module Language.Reflection import Builtins import Prelude.Applicative import Prelude.Basics import Prelude.Foldable import Prelude.Functor import Prelude.List import Prelude.Nat import Prelude.Traversable %access public mutual data TTName = ||| A user-provided name UN String | ||| A name in some namespace. ||| ||| The namespace is in reverse order, so `(NS (UN "foo") ["B", "A"])` ||| represents the name `A.B.foo` NS TTName (List String) | ||| Machine-chosen names MN Int String | ||| Special names, to make conflicts impossible and language features ||| predictable SN SpecialName | ||| Name of something which is never used in scope NErased %name TTName n, n' data SpecialName = WhereN Int TTName TTName | WithN Int TTName | InstanceN TTName (List String) | ParentN TTName String | MethodN TTName | CaseN TTName | ElimN TTName | InstanceCtorN TTName | MetaN TTName TTName implicit userSuppliedName : String -> TTName userSuppliedName = UN data TTUExp = ||| Universe variable UVar Int | ||| Explicit universe level UVal Int %name TTUExp uexp data NativeTy = IT8 | IT16 | IT32 | IT64 data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar data ArithTy = ATInt Language.Reflection.IntTy | ATFloat ||| Primitive constants data Const = I Int | BI Integer | Fl Float | Ch Char | Str String | B8 Bits8 | B16 Bits16 | B32 Bits32 | B64 Bits64 | AType ArithTy | StrType | VoidType | Forgot | WorldType | TheWorld %name Const c, c' abstract class ReflConst (a : Type) where toConst : a -> Const instance ReflConst Int where toConst x = I x instance ReflConst Integer where toConst = BI instance ReflConst Float where toConst = Fl instance ReflConst Char where toConst = Ch instance ReflConst String where toConst = Str instance ReflConst Bits8 where toConst = B8 instance ReflConst Bits16 where toConst = B16 instance ReflConst Bits32 where toConst = B32 instance ReflConst Bits64 where toConst = B64 implicit reflectConstant: (ReflConst a) => a -> Const reflectConstant = toConst ||| Types of named references data NameType = ||| A reference which is just bound, e.g. by intro Bound | ||| A reference to a de Bruijn-indexed variable Ref | ||| Data constructor with tag and number DCon Int Int | ||| Type constructor with tag and number TCon Int Int %name NameType nt, nt' ||| Types annotations for bound variables in different ||| binding contexts data Binder a = Lam a | Pi a a | Let a a | NLet a a | Hole a | GHole a | Guess a a | PVar a | PVTy a %name Binder b, b' instance Functor Binder where map f (Lam x) = Lam (f x) map f (Pi x k) = Pi (f x) (f k) map f (Let x y) = Let (f x) (f y) map f (NLet x y) = NLet (f x) (f y) map f (Hole x) = Hole (f x) map f (GHole x) = GHole (f x) map f (Guess x y) = Guess (f x) (f y) map f (PVar x) = PVar (f x) map f (PVTy x) = PVTy (f x) instance Foldable Binder where foldr f z (Lam x) = f x z foldr f z (Pi x k) = f x (f k z) foldr f z (Let x y) = f x (f y z) foldr f z (NLet x y) = f x (f y z) foldr f z (Hole x) = f x z foldr f z (GHole x) = f x z foldr f z (Guess x y) = f x (f y z) foldr f z (PVar x) = f x z foldr