Require Import NaturalDeductionToLatex.
Require Import Coq.Strings.String.
Require Import Coq.Lists.List.
-Require Import HaskGeneral.
-Require Import HaskLiterals.
+Require Import HaskKinds.
+Require Import HaskWeakVars.
+Require Import HaskWeakTypes.
+Require Import HaskLiteralsAndTyCons.
Require Import HaskStrongTypes.
Require Import HaskStrong.
Require Import HaskProof.
-
-(* 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".
+Require Import HaskCoreTypes.
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{?}}"
+Section HaskProofToLatex.
+
+ Context {TV:Kind -> Type}.
+ Context {TVLatex:forall k, ToLatex (TV k)}.
+ Context {freshM:FreshMonad (∀ κ, TV κ)}.
+ Definition FreshM' := FMT freshM.
+ Instance FreshMon' : Monad FreshM' := FMT_Monad freshM.
+
+ Instance ToLatexTyCon : ToLatex TyCon.
+ admit.
+ Defined.
+
+ Fixpoint typeToLatex (needparens:bool){κ}(t:RawHaskType TV κ) {struct t} : FMT freshM Latex :=
+ match t with
+ | TVar _ v => return toLatex v
+ | TCon tc => return (latex "\text{\tt{")+=+tc+=+(latex "}}")
+ | TArrow => return latex "\text{\tt{(->)}}"
+ | TCoerc _ t1 t2 t => bind t1' = typeToLatex false t1
+ ; bind t2' = typeToLatex false t2
+ ; bind t' = typeToLatex needparens t
+ ; return (latex "{(")+=+t1'+=+(latex "{\sim}")+=+
+ t2'+=+(latex ")}\Rightarrow{")+=+t'+=+(latex "}")
+ | TApp _ _ t1 t2 => match t1 with
+ | TApp _ _ TArrow tx => bind t1' = typeToLatex true tx
+ ; bind t2' = typeToLatex true t2
+ ; let body := t1'+=+(latex "{\rightarrow}")+=+t2'
+ in return if needparens then (latex "(")+=+body+=+(latex ")") else body
+ | _ => bind t1' = typeToLatex true t1
+ ; bind t2' = typeToLatex true t2
+ ; let body := t1'+=+(latex " ")+=+t2'
+ in return if needparens then (latex "(")+=+body+=+(latex ")") else body
+ end
+ | TCode ec t => bind ec' = typeToLatex true ec
+ ; bind t' = typeToLatex false t
+ ; return (latex "\code{")+=+ec'+=+(latex "}{")+=+t'+=+(latex "}")
+ | TyFunApp tfc lt => bind rest = typeListToLatex false lt
+ ; return (latex "{\text{\tt{")+=+(sanitizeForLatex (toString tfc))+=+(latex "}}}")+=+
+ (*(latex "_{")+=+(latex (toString (tfc:nat)))+=+(latex "}")+=+*)
+ (fold_left (fun x y => (latex " \ ")+=+x+=+y)
+ rest (latex ""))
+ | TAll k f => (*bind alpha = next
+ ; bind t' = typeToLatex false (f (alpha k))
+ ; *)return (latex "(\forall ")(*+=+(@toLatex _ (TVLatex k) (alpha k))*)
+ +=+(latex "{:}")+=+(kindToLatex k)+=+(latex ")")(*+=+t'*)
+ end
+ with typeListToLatex (needparens:bool){κ}(t:RawHaskTypeList κ) {struct t} : FreshM' (list Latex) :=
+ match t with
+ | TyFunApp_nil => return nil
+ | TyFunApp_cons κ kl rhk rhkl => bind r = typeToLatex needparens rhk
+ ; bind rl = typeListToLatex needparens rhkl
+ ; return (r::rl)
+ end.
+(*
+ Definition ltypeToLatex {Γ:TypeEnv}{κ}(t:RawHaskType TV κ)(lev:list nat) : FreshM' Latex :=
+ match lev with
+ | nil => typeToLatex false t
+ | lv => bind t' = typeToLatex true t
+ ;
+ (latex "{")
+ +=+
+
+ +=+
+ (latex "}^{")
+ +=+
+ (fold_left (fun x y => x+=+":"+=+y) (map tyvar2greek lv) "")+=+"}"
end.
