-
-(* escapifies any characters which might cause trouble for LaTeX *)
-Variable sanitizeForLatex : string -> string. Extract Inlined Constant sanitizeForLatex => "sanitizeForLatex".
-Variable nat2string : nat -> string. Extract Inlined Constant nat2string => "nat2string".
-
-Open Scope string_scope.
-Section ToLatex.
-
- Fixpoint kind2latex (k:Kind) : string :=
- match k with
- | KindType => "\star"
- | KindTypeFunction KindType k2 => "\star\Rightarrow "+++kind2latex k2
- | KindTypeFunction k1 k2 => "("+++kind2latex k1+++")\Rightarrow "+++kind2latex k2
- | KindUnliftedType => "\text{\tt{\#}}"
- | KindUnboxedTuple => "\text{\tt{(\#)}}"
- | KindArgType => "\text{\tt{?}}"
- | KindOpenType => "\text{\tt{?}}"
- end.
-
- Open Scope nat_scope.
- Definition var2string (n:nat) :=
- match n with
- | 0 => "x"
- | 1 => "y"
- | 2 => "z"
- | 3 => "a"
- | 4 => "b"
- | 5 => "c"
- | 6 => "d"
- | 7 => "e"
- | 8 => "f"
- | 9 => "g"
- | 10 => "h"
- | S (S (S (S (S (S (S (S (S (S (S x)))))))))) => "z_{"+++(nat2string x)+++"}"
- end.
- Close Scope nat_scope.
-
- Definition tyvar2greek (n:nat) :=
- match n with
- | O => "\alpha"
- | S O => "\beta"
- | S (S O) => "\xi"
- | S (S (S n)) => "\alpha_{"+++nat2string n+++"}"
- end.
-
- Definition covar2greek (n:nat) :=
- "{\gamma_{"+++(nat2string n)+++"}}".
-
- Fixpoint count (n:nat) : vec nat n :=
- match n with
- | O => vec_nil
- | S n' => n':::(count n')
+Require Import HaskCoreTypes.
+
+
+
+Inductive VarNameStore :=
+ varNameStore : nat -> nat -> nat -> VarNameStore.
+Inductive VarNameStoreM {T} :=
+ varNameStoreM : (VarNameStore -> (T * VarNameStore)) -> VarNameStoreM.
+Implicit Arguments VarNameStoreM [ ].
+
+Open Scope nat_scope.
+Instance VarNameMonad : Monad VarNameStoreM :=
+{ returnM := fun _ x => varNameStoreM (fun v => (x,v))
+; bindM := fun _ _ x f =>
+ match x with
+ varNameStoreM xf =>
+ varNameStoreM (fun vns =>
+ match xf vns with
+ (x',vns') => match f x' with
+ varNameStoreM fx' => fx' vns'
+ end
+ end) end }.
+
+Definition freshTyVarName : Kind -> VarNameStoreM LatexMath :=
+ fun κ => varNameStoreM (fun vns =>
+ match vns with
+ varNameStore n1 n2 n3 =>
+ let name := (rawLatexMath "\alpha_{")+++toLatexMath (toString n1)+++(rawLatexMath "}")
+ in (name,(varNameStore (S n1) n2 n3))
+ end).
+Definition freshCoVarName : VarNameStoreM LatexMath :=
+ varNameStoreM (fun vns =>
+ match vns with
+ varNameStore n1 n2 n3 =>
+ let name := (rawLatexMath "\gamma_{")+++toLatexMath (toString n2)+++(rawLatexMath "}")
+ in (name,(varNameStore n1 (S n2) n3))
+ end).
+Definition freshValVarName : VarNameStoreM LatexMath :=
+ varNameStoreM (fun vns =>
+ match vns with
+ varNameStore n1 n2 n3 =>
+ let vn := match n3 with
+ | 0 => "x"
+ | 1 => "y"
+ | 2 => "z"
+ | 3 => "a"
+ | 4 => "b"
+ | 5 => "c"
+ | 6 => "d"
+ | 7 => "e"
+ | 8 => "f"
+ | 9 => "g"
+ | 10 => "h"
+ | S (S (S (S (S (S (S (S (S (S (S x)))))))))) => "z_{"+++toString x+++"}"
+ end
+ in let name := rawLatexMath ("x_{"+++vn+++"}")
+ in (name,(varNameStore n1 n2 (S n3)))
+ end).
