Safe Haskell	None
Language	Haskell98

Idris.Core.TT

Contents

A few handy operations on well typed terms:

Description

TT is the core language of Idris. The language has:

Full dependent types
A hierarchy of universes, with cumulativity: Type : Type1, Type1 : Type2, ...
Pattern matching letrec binding
(primitive types defined externally)

Some technical stuff:

Typechecker is kept as simple as possible - no unification, just a checker for incomplete terms.
We have a simple collection of tactics which we use to elaborate source programs with implicit syntax into fully explicit terms.

Synopsis

Documentation

data Option Source

Constructors

TTypeInTType
CheckConv

Instances

Eq Option

data FC Source

Source location. These are typically produced by the parser getFC

Constructors

FC
Fields _fc_fname :: String Filename _fc_start :: (Int, Int) Line and column numbers for the start of the location span _fc_end :: (Int, Int) Line and column numbers for the end of the location span
NoFC	Locations for machine-generated terms
FileFC	Locations with file only
Fields _fc_fname :: String Filename

Instances

Eq FC	Ignore source location equality (so deriving classes do not compare FCs)
Data FC
Ord FC
Show FC
Binary FC
NFData FC
SExpable FC
Typeable * FC

fc_fname :: FC -> String Source

Give a notion of filename associated with an FC

fc_start :: FC -> (Int, Int) Source

Give a notion of start location associated with an FC

fc_end :: FC -> (Int, Int) Source

Give a notion of end location associated with an FC

spanFC :: FC -> FC -> FC Source

Get the largest span containing the two FCs

newtype FC' Source

FC with equality

Constructors

FC'
Fields unwrapFC :: FC

Instances

Eq FC'

emptyFC :: FC Source

Empty source location

fileFC :: String -> FC Source

Source location with file only

data NameOutput Source

Output annotation for pretty-printed name - decides colour

Constructors

TypeOutput
FunOutput
DataOutput
MetavarOutput
PostulateOutput

Instances

Show NameOutput
SExpable NameOutput

data TextFormatting Source

Text formatting output

Constructors

BoldText
ItalicText
UnderlineText

Instances

Show TextFormatting

data OutputAnnotation Source

Output annotations for pretty-printing

Constructors

AnnName Name (Maybe NameOutput) (Maybe String) (Maybe String)	^ The name, classification, docs overview, and pretty-printed type
AnnBoundName Name Bool	^ The name and whether it is implicit
AnnConst Const
AnnData String String	type, doc overview
AnnType String String	name, doc overview
AnnKeyword
AnnFC FC
AnnTextFmt TextFormatting
AnnTerm [(Name, Bool)] (TT Name)	pprint bound vars, original term
AnnSearchResult Ordering	more general, isomorphic, or more specific
AnnErr Err
AnnNamespace [Text] (Maybe FilePath)	A namespace (e.g. on an import line or in a namespace declaration). Stored starting at the root, with the hierarchy fully resolved. If a file path is present, then the namespace represents a module imported from that file.

Instances

Show OutputAnnotation
SExpable OutputAnnotation

data ErrorReportPart Source

Used for error reflection

Constructors

TextPart String
NamePart Name
TermPart Term
SubReport [ErrorReportPart]

Instances

Eq ErrorReportPart
Data ErrorReportPart
Show ErrorReportPart
Binary ErrorReportPart
NFData ErrorReportPart
Typeable * ErrorReportPart

data Provenance Source

Constructors

ExpectedType
TooManyArgs Term
InferredVal
GivenVal
SourceTerm Term

Instances

Eq Provenance
Data Provenance
Show Provenance
Binary Provenance
NFData Provenance
Typeable * Provenance

data Err' t Source

Idris errors. Used as exceptions in the compiler, but reported to users if they reach the top level.

Constructors

Msg String
InternalMsg String
CantUnify Bool (t, Maybe Provenance) (t, Maybe Provenance) (Err' t) [(Name, t)] Int
InfiniteUnify Name t [(Name, t)]
CantConvert t t [(Name, t)]
CantSolveGoal t [(Name, t)]
UnifyScope Name Name t [(Name, t)]
CantInferType String
NonFunctionType t t
NotEquality t t
TooManyArguments Name
CantIntroduce t
NoSuchVariable Name
WithFnType t
NoTypeDecl Name
NotInjective t t t
CantResolve Bool t
InvalidTCArg Name t
CantResolveAlts [Name]
IncompleteTerm t
NoEliminator String t
UniverseError FC UExp (Int, Int) (Int, Int) [ConstraintFC]	Location, bad universe, old domain, new domain, suspects
UniqueError Universe Name
UniqueKindError Universe Name
ProgramLineComment
Inaccessible Name
UnknownImplicit Name Name
CantMatch t
NonCollapsiblePostulate Name
AlreadyDefined Name
ProofSearchFail (Err' t)
NoRewriting t
At FC (Err' t)
Elaborating String Name (Err' t)
ElaboratingArg Name Name [(Name, Name)] (Err' t)
ProviderError String
LoadingFailed String (Err' t)
ReflectionError [[ErrorReportPart]] (Err' t)
ReflectionFailed String (Err' t)
ElabScriptDebug (Maybe String) t [(Name, t, [(Name, Binder t)])]	User-specified message, proof term, goals with context (first goal is focused)
ElabScriptStuck t