Open Scope nat_scope.
| 8 => "f"
| 9 => "g"
| 10 => "h"
- | S (S (S (S (S (S (S (S (S (S (S x)))))))))) => "z_{"+++(nat2string x)+++"}"
+ | S (S (S (S (S (S (S (S (S (S (S x)))))))))) => "z_{"+++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')
- end.
-
- Fixpoint type2latex (needparens:bool)(n:nat)(t:RawHaskType nat) {struct t} : string :=
- match t with
- | TVar v => tyvar2greek v
- | TCon _ tc => "\text{\tt{"+++sanitizeForLatex (tyConToString _ tc) +++"}}"
- | TCoerc κ => "{\text{\tt{(+>)}}}_{"+++ kind2latex κ +++"}"
- | TApp t1 t2 =>
- match (match t1 with
- | TApp (TCon 2 tc) t1' =>
- if (tyCon_eq tc ArrowTyCon)
- then inl _ (if needparens
- then "("+++(type2latex true n t1')+++"{\rightarrow}"+++(type2latex true n t2)+++")"
- else (type2latex true n t1')+++"{\rightarrow}"+++(type2latex true n t2))
- else inr _ tt
- | _ => inr _ tt
- end) with
- | inl x => x
- | _ => if needparens
- then "("+++(type2latex true n t1)+++" "+++(type2latex false n t2)+++")"
- else (type2latex true n t1)+++" "+++(type2latex false n t2)
- end
- | TFCApp n tfc lt => "{\text{\tt{"+++sanitizeForLatex (tyFunToString _ tfc) +++"}}}"+++
- "_{"+++(nat2string n)+++"}"+++
- fold_left (fun x y => " \ "+++x+++y)
- ((fix type2latex_vec (needparens:bool)(n:nat){m}(lt:vec (RawHaskType nat) m)
- : list string :=
- match lt with
- | vec_nil => nil
- | a:::b => (type2latex needparens n a)::(type2latex_vec needparens n _ b)
- end )
- false n _ lt) ""
- | TAll k f => let alpha := tyvar2greek n
- in "(\forall "+++ alpha +++ "{:}"+++ kind2latex k +++")"+++
- type2latex false (S n) (f n)
- | TCode ec t => "\code{"+++(type2latex true n ec)+++"}{"+++(type2latex false n t)+++"}"
- end.
-
- Definition ltype2latex {Γ:TypeEnv}(t:RawHaskType nat)(lev:list nat) : string :=
- match lev with
- | nil => type2latex false O t
- | lv => "{"+++type2latex true O t+++"}^{"+++(fold_left (fun x y => x+++":"+++y) (map tyvar2greek lv) "")+++"}"
- end.
+ "{\gamma_{"+++n+++"}}".
Fixpoint enumerate' (n:nat){T:Type}(l:list T) : list (nat * T) :=
match l with
Definition enumerate {T:Type}(l:list T) := enumerate' O l.
- Definition InstantiatedTypeEnvString Γ : @InstantiatedTypeEnv nat Γ := count (length Γ).
- Definition InstantiatedCoercionEnvString Γ Δ : @InstantiatedCoercionEnv nat nat Γ Δ := count (length Δ).
- Definition judgment2latex (j:Judg) : string :=
+ Fixpoint count (n:nat) : vec nat n :=
+ match n with
+ | O => vec_nil
+ | S n' => n':::(count n')
+ end.
+
+ Fixpoint count' (lk:list Kind)(n:nat) : IList _ (fun _ => nat) lk :=
+ match lk as LK return IList _ _ LK with
+ | nil => INil
+ | h::t => n::::(count' t (S n))
+ end.
+
+ Definition InstantiatedTypeEnvString Γ : @InstantiatedTypeEnv (fun _ => nat) Γ := count' Γ O.
+ Definition InstantiatedCoercionEnvString Γ Δ : @InstantiatedCoercionEnv (fun _ => nat) nat Γ Δ := count (length Δ).