f z (PVTy x) = f x z instance Traversable Binder where traverse f (Lam x) = [| Lam (f x) |] traverse f (Pi x k) = [| Pi (f x) (f k) |] traverse f (Let x y) = [| Let (f x) (f y) |] traverse f (NLet x y) = [| NLet (f x) (f y) |] traverse f (Hole x) = [| Hole (f x) |] traverse f (GHole x) = [| GHole (f x) |] traverse f (Guess x y) = [| Guess (f x) (f y) |] traverse f (PVar x) = [| PVar (f x) |] traverse f (PVTy x) = [| PVTy (f x) |] ||| Universes data Universe = NullType | UniqueType | AllTypes ||| Reflection of the well typed core language data TT = ||| A reference to some name (P for Parameter) P NameType TTName TT | ||| de Bruijn variables V Int | ||| Bind a variable Bind TTName (Binder TT) TT | ||| Apply one term to another App TT TT | ||| Embed a constant TConst Const | ||| Argument projection; runtime only Proj TT Int | ||| Erased terms Erased | ||| Impossible terms Impossible | ||| The type of types along (with universe constraints) TType TTUExp | UType Universe %name TT tm, tm' ||| Raw terms without types data Raw = ||| Variables, global or local Var TTName | ||| Bind a variable RBind TTName (Binder Raw) Raw | ||| Application RApp Raw Raw | ||| The type of types RType | RUType Universe | RForce Raw | ||| Embed a constant RConstant Const %name Raw tm, tm' data SourceLocation : Type where FileLoc : (filename : String) -> (start : (Int, Int)) -> (end : (Int, Int)) -> SourceLocation %name SourceLocation loc ||| Error reports are a list of report parts data ErrorReportPart = ||| A human-readable string TextPart String | ||| An Idris name (to be semantically coloured) NamePart TTName | ||| An Idris term, to be pretty printed TermPart TT | ||| An indented sub-report, to provide more details SubReport (List ErrorReportPart) %name ErrorReportPart part, p ||| A representation of Idris's tactics that can be returned from custom ||| tactic implementations. Generate these using `applyTactic`. data Tactic = ||| Try the first tactic and resort to the second one on failure Try Tactic Tactic | ||| Only run if the goal has the right type GoalType String Tactic | ||| Resolve function name, find matching arguments in the ||| context and compute the proof target Refine TTName | ||| Apply both tactics in sequence Seq Tactic Tactic | ||| Introduce a new hole with a particular type Claim TTName TT | ||| Move the current hole to the end Unfocus | ||| Intelligently construct the proof target from the context Trivial | ||| Build a proof by applying contructors up to a maximum depth Search Int | ||| Resolve a type class Instance | ||| Infer the proof target from the context Solve | ||| introduce all variables into the context Intros | ||| Introduce a named variable into the context, use the ||| first one if the given name is not found Intro TTName | ||| Invoke the reflected rep. of another tactic ApplyTactic TT | ||| Turn a value into its reflected representation Reflect TT | ||| Use a `%reflection` function ByReflection TT | ||| Turn a raw value back into a term Fill Raw | ||| Use the given value to conclude the proof Exact TT | ||| Focus on a particular hole Focus TTName | ||| Rewrite with an equality Rewrite TT | ||| Perform induction on a particular expression Induction TT | ||| Perform case analysis on a particular expression Case TT | ||| Name a reflected term LetTac TTName TT | ||| Name a reflected term and type it LetTacTy TTName TT TT | ||| Normalise the goal Compute | ||| Do nothing Skip | ||| Fail with an error message Fail (List ErrorReportPart) | ||| Attempt to fill the hole with source code information SourceFC %name Tactic tac, tac' ||| Things with a canonical representation as a reflected term. ||| ||| This type class is intended to be used during proof automation and the ||| construction of custom tactics. ||| ||| @ a the type to be quoted ||| @ t the type to quote it to (typically `TT` or `Raw`) class Quotable a t where ||| A representation of the type `a`. ||| ||| This is to enable quoting polymorphic datatypes quotedTy : t ||| Quote a particular element of `a`. ||| ||| Each equation should look something like ```quote (Foo x y) = `(Foo ~(quote x) ~(quote y))``` quote : a -> t instance Quotable Nat TT where quotedTy = `(Nat) quote Z = `(Z) quote (S k) = `(S ~(quote k)) instance Quotable Nat Raw where quotedTy = `(Nat) quote Z = `(Z) quote (S k) = `(S ~(quote k)) instance Quotable Int TT where quotedTy = `(Int) quote x = TConst (I x) instance Quotable Int Raw where quotedTy = `(Int) quote x = RConstant (I x) instance Quotable Float TT where quotedTy = `(Float) quote x = TConst (Fl x) instance Quotable Float Raw where quotedTy = `(Float) quote x = RConstant (Fl x) instance Quotable Char TT where quotedTy = `(Char) quote x = TConst (Ch x) instance Quotable Char Raw where quotedTy = `(Char) quote x = RConstant (Ch x) instance Quotable Bits8 TT where quotedTy = `(Bits8) quote x = TConst (B8 x) instance Quotable Bits8 Raw where quotedTy = `(Bits8) quote x = RConstant (B8 x) instance Quotable Bits16 TT where quotedTy = `(Bits16) quote x = TConst (B16 x) instance Quotable Bits16 Raw where quotedTy = `(Bits16) quote x = RConstant (B16 x) instance Quotable Bits32 TT where quotedTy = `(Bits32) quote x = TConst (B32 x) instance Quotable Bits32 Raw where quotedTy = `(Bits32) quote x = RConstant (B32 x) instance Quotable Bits64 TT where quotedTy = `(Bits64) quote x = TConst (B64 x) instance Quotable Bits64 Raw where quotedTy = `(Bits64) quote x = RConstant (B64 x) instance Quotable Integer TT where quotedTy = `(Integer) quote x = TConst (BI x) instance Quotable Integer Raw where quotedTy = `(Integer) quote x = RConstant (BI x) instance Quotable String TT where quotedTy = `(String) quote x = TConst (Str x) instance Quotable String Raw where quotedTy = `(String) quote x = RConstant (Str x) instance Quotable NameType TT where quotedTy = `(NameType) quote Bound = `(Bound) quote Ref = `(Ref) quote (DCon x y) = `(DCon ~(quote x) ~(quote y)) quote (TCon x y) = `(TCon ~(quote x) ~(quote y)) instance Quotable NameType Raw where quotedTy = `(NameType) quote Bound = `(Bound) quote Ref = `(Ref) quote (DCon x y) = `(DCon ~(quote {t=Raw} x) ~(quote {t=Raw} y)) quote (TCon x y) = `(TCon ~(quote {t=Raw} x) ~(quote {t=Raw} y)) instance Quotable a TT => Quotable (List a) TT where quotedTy = `(List ~(quotedTy {a})) quote [] = `(List.Nil {a=~(quotedTy {a})}) quote (x :: xs) = `(List.