Instances

Functor Err'
Show Err
NFData Err
Eq t => Eq (Err' t)
Data t => Data (Err' t)
Binary a => Binary (Err' a)
MonadException m => MonadException (ExceptT Err m)
Typeable (* -> *) Err'

type Err = Err' Term Source

data TC a Source

Constructors

OK !a
Error Err

Instances

Alternative TC
Monad TC
Functor TC
MonadPlus TC
Applicative TC
Eq a => Eq (TC a)
Show a => Show (TC a)

bindTC :: TC a -> (a -> TC b) -> TC b Source

score :: Err -> Int Source

tfail :: Err -> TC a Source

failMsg :: String -> TC a Source

trun :: FC -> TC a -> TC a Source

discard :: Monad m => m a -> m () Source

showSep :: String -> [String] -> String Source

pmap :: (t -> t1) -> (t, t) -> (t1, t1) Source

traceWhen :: Bool -> String -> a -> a Source

data Name Source

Names are hierarchies of strings, describing scope (so no danger of duplicate names, but need to be careful on lookup).

Constructors

UN Text	User-provided name
NS Name [Text]	Root, namespaces
MN Int Text	Machine chosen names
NErased	Name of something which is never used in scope
SN SpecialName	Decorated function names
SymRef Int	Reference to IBC file symbol table (used during serialisation)

Instances

Eq Name
Data Name
Ord Name
Show Name
Show Err
Binary Name
Binary CaseAlt
Binary SC
NFData Name
NFData Err
TermSize CaseAlt
TermSize SC
SExpable Name
Typeable * Name
Binary (TT Name)
TermSize (TT Name)
Optimisable (TT Name)
Optimisable (Binder (TT Name))
MonadException m => MonadException (ExceptT Err m)

txt :: String -> Text Source

str :: Text -> String Source

tnull :: Text -> Bool Source

thead :: Text -> Char Source

sUN :: String -> Name Source

sNS :: Name -> [String] -> Name Source

sMN :: Int -> String -> Name Source

data SpecialName Source

Constructors

WhereN Int Name Name
WithN Int Name
InstanceN Name [Text]
ParentN Name Text
MethodN Name
CaseN Name
ElimN Name
InstanceCtorN Name
MetaN Name Name

Instances

Eq SpecialName
Data SpecialName
Ord SpecialName
Show SpecialName
Binary SpecialName
NFData SpecialName
Typeable * SpecialName

sInstanceN :: Name -> [String] -> SpecialName Source

sParentN :: Name -> String -> SpecialName Source

showCG :: Name -> String Source

type Ctxt a = Map Name (Map Name a) Source

Contexts allow us to map names to things. A root name maps to a collection of things in different namespaces with that name.

emptyContext :: Map k a Source

mapCtxt :: (a -> b) -> Ctxt a -> Ctxt b Source

tcname :: Name -> Bool Source

Return True if the argument Name should be interpreted as the name of a typeclass.

implicitable :: Name -> Bool Source

nsroot :: Name -> Name Source

addDef :: Name -> a -> Ctxt a -> Ctxt a Source

lookupCtxtName :: Name -> Ctxt a -> [(Name, a)] Source

Look up a name in the context, given an optional namespace. The name (n) may itself have a (partial) namespace given.

