specification string is one of the following


evaluate first argument to WHNF, then return the second argument


the values zero and one of any primitive type.


the text following const is directly inserted into the resulting C file


the peek primitive for raw value TYPE


the poke primitive for raw value TYPE

sizeOf.TYPE, alignmentOf.TYPE, minBound.TYPE, maxBound.TYPE, umaxBound.TYPE

various properties of a given internal type.


results in an error with constant message MESSAGE.


peek of a constant value specialized to bytes, used internally by Jhc.String


take an unboxed value and box it, the shape of the box is determined by the type at which this is imported


take an boxed value and unbox it, the shape of the box is determined by the type at which this is imported

increment, decrement

increment or decrement a numerical integral primitive value

fincrement, fdecrement

increment or decrement a numerical floating point primitive value

exitFailure__ : abort the program immediately

C-- Primitive, such as Sub,Mul,NEq...
any C-- primitive may be imported in this manner.


Differences from Haskell 98

Language Differences

Notable Differences from GHC

Jhc differs from GHC in certain ways that are allowed by Haskell 98, but might come as a surprise to some.

Differences That are Considered Misfeatures

These misfeatures will be fixed at some point.



The Run Time System

Jhc is very minimalist in that it does not have a precompiled run time system, but rather generates what is needed as part of the compilation process. However, back ends do have specific run-time representations of data, which can be affected by things like the choice of garbage collector. The following describes the general layout for the C based back-ends, but compiler options such as garbage collection method or whether we do full program analysis, will affect which features are used and whether certain optimized layouts are possible.

Unboxed values directly translate to values in the target language, an unboxed Int will translate directly into an 'int' as an argument and an unboxed pointer will be a raw pointer. Unboxed values have no special interpretation and are not followed by the garbage collector. If the target language does not support a feature such as multiple return values, it will have to be simulated. It would not be wrong to think of Grin code that only deals with unboxed values to be isomorphic to C-- or C augmented with multiple return values.

Boxed values have a standard representation and can be followed. Unlike some other implementation, being boxed does not imply the object is located on the heap. It may be on the stack, heap, or even embedded within the smart pointer itself. Being boxed only means that the object may be represented by a smart pointer, which may or may not actually be a pointer in the traditional sense.

A boxed value in jhc is represented by a 'smart pointer' of c type sptr_t. a smart pointer is the size of a native pointer, but can take on different roles depending on a pair of tag bits, called the ptype.

smart pointers take on a general form as follows:

|    payload        | GL|

  G - if set, then the garbage collector should not treat value as a pointer to be followed
  L - lazy, this bit being set means the value is potentially not in WHNF

A sptr_t on its own in the wild can only take on one of the following forms:

|    whnf raw value | 10|

|    whnf location  | 00|

WHNF stands for 'Weak Head Normal Form' and means that the value is not a suspended function and hence not a pointer to a thunk. It may be directly examined and need not be evaluated. wptr_t is an alias for sptr_t that is guarenteed to be of one of the above forms. It is used to improve safety for when we can statically know that a value is WHNF and hence we can skip the expensive 'eval'.

The difference between the raw value and the whnf location is that the first contains uninterpreted bits, while the second is a pointer to a location on the heap or stack and hence the garbage collector should follow it. The format of the memory pointed to by the whnf location is unspecified and dependent on the actual type being represented.

Partial (unsaturated) applications are normal WHNF values. Saturated applications which may be 'eval'ed and updated are called thunks and must not be pointed to by WHNF pointers. Their representation follows.

|   lazy location   | 01|

A lazy location points to either a thunk, or a redirection to a WHNF value. A lazy location is always a pointer to an allocated block of memory which always begins with a restricted smart pointer. This restricted smart pointer is represented by the C type alias 'fptr_t'. fptr_t's only occur as the first entry in a lazy location, they never are passed around as objects in their own right.

A fptr_t may be a whnf value or a code pointer. If a fptr_t is a whnf value (of one of the two forms given above) then it is called a redirection, the lazy location should be treated exactly as if it were the whnf given. This is used to redirect an evaluated thunk to its computed value.

A fptr_t may also be a 'code pointer' in which case the lazy location is called a thunk. A code pointer is a pointer to executable machine code that evaluates a closure and returns a wptr_t, the returned wptr_t is then generally written over the code pointer, turning the thunk into a redirection. It is the responsibility of the code pointed to to perform this redirection.

|    code pointer   | 11|
|     data ...          |

When debugging, the special code pointer BLACK_HOLE is also sometimes stored in a fptr_t to detect certain run-time errors.