(::) {a=~(quotedTy {a})} ~(quote x) ~(quote xs)) instance Quotable a Raw => Quotable (List a) Raw where quotedTy = `(List ~(quotedTy {a})) quote [] = `(List.Nil {a=~(quotedTy {a})}) quote (x :: xs) = `(List.(::) {a=~(quotedTy {a})} ~(quote x) ~(quote xs)) mutual instance Quotable TTName TT where quotedTy = `(TTName) quote (UN x) = `(UN ~(quote x)) quote (NS n xs) = `(NS ~(quote n) ~(quote xs)) quote (MN x y) = `(MN ~(quote x) ~(quote y)) quote (SN sn) = `(SN ~(assert_total $ quote sn)) quote NErased = `(NErased) instance Quotable SpecialName TT where quotedTy = `(SpecialName) quote (WhereN i n1 n2) = `(WhereN ~(quote i) ~(quote n1) ~(quote n2)) quote (WithN i n) = `(WithN ~(quote i) ~(quote n)) quote (InstanceN i ss) = `(InstanceN ~(quote i) ~(quote ss)) quote (ParentN n s) = `(ParentN ~(quote n) ~(quote s)) quote (MethodN n) = `(MethodN ~(quote n)) quote (CaseN n) = `(CaseN ~(quote n)) quote (ElimN n) = `(ElimN ~(quote n)) quote (InstanceCtorN n) = `(InstanceCtorN ~(quote n)) quote (MetaN parent meta) = `(MetaN ~(quote parent) ~(quote meta)) mutual instance Quotable TTName Raw where quotedTy = `(TTName) quote (UN x) = `(UN ~(quote {t=Raw} x)) quote (NS n xs) = `(NS ~(quote {t=Raw} n) ~(quote {t=Raw} xs)) quote (MN x y) = `(MN ~(quote {t=Raw} x) ~(quote {t=Raw} y)) quote (SN sn) = `(SN ~(assert_total $ quote sn)) quote NErased = `(NErased) instance Quotable SpecialName Raw where quotedTy = `(SpecialName) quote (WhereN i n1 n2) = `(WhereN ~(quote i) ~(quote n1) ~(quote n2)) quote (WithN i n) = `(WithN ~(quote i) ~(quote n)) quote (InstanceN i ss) = `(InstanceN ~(quote i) ~(quote ss)) quote (ParentN n s) = `(ParentN ~(quote n) ~(quote s)) quote (MethodN n) = `(MethodN ~(quote n)) quote (CaseN n) = `(CaseN ~(quote n)) quote (ElimN n) = `(ElimN ~(quote n)) quote (InstanceCtorN n) = `(InstanceCtorN ~(quote n)) quote (MetaN parent meta) = `(MetaN ~(quote parent) ~(quote meta)) instance Quotable NativeTy TT where quotedTy = `(NativeTy) quote IT8 = `(Reflection.IT8) quote IT16 = `(Reflection.IT16) quote IT32 = `(Reflection.IT32) quote IT64 = `(Reflection.IT64) instance Quotable NativeTy Raw where quotedTy = `(NativeTy) quote IT8 = `(Reflection.IT8) quote IT16 = `(Reflection.IT16) quote IT32 = `(Reflection.IT32) quote IT64 = `(Reflection.IT64) instance Quotable Reflection.IntTy TT where quotedTy = `(Reflection.IntTy) quote (ITFixed x) = `(ITFixed ~(quote x)) quote ITNative = `(Reflection.ITNative) quote ITBig = `(ITBig) quote ITChar = `(Reflection.ITChar) instance Quotable Reflection.IntTy Raw where quotedTy = `(Reflection.IntTy) quote (ITFixed x) = `(ITFixed ~(quote {t=Raw} x)) quote ITNative = `(Reflection.ITNative) quote ITBig = `(ITBig) quote ITChar = `(Reflection.ITChar) instance Quotable ArithTy TT where quotedTy = `(ArithTy) quote (ATInt x) = `(ATInt ~(quote x)) quote