+
+Fixpoint typeToLatexMath (needparens:bool){κ}(t:RawHaskType (fun _ => LatexMath) κ) {struct t} : VarNameStoreM LatexMath :=
+ match t return VarNameStoreM LatexMath with
+ | TVar _ v => return toLatexMath v
+ | TCon tc => return ((rawLatexMath "\text{\tt{")+++toLatexMath (toString tc)+++(rawLatexMath "}}"))
+ | TArrow => return rawLatexMath "\text{\tt{(->)}}"
+ | TCoerc _ t1 t2 t => bind t1' = typeToLatexMath false t1
+ ; bind t2' = typeToLatexMath false t2
+ ; bind t' = typeToLatexMath needparens t
+ ; return ((rawLatexMath "{(")+++t1'+++(rawLatexMath "{\sim}")+++
+ t2'+++(rawLatexMath ")}\Rightarrow{")+++t'+++(rawLatexMath "}"))
+ | TCode ec t => bind ec' = typeToLatexMath true ec
+ ; bind t' = typeToLatexMath false t
+ ; return (rawLatexMath "\code{")+++ec'+++(rawLatexMath "}{")+++t'+++(rawLatexMath "}")
+ | TAll k f => bind alpha = freshTyVarName k
+ ; bind t' = typeToLatexMath false (f alpha)
+ ; return (rawLatexMath "(\forall ")+++alpha+++(rawLatexMath "{:}")+++
+ (kindToLatexMath k)+++(rawLatexMath ")")+++t'
+ | TApp _ _ t1 t2 => match t1 return VarNameStoreM LatexMath with
+ | TApp _ _ TArrow tx => bind t1' = typeToLatexMath true tx
+ ; bind t2' = typeToLatexMath true t2
+ ; let body := t1'+++(rawLatexMath "{\rightarrow}")+++t2'
+ in return (if needparens then (rawLatexMath "(")+++body+++(rawLatexMath ")") else body)
+ | _ => bind t1' = typeToLatexMath true t1
+ ; bind t2' = typeToLatexMath true t2
+ ; let body := t1'+++(rawLatexMath " ")+++t2'
+ in return (if needparens then (rawLatexMath "(")+++body+++(rawLatexMath ")") else body)
+ end
+ | TyFunApp tfc lt => bind rest = typeListToRawLatexMath false lt
+ ; return (rawLatexMath "{\text{\tt{")+++(toLatexMath (toString tfc))+++(rawLatexMath "}}}")+++
+ (rawLatexMath "_{")+++(rawLatexMath (toString (length (fst (tyFunKind tfc)))))+++
+ (rawLatexMath "}")+++
+ (fold_left (fun x y => (rawLatexMath " \ ")+++x+++y)
+ rest (rawLatexMath ""))
+end
+with typeListToRawLatexMath (needparens:bool){κ}(t:RawHaskTypeList κ) {struct t} : VarNameStoreM (list LatexMath) :=
+match t return VarNameStoreM (list LatexMath) with
+| TyFunApp_nil => return nil
+| TyFunApp_cons κ kl rhk rhkl => bind r = typeToLatexMath needparens rhk
+ ; bind rl = typeListToRawLatexMath needparens rhkl
+ ; return (r::rl)
+end.
+
+Definition ltypeToLatexMath {Γ:TypeEnv}{κ}(t:LeveledHaskType Γ κ) : VarNameStoreM LatexMath.
+ refine (
+ match t with
+ t' @@ lev =>
+ bind ite = _ ;
+ bind t'' = typeToLatexMath false (t' (fun _ => LatexMath) ite) ;
+ return match lev with
+ | nil => t''
+ | lv => (rawLatexMath " ")+++t''+++(rawLatexMath " @ ")+++
+ (fold_left (fun x y => x+++(rawLatexMath ":")+++y)
+ (map (fun l:HaskTyVar Γ ★ => l (fun _ => LatexMath) ite) lv) (rawLatexMath ""))
+ end
+ end); try apply ConcatenableLatexMath.
+ try apply VarNameMonad.
+ clear t t' lev κ.
+ induction Γ.
+ apply (return INil).
+ refine (bind tv' = freshTyVarName a ; _).
+ apply VarNameMonad.
+ refine (bind IHΓ' = IHΓ ; return _).
+ apply VarNameMonad.
+ apply ICons.
+ apply tv'.
+ apply IHΓ'.
+ apply VarNameMonad.
+ Defined.
+
+Definition judgmentToRawLatexMath (j:Judg) : LatexMath :=
+ match match j return VarNameStoreM LatexMath with
+ | mkJudg Γ Δ Σ₁ Σ₂ =>
+ bind Σ₁' = treeM (mapOptionTree ltypeToLatexMath Σ₁)
+ ; bind Σ₂' = treeM (mapOptionTree ltypeToLatexMath Σ₂)
+ ; return treeToLatexMath Σ₁' +++ (rawLatexMath "\vdash") +++ treeToLatexMath Σ₂'
+ end with
+ varNameStoreM f => fst (f (varNameStore 0 0 0))