+ Definition judgmentToLatex (j:Judg) : string :=
match j with
| mkJudg Γ Δ a b =>
let Γ' := InstantiatedTypeEnvString Γ in
let Δ' := InstantiatedCoercionEnvString Γ Δ in
- let lt2l := fun nt:nat*(LeveledHaskType Γ) =>
+ let lt2l := fun nt:nat*(LeveledHaskType Γ ★) =>
let (n,lt) := nt in
match lt with
t @@ l =>
- (var2string n)+++"{:}"+++(@ltype2latex Γ (t nat Γ') (map (fun x:HaskTyVar Γ => x nat Γ') l))
+ (var2string n)+++"{:}"+++(@ltypeToLatex Γ _ (t (fun _ => nat) Γ')
+ (map (fun x:HaskTyVar Γ _ => x (fun _ => nat) Γ') l))
end in
- let lt2l' := fun lt:(LeveledHaskType Γ) =>
+ let lt2l' := fun lt:(LeveledHaskType Γ ★) =>
match lt with
t @@ l =>
- "e{:}"+++(@ltype2latex Γ (t nat Γ') (map (fun x:HaskTyVar Γ => x nat Γ') l))
+ (@ltypeToLatex Γ _ (t (fun _ => nat) Γ')
+ (map (fun x:HaskTyVar Γ _ => x (fun _ => nat) Γ') l))
end in
- (list2latex "" lt2l "\ ,\ " (enumerate (leaves a)))
+ (listToLatex "" lt2l "\ ,\ " (enumerate (leaves a)))
+++" \ \vdash_e\ "(*+++"e{:}"*)
- +++(list2latex "" lt2l' "\ ,\ " (leaves b))
+ +++(listToLatex "" lt2l' "\ ,\ " (leaves b))
end.
Definition j2l (j2j:Judg -> Judg) jt :=
- @judgments2latex Judg judgment2latex (mapOptionTree j2j jt).
+ @judgmentsToLatex Judg judgmentToLatex (mapOptionTree j2j jt).
- Fixpoint nd_urule2latex {Γ}{Δ}{h}{c}(r:@URule Γ Δ h c) : string :=
+ Fixpoint nd_uruleToLatex {Γ}{Δ}{h}{c}(r:@URule Γ Δ h c) : string :=
match r with
- | (RLeft _ _ c r ) => nd_urule2latex r
- | (RRight _ _ c r ) => nd_urule2latex r
- | (RCanL t a ) => "CanL"
- | (RCanR t a ) => "CanR"
- | (RuCanL t a ) => "uCanL"
- | (RuCanR t a ) => "uCanR"
- | (RAssoc t a b c ) => "Assoc"
- | (RCossa t a b c ) => "Cossa"
- | (RExch t a b ) => "Exch"
- | (RWeak t a ) => "Weak"
- | (RCont t a ) => "Cont"
+ | RLeft _ _ _ r => nd_uruleToLatex r
+ | RRight _ _ _ r => nd_uruleToLatex r
+ | RCanL _ _ => "CanL"
+ | RCanR _ _ => "CanR"
+ | RuCanL _ _ => "uCanL"
+ | RuCanR _ _ => "uCanR"
+ | RAssoc _ _ _ _ => "Assoc"
+ | RCossa _ _ _ _ => "Cossa"
+ | RExch _ _ _ => "Exch"
+ | RWeak _ _ => "Weak"
+ | RCont _ _ => "Cont"
end.