ATFloat = `(ATFloat) instance Quotable ArithTy Raw where quotedTy = `(ArithTy) quote (ATInt x) = `(ATInt ~(quote {t=Raw} x)) quote ATFloat = `(ATFloat) instance Quotable Const TT where quotedTy = `(Const) quote (I x) = `(I ~(quote x)) quote (BI x) = `(BI ~(quote x)) quote (Fl x) = `(Fl ~(quote x)) quote (Ch x) = `(Ch ~(quote x)) quote (Str x) = `(Str ~(quote x)) quote (B8 x) = `(B8 ~(quote x)) quote (B16 x) = `(B16 ~(quote x)) quote (B32 x) = `(B32 ~(quote x)) quote (B64 x) = `(B64 ~(quote x)) quote (AType x) = `(AType ~(quote x)) quote StrType = `(StrType) quote VoidType = `(VoidType) quote Forgot = `(Forgot) quote WorldType = `(WorldType) quote TheWorld = `(TheWorld) instance Quotable Const Raw where quotedTy = `(Const) quote (I x) = `(I ~(quote {t=Raw} x)) quote (BI x) = `(BI ~(quote {t=Raw} x)) quote (Fl x) = `(Fl ~(quote {t=Raw} x)) quote (Ch x) = `(Ch ~(quote {t=Raw} x)) quote (Str x) = `(Str ~(quote {t=Raw} x)) quote (B8 x) = `(B8 ~(quote {t=Raw} x)) quote (B16 x) = `(B16 ~(quote {t=Raw} x)) quote (B32 x) = `(B32 ~(quote {t=Raw} x)) quote (B64 x) = `(B64 ~(quote {t=Raw} x)) quote (AType x) = `(AType ~(quote {t=Raw} x)) quote StrType = `(StrType) quote VoidType = `(VoidType) quote Forgot = `(Forgot) quote WorldType = `(WorldType) quote TheWorld = `(TheWorld) instance Quotable TTUExp TT where quotedTy = `(TTUExp) quote (UVar x) = `(UVar ~(quote x)) quote (UVal x) = `(UVal ~(quote x)) instance Quotable TTUExp Raw where quotedTy = `(TTUExp) quote (UVar x) = `(UVar ~(quote {t=Raw} x)) quote (UVal x) = `(UVal ~(quote {t=Raw} x)) instance Quotable Universe TT where quotedTy = `(Universe) quote Reflection.NullType = `(NullType) quote Reflection.UniqueType = `(UniqueType) quote Reflection.AllTypes = `(AllTypes) instance Quotable Universe Raw where quotedTy = `(Universe) quote Reflection.NullType = `(NullType) quote Reflection.UniqueType = `(UniqueType) quote Reflection.AllTypes = `(AllTypes) mutual instance Quotable TT TT where quotedTy = `(TT) quote (P nt n tm) = `(P ~(quote nt) ~(quote n) ~(quote tm)) quote (V x) = `(V ~(quote x)) quote (Bind n b tm) = `(Bind ~(quote n) ~(assert_total (quote b)) ~(quote tm)) quote (App f x) = `(App ~(quote f) ~(quote x)) quote (TConst c) = `(TConst ~(quote c)) quote (Proj tm x) = `(Proj ~(quote tm) ~(quote x)) quote Erased = `(Erased) quote Impossible = `(Impossible) quote (TType uexp) = `(TType ~(quote uexp)) quote (UType u) = `(UType ~(quote u)) instance Quotable (Binder TT) TT where quotedTy = `(Binder TT) quote (Lam x) = `(Lam {a=TT} ~(assert_total (quote x))) quote (Pi x k) = `(Pi {a=TT} ~(assert_total (quote x)) ~(assert_total (quote k))) quote (Let x y) = `(Let {a=TT} ~(assert_total (quote x)) ~(assert_total (quote y))) quote (NLet x y) = `(NLet {a=TT} ~(assert_total (quote x)) ~(assert_total (quote y))) quote (Hole x) = `(Hole {a=TT} ~(assert_total (quote x))) quote (GHole x) = `(GHole {a=TT} ~(assert_total (quote x))) quote (Guess x y) = `(Guess {a=TT} ~(assert_total (quote x)) ~(assert_total (quote y))) quote (PVar x) = `(PVar {a=TT} ~(assert_total (quote