Rules for resolution:

if an explicit namespace is given, return the names which match it. If none match, return all names.
- if the name has has explicit namespace given, return the names which match it and ignore the given namespace.
- otherwise, return all names.

lookupCtxt :: Name -> Ctxt a -> [a] Source

lookupCtxtExact :: Name -> Ctxt a -> Maybe a Source

deleteDefExact :: Name -> Ctxt a -> Ctxt a Source

updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a Source

toAlist :: Ctxt a -> [(Name, a)] Source

addAlist :: [(Name, a)] -> Ctxt a -> Ctxt a Source

data NativeTy Source

Constructors

IT8
IT16
IT32
IT64

Instances

Enum NativeTy
Eq NativeTy
Data NativeTy
Ord NativeTy
Show NativeTy
NFData NativeTy
Typeable * NativeTy

data IntTy Source

Constructors

ITFixed NativeTy
ITNative
ITBig
ITChar

Instances

Eq IntTy
Data IntTy
Ord IntTy
Show IntTy
NFData IntTy
Typeable * IntTy

intTyName :: IntTy -> String Source

data ArithTy Source

Constructors

ATInt IntTy
ATFloat

Instances

Eq ArithTy
Data ArithTy
Ord ArithTy
Show ArithTy
NFData ArithTy
Typeable * ArithTy

nativeTyWidth :: NativeTy -> Int Source

intTyWidth :: IntTy -> Int Source

Deprecated: Non-total function, use nativeTyWidth and appropriate casing

data Const Source

Constructors

I Int
BI Integer
Fl Double
Ch Char
Str String
B8 Word8
B16 Word16
B32 Word32
B64 Word64
AType ArithTy
StrType
WorldType
TheWorld
VoidType
Forgot

Instances

Eq Const
Data Const
Ord Const
Show Const
Binary Const
NFData Const
Typeable * Const

isTypeConst :: Const -> Bool Source

constIsType :: Const -> Bool Source

Determines whether the input constant represents a type

constDocs :: Const -> String Source

Get the docstring for a Const

data Universe Source

Constructors

NullType
UniqueType
AllTypes

Instances

Eq Universe
Data Universe
Ord Universe
Show Universe
Binary Universe
NFData Universe
Typeable * Universe

data Raw Source

Constructors

Var Name
RBind Name (Binder Raw) Raw
RApp Raw Raw
RType
RUType Universe
RForce Raw
RConstant Const

Instances

Eq Raw
Data Raw
Show Raw
Binary Raw
NFData Raw
Optimisable Raw
Typeable * Raw
Optimisable (Binder Raw)

data ImplicitInfo Source

Constructors

Impl
Fields tcinstance :: Bool

Instances

Eq ImplicitInfo
Data ImplicitInfo
Ord ImplicitInfo
Show ImplicitInfo
Binary ImplicitInfo
NFData ImplicitInfo
Typeable * ImplicitInfo

data Binder b Source

All binding forms are represented in a uniform fashion. This type only represents the types of bindings (and their values, if any); the attached identifiers are part of the Bind constructor for the TT type.

Constructors

Lam
Fields binderTy :: !b type annotation for bound variable
Pi	A binding that occurs in a function type expression, e.g. `(x:Int) -> ...` The `binderImpl` flag says whether it was a scoped implicit (i.e. forall bound) in the high level Idris, but otherwise has no relevance in TT.
Fields binderImpl :: Maybe ImplicitInfo binderTy :: !b type annotation for bound variable binderKind :: !b
Let	A binding that occurs in a `let` expression
Fields binderTy :: !b type annotation for bound variable binderVal :: b value for bound variable
NLet
Fields binderTy :: !b type annotation for bound variable binderVal :: b value for bound variable
Hole
Fields binderTy :: !b type annotation for bound variable
GHole
Fields envlen :: Int binderTy :: !b type annotation for bound variable
Guess
Fields binderTy :: !b type annotation for bound variable binderVal :: b value for bound variable
PVar	A pattern variable
Fields binderTy :: !b type annotation for bound variable
PVTy
Fields binderTy :: !b type annotation for bound variable

Instances

Functor Binder
Foldable Binder
Traversable Binder
Eq b => Eq (Binder b)
Data b => Data (Binder b)
Ord b => Ord (Binder b)
Show b => Show (Binder b)
Binary b => Binary (Binder b)
NFData b => NFData (Binder b)
Optimisable (Binder (TT Name))
Optimisable (Binder Raw)
Typeable (* -> *) Binder

fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b) Source

raw_apply :: Raw -> [Raw] -> Raw Source

raw_unapply :: Raw -> (Raw, [Raw]) Source

data UExp Source

Universe expressions for universe checking

Constructors

UVar Int	universe variable
UVal Int	explicit universe level

Instances

Eq UExp
Data UExp
Ord UExp
Show UExp
Binary UExp
NFData UExp
Typeable * UExp

data UConstraint Source

Universe constraints

Constructors

ULT UExp UExp	Strictly less than
ULE UExp UExp	Less than or equal to

Instances

Eq UConstraint
Data UConstraint
Ord UConstraint
Show UConstraint
Binary UConstraint
NFData UConstraint
Typeable * UConstraint

data ConstraintFC Source

Constructors

ConstraintFC
Fields uconstraint :: UConstraint ufc :: FC

Instances

Eq ConstraintFC
Data ConstraintFC
Ord ConstraintFC
Show ConstraintFC
Binary ConstraintFC
NFData ConstraintFC
Typeable * ConstraintFC

type UCs = (Int, [UConstraint]) Source

data NameType Source

Constructors

Bound
Ref
DCon	Data constructor
Fields nt_tag :: Int nt_arity :: Int nt_unique :: Bool
TCon	Type constructor
Fields nt_tag :: Int nt_arity :: Int