Note that unlike other implementations, a fptr_t may not be another lazy location. you can not have chained redirections, a redirection is always a redirection to a whnf value.

sptr_t - a tagged smart pointer, may contain a whnf value or a lazy location.
wptr_t - a tagged smart pointer that contains a whnf value (either raw or a location)
fptr_t - a tagged smart pointer, may contain a whnf value indicating a redirection, or a code pointer indicating a thunk.

Jhc Core Type System

Jhc's core is based on a pure type system. A pure type system (also called a PTS) is actually a parameterized set of type systems. Jhc's version is described by the following.

Sorts  = (*, !, **, #, (#), ##, □)
Axioms = (*:**, #:##, !:**, **:□, ##:□)

-- sort kind
*   is the kind of boxed values
!   is the kind of boxed strict values
#   is the kind of unboxed values
(#) is the kind of unboxed tuples
-- sort superkind
**  is the superkind of all boxed value
##  is the superkind of all unboxed values
-- sort box
□   superkinds inhabit this

in addition there exist user defined kinds, which are always of supersort ##

The following Rules table shows what sort of abstractions are allowed, a rule of the form (A,B,C) means you can have functions of things of sort A to things of sort B and the result is something of sort C. Function in this context subsumes both term and type level abstractions.

Notice that functions are always boxed, but may be strict if they take an unboxed tuple as an argument. When a function is strict it means that it is represented by a pointer to code directly, it cannot be a suspended value that evaluates to a function.

These type system rules apply to lambda abstractions. It is possible that data constructors might exist that cannot be given a type on their own with these rules, even though when fully applied it has a well formed type. An example would be unboxed tuples. This presents no difficulty as one concludes correctly that it is a type error for these constructors to ever appear when not fully saturated with arguments.

as a shortcut we will use *# to mean every combination involving * and #, and so forth.
for instance, (*#,*#,*) means the set (*,*,*) (#,*,*) (*,#,*) (#,#,*)

Rules =
   (*#!,*#!,*)  -- functions from values to values are boxed and lazy
   (*#!,(#),*)  -- functions from values to unboxed tuples are boxed and lazy
   ((#),*#!,!)  -- functions from unboxed tuples to values are boxed and strict
   ((#),(#),!)  -- functions from unboxed tuples to unboxed tuples are boxed and strict
   (**,*,*)     -- may have a function from an unboxed type to a value
   (**,**,**)  -- we have functions from types to types
   (**,##,##)  -- MutArray_ :: * -> #
   (##,##,##)  -- Complex_ :: # -> #

The defining feature of boxed values is

_|_ :: t iff t::*

This PTS is functional but not injective

The PTS can be considered stratified into the following levels

□                - sort box
**,##,           - sort superkind
*,#,(#),!        - sort kind
Int,Bits32_,Char - sort type
3,True,"bob"     - sort value

On boxed kinds

The boxed kinds (* and !) represent types that have a uniform run time representation. Due to this, functions may be written that are polymorphic in types of these kinds. Hence the rules of the form (**,?,?), allowing taking types of boxed kinds as arguments.

the unboxed kind # is inhabited with types that have their own specific run time representation. Hence you cannot write functions that are polymorphic in unboxed types

On sort box, the unboxed tuple, and friends

Although sort box does not appear in the code, it is useful from a theoretical point of view to talk about certain types such as the types of unboxed tuples. Unboxed tuples may have boxed and unboxed arguments, without sort box it would be impossible to express this since it must be superkind polymorphic. sort box allows one to express this as (in the case of the unboxed 2-tuple)

∀s1:□ ∀s2:□ ∀k1:s1 ∀k2:s2 ∀t1:k1 ∀t2:k2 . (# t1, t2 #)

However, although this is a valid typing of what it would mean if a unboxed tuple were not fully applied, since we do not have any rules of form (##,?,?) or (□,?,?) this type obviously does not typecheck. Which is what enforces the invarient that unboxed tuples are always fully applied, and is also why we do not need a code representation of sort box.

Do we need a superbox?

You will notice that if you look at the axioms involving the sorts, you end up with a disjoint graph

         □             - the box
        / \
      **   ##          - superkind
      /\     \
     *  !     #   (#)  - kind

This is simply due to the fact that nothing is polymorphic in unboxed tuples of kind (#) so we never need to refer to any super-sorts of them. We can add sorts (##),(□) and □□ to fill in the gaps, but since these sorts will never appear in code or discourse, we will ignore them from now on.

           □□            - sort superbox
          /  \
         □    (□)        - sort box
        / \      \
      **   ##     (##)   - sort superkind
      /\     \    |
     *  !     #   (#)    - sort kind