x))) quote (PVTy x) = `(PVTy {a=TT} ~(assert_total (quote x))) instance Quotable ErrorReportPart TT where quotedTy = `(ErrorReportPart) quote (TextPart x) = `(TextPart ~(quote x)) quote (NamePart n) = `(NamePart ~(quote n)) quote (TermPart tm) = `(TermPart ~(quote tm)) quote (SubReport xs) = `(SubReport ~(assert_total $ quote xs)) mutual quoteRaw : Raw -> TT quoteRaw (Var n) = `(Var ~(quote n)) quoteRaw (RBind n b tm) = `(RBind ~(quote n) ~(assert_total $ quoteRawBinder b) ~(quoteRaw tm)) quoteRaw (RApp tm tm') = `(RApp ~(quoteRaw tm) ~(quoteRaw tm')) quoteRaw RType = `(RType) quoteRaw (RUType u) = `(RUType ~(quote u)) quoteRaw (RForce tm) = `(RForce ~(quoteRaw tm)) quoteRaw (RConstant c) = `(RConstant ~(quote c)) quoteRawBinder : Binder Raw -> TT quoteRawBinder (Lam x) = `(Lam {a=Raw} ~(quoteRaw x)) quoteRawBinder (Pi x k) = `(Pi {a=Raw} ~(quoteRaw x) ~(quoteRaw k)) quoteRawBinder (Let x y) = `(Let {a=Raw} ~(quoteRaw x) ~(quoteRaw y)) quoteRawBinder (NLet x y) = `(NLet {a=Raw} ~(quoteRaw x) ~(quoteRaw y)) quoteRawBinder (Hole x) = `(Hole {a=Raw} ~(quoteRaw x)) quoteRawBinder (GHole x) = `(GHole {a=Raw} ~(quoteRaw x)) quoteRawBinder (Guess x y) = `(Guess {a=Raw} ~(quoteRaw x) ~(quoteRaw y)) quoteRawBinder (PVar x) = `(PVar {a=Raw} ~(quoteRaw x)) quoteRawBinder (PVTy x) = `(PVTy {a=Raw} ~(quoteRaw x)) instance Quotable Raw TT where quotedTy = `(Raw) quote = quoteRaw instance Quotable (Binder Raw) TT where quotedTy = `(Binder Raw) quote = quoteRawBinder instance Quotable Tactic TT where quotedTy = `(Tactic) quote (Try tac tac') = `(Try ~(quote tac) ~(quote tac')) quote (GoalType x tac) = `(GoalType ~(quote x) ~(quote tac)) quote (Refine n) = `(Refine ~(quote n)) quote (Claim n ty) = `(Claim ~(quote n) ~(quote ty)) quote Unfocus = `(Unfocus) quote (Seq tac tac') = `(Seq ~(quote tac) ~(quote tac')) quote Trivial = `(Trivial) quote (Search x) = `(Search ~(quote x)) quote Instance = `(Instance) quote Solve = `(Solve) quote Intros = `(Intros) quote (Intro n) = `(Intro ~(quote n)) quote (ApplyTactic tm) = `(ApplyTactic ~(quote tm)) quote (Reflect tm) = `(Reflect ~(quote tm)) quote (ByReflection tm) = `(ByReflection ~(quote tm)) quote (Fill tm) = `(Fill ~(quote tm)) quote (Exact tm) = `(Exact ~(quote tm)) quote (Focus n) = `(Focus ~(quote n)) quote (Rewrite tm) = `(Rewrite ~(quote tm)) quote (Induction tm) = `(Induction ~(quote tm)) quote (Case tm) = `(Case ~(quote tm)) quote (LetTac n tm) = `(LetTac ~(quote n) ~(quote tm)) quote (LetTacTy n tm tm') = `(LetTacTy ~(quote n) ~(quote tm) ~(quote tm')) quote Compute = `(Compute) quote Skip = `(Skip) quote (Fail xs) = `(Fail ~(quote xs)) quote SourceFC = `(SourceFC) instance Quotable SourceLocation TT where quotedTy = `(SourceLocation) quote (FileLoc fn (sl, sc) (el, ec)) = `(FileLoc ~(quote fn) (~(quote sl), ~(quote sc)) (~(quote el), ~(quote ec))) instance Quotable SourceLocation Raw where quotedTy = `(SourceLocation) quote (FileLoc fn (sl, sc) (el, ec)) = `(FileLoc ~(quote {t=Raw} fn) (~(quote {t=Raw} sl), ~(quote {t=Raw} sc)) (~(quote {t=Raw} el), ~(quote {t=Raw} ec)))