- Fixpoint nd_rule2latex {h}{c}(r:Rule h c) : string :=
+ Fixpoint nd_ruleToLatex {h}{c}(r:Rule h c) : string :=
match r with
- | RURule _ _ _ _ r => nd_urule2latex r
- | RNote x n z => "Note"
- | RLit Γ _ l _ => "Lit"
- | RVar Γ _ σ p => "Var"
- | RLam Γ _ Σ tx te p x => "Abs"
- | RCast Γ _ Σ σ τ γ p x => "Cast"
- | RAbsT Γ Σ κ σ a p => "AbsT"
- | RAppT Γ _ Σ κ σ τ p y => "AppT"
- | RAppCo Γ _ Σ κ _ σ₁ σ₂ σ γ p => "AppCo"
- | RAbsCo Γ Σ κ σ cc σ₁ σ₂ p y q => "AbsCo"
- | RApp Γ _ Σ₁ Σ₂ tx te p => "App"
- | RLet Γ _ Σ₁ Σ₂ σ₁ σ₂ p => "Let"
- | REmptyGroup _ a => "REmptyGroup"
- | RBindingGroup _ a b c d e => "RBindingGroup"
- | RLetRec Γ _ p lri q => "LetRec"
- | RCase Σ Γ T κlen κ ldcd τ _ _ => "Case"
- | RBrak Σ _ a b c _ => "Brak"
- | REsc Σ _ a b c _ => "Esc"
+ | RURule _ _ _ _ r => nd_uruleToLatex r
+ | RNote _ _ _ _ _ _ => "Note"
+ | RLit _ _ _ _ => "Lit"
+ | RVar _ _ _ _ => "Var"
+ | RGlobal _ _ _ _ _ => "Global"
+ | RLam _ _ _ _ _ _ => "Abs"
+ | RCast _ _ _ _ _ _ _ => "Cast"
+ | RAbsT _ _ _ _ _ _ => "AbsT"
+ | RAppT _ _ _ _ _ _ _ => "AppT"
+ | RAppCo _ _ _ _ _ _ _ _ _ => "AppCo"
+ | RAbsCo _ _ _ _ _ _ _ _ => "AbsCo"
+ | RApp _ _ _ _ _ _ _ => "App"
+ | RLet _ _ _ _ _ _ _ => "Let"
+ | RBindingGroup _ _ _ _ _ _ => "RBindingGroup"
+ | RLetRec _ _ _ _ _ _ => "LetRec"
+ | RCase _ _ _ _ _ _ _ _ => "Case"
+ | RBrak _ _ _ _ _ _ => "Brak"
+ | REsc _ _ _ _ _ _ => "Esc"
+ | REmptyGroup _ _ => "REmptyGroup"
end.
Fixpoint nd_hideURule {Γ}{Δ}{h}{c}(r:@URule Γ Δ h c) : bool :=
match r with
- | RLeft h c ctx r => nd_hideURule r
- | RRight h c ctx r => nd_hideURule r
- | RCanL t a => true
- | RCanR t a => true
- | RuCanL t a => true
- | RuCanR t a => true
- | RAssoc t a b c => true
- | RCossa t a b c => true
- | RExch t (T_Leaf None) b => true
- | RExch t a (T_Leaf None) => true
- | RWeak t (T_Leaf None) => true
- | RCont t (T_Leaf None) => true
- | _ => false
+ | RLeft _ _ _ r => nd_hideURule r
+ | RRight _ _ _ r => nd_hideURule r
+ | RCanL _ _ => true
+ | RCanR _ _ => true
+ | RuCanL _ _ => true
+ | RuCanR _ _ => true
+ | RAssoc _ _ _ _ => true
+ | RCossa _ _ _ _ => true
+ | RExch _ (T_Leaf None) b => true
+ | RExch _ a (T_Leaf None) => true
+ | RWeak _ (T_Leaf None) => true
+ | RCont _ (T_Leaf None) => true
+ | _ => false
end.
Fixpoint nd_hideRule {h}{c}(r:Rule h c) : bool :=
match r with
- | RURule _ _ _ _ r => nd_hideURule r
- | REmptyGroup a _ => true
- | RBindingGroup _ _ _ _ _ _ => true
- | _ => false
+ | RURule _ _ _ _ r => nd_hideURule r
+ | REmptyGroup _ _ => true
+ | RBindingGroup _ _ _ _ _ _ => true
+ | _ => false
end.
-End ToLatex.
+ *)
+
+End HaskProofToLatex.
+(*
Definition nd_ml_toLatex {c}(pf:@ND _ Rule [] c) :=
@SCND_toLatex _ _
- judgment2latex
- (fun h c r => @nd_rule2latex h c r)
+ judgmentToLatex
+ (fun h c r => @nd_ruleToLatex h c r)
(fun h c r => @nd_hideRule h c r)
_ _ (mkSCND (systemfc_all_rules_one_conclusion) _ _ _ pf (scnd_weak [])).
+*)
\ No newline at end of file