Instances

Eq NameType
Data NameType
Ord NameType
Show NameType
Binary NameType
NFData NameType
Typeable * NameType

data AppStatus n Source

Constructors

Complete
MaybeHoles
Holes [n]

Instances

Functor AppStatus
Eq n => Eq (AppStatus n)
Data n => Data (AppStatus n)
Ord n => Ord (AppStatus n)
Show n => Show (AppStatus n)
Typeable (* -> *) AppStatus

data TT n Source

Terms in the core language. The type parameter is the type of identifiers used for bindings and explicit named references; usually we use TT Name.

Constructors

P NameType n (TT n)	named references with type (P for Parameter, motivated by McKinna and Pollack's Pure Type Systems Formalized)
V !Int	a resolved de Bruijn-indexed variable
Bind n !(Binder (TT n)) (TT n)	a binding
App (AppStatus n) !(TT n) (TT n)	function, function type, arg
Constant Const	constant
Proj (TT n) !Int	argument projection; runtime only (-1) is a special case for 'subtract one from BI'
Erased	an erased term
Impossible	special case for totality checking
TType UExp	the type of types at some level
UType Universe	Uniqueness type universe (disjoint from TType)

Instances

Functor TT
Show Err
Binary CaseAlt
Binary SC
NFData Err
TermSize CaseAlt
TermSize SC
Eq n => Eq (TT n)
Data n => Data (TT n)
Ord n => Ord (TT n)
(Eq n, Show n) => Show (TT n)
Binary (TT Name)
NFData n => NFData (TT n)
TermSize (TT Name)
Optimisable (TT Name)
Optimisable (Binder (TT Name))
MonadException m => MonadException (ExceptT Err m)
Typeable (* -> *) TT

class TermSize a where Source

Methods

termsize :: Name -> a -> Int Source

Instances

TermSize CaseAlt
TermSize SC
TermSize a => TermSize [a]
TermSize (TT Name)

type EnvTT n = [(n, Binder (TT n))] Source

data Datatype n Source

Constructors

Data
Fields d_typename :: n d_typetag :: Int d_type :: TT n d_unique :: Bool d_cons :: [(n, TT n)]

Instances

Functor Datatype
Eq n => Eq (Datatype n)
(Eq n, Show n) => Show (Datatype n)

data DataOpt Source

Data declaration options

Constructors

Codata	Set if the the data-type is coinductive
DefaultEliminator	Set if an eliminator should be generated for data type
DefaultCaseFun	Set if a case function should be generated for data type
DataErrRev

Instances

Eq DataOpt
Show DataOpt
Binary DataOpt
NFData DataOpt

type DataOpts = [DataOpt] Source

data TypeInfo Source

Constructors

TI
Fields con_names :: [Name] codata :: Bool data_opts :: DataOpts param_pos :: [Int] mutual_types :: [Name]

Instances

Show TypeInfo
Binary TypeInfo
NFData TypeInfo

A few handy operations on well typed terms:

isInjective :: TT n -> Bool Source

A term is injective iff it is a data constructor, type constructor, constant, the type Type, pi-binding, or an application of an injective term.

vinstances :: Int -> TT n -> Int Source

Count the number of instances of a de Bruijn index in a term

instantiate :: TT n -> TT n -> TT n Source

Replace the outermost (index 0) de Bruijn variable with the given term

substV :: TT n -> TT n -> TT n Source

As instantiate, but also decrement the indices of all de Bruijn variables remaining in the term, so that there are no more references to the variable that has been substituted.

explicitNames :: TT n -> TT n Source

Replace all non-free de Bruijn references in the given term with references to the name of their binding.

pToV :: Eq n => n -> TT n -> TT n Source

Replace references to the given Name-like id with references to de Bruijn index 0.

pToV' :: Eq n => n -> Int -> TT n -> TT n Source

addBinder :: TT n -> TT n Source

pToVs :: Eq n => [n] -> TT n -> TT n Source

Convert several names. First in the list comes out as V 0

vToP :: TT n -> TT n Source

Replace de Bruijn indices in the given term with explicit references to the names of the bindings they refer to. It is an error if the given term contains free de Bruijn indices.

