X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FGeneral.v;h=d017894f651da7db29cc03dcd2c587861b3e857b;hp=f2e451f60b44ef7a203ac65db7ee1598abbef0dd;hb=3351499d7cb3d32c8df441426309ec6a1ef2a035;hpb=5e84f66deaef748276d41f29a00652c4adf5fb95

diff --git a/src/General.v b/src/General.v
index f2e451f..d017894 100644
--- a/src/General.v
+++ b/src/General.v
@@ -24,7 +24,15 @@ Coercion eqd_type : EqDecidable >-> Sortclass.
 Class ToString (T:Type) := { toString : T -> string }.
 Instance StringToString : ToString string := { toString := fun x => x }.
 
-Notation "a +++ b" := (append (toString a) (toString b)) (at level 100).
+Class Concatenable {T:Type} :=
+ { concatenate : T -> T -> T }.