finalise :: Eq n => TT n -> TT n Source

Replace every non-free reference to the name of a binding in the given term with a de Bruijn index.

pEraseType :: TT n -> TT n Source

subst Source

Arguments

:: Eq n
=> n	The id to replace
-> TT n	The replacement term
-> TT n	The term to replace in
-> TT n

As instantiate, but in addition to replacing V 0, replace references to the given Name-like id.

psubst :: Eq n => n -> TT n -> TT n -> TT n Source

substNames :: Eq n => [(n, TT n)] -> TT n -> TT n Source

As subst, but takes a list of (name, substitution) pairs instead of a single name and substitution

substTerm Source

Arguments

:: Eq n
=> TT n	Old term
-> TT n	New term
-> TT n	template term
-> TT n

Replaces all terms equal (in the sense of (==)) to the old term with the new term.

occurrences :: Eq n => n -> TT n -> Int Source

Return number of occurrences of V 0 or bound name i the term

noOccurrence :: Eq n => n -> TT n -> Bool Source

Returns true if V 0 and bound name n do not occur in the term

freeNames :: Eq n => TT n -> [n] Source

Returns all names used free in the term

arity :: TT n -> Int Source

Return the arity of a (normalised) type

unApply :: TT n -> (TT n, [TT n]) Source

Deconstruct an application; returns the function and a list of arguments

mkApp :: TT n -> [TT n] -> TT n Source

Returns a term representing the application of the first argument (a function) to every element of the second argument.

unList :: Term -> Maybe [Term] Source

forget :: TT Name -> Raw Source

Cast a TT term to a Raw value, discarding universe information and the types of named references and replacing all de Bruijn indices with the corresponding name. It is an error if there are free de Bruijn indices.

safeForget :: TT Name -> Maybe Raw Source

forgetEnv :: [Name] -> TT Name -> Raw Source

safeForgetEnv :: [Name] -> TT Name -> Maybe Raw Source

bindAll :: [(n, Binder (TT n))] -> TT n -> TT n Source

Introduce a Bind into the given term for each element of the given list of (name, binder) pairs.

bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n Source

Like bindAll, but the Binders are TT terms instead. The first argument is a function to map TT terms to Binders. This function might often be something like Lam, which directly constructs a Binder from a TT term.

getArgTys :: TT n -> [(n, TT n)] Source

Return a list of pairs of the names of the outermost Pi-bound variables in the given term, together with their types.

getRetTy :: TT n -> TT n Source

uniqueNameFrom :: [Name] -> [Name] -> Name Source

uniqueName :: Name -> [Name] -> Name Source

uniqueNameSet :: Name -> Set Name -> Name Source

uniqueBinders :: [Name] -> TT Name -> TT Name Source

nextName :: Name -> Name Source

type Term = TT Name Source

type Type = Term Source

type Env = EnvTT Name Source

newtype WkEnvTT n Source

an environment with de Bruijn indices normalised so that they all refer to this environment

Constructors

Wk (EnvTT n)

type WkEnv = WkEnvTT Name Source

itBitsName :: NativeTy -> [Char] Source

showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String Source

showEnvDbg :: (Show a, Eq a) => [(a, Binder (TT a))] -> TT a -> [Char] Source

prettyEnv :: Env -> Term -> Doc OutputAnnotation Source

showEnv' :: (Show a, Eq a) => [(a, Binder (TT a))] -> TT a -> Bool -> [Char] Source

pureTerm :: TT Name -> Bool Source

Check whether a term has any hole bindings in it - impure if so

weakenTm :: Int -> TT n -> TT n Source

Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)

weakenEnv :: EnvTT n -> EnvTT n Source

Weaken an environment so that all the de Bruijn indices are correct according to the latest bound variable

weakenTmEnv :: Int -> EnvTT n -> EnvTT n Source

Weaken every term in the environment by the given amount

orderPats :: Term -> Term Source

Gather up all the outer PVars and Holes in an expression and reintroduce them in a canonical order

refsIn :: TT Name -> [Name] Source

liftPats :: Term -> Term Source

allTTNames :: Eq n => TT n -> [n] Source

pprintTT Source

Arguments

:: [Name]	The bound names (for highlighting and de Bruijn indices)
-> TT Name	The term to be printed
-> Doc OutputAnnotation

Pretty-print a term

bindingOf Source

Arguments

:: Name	^ the bound name
-> Bool	^ whether the name is implicit
-> Doc OutputAnnotation

Pretty-printer helper for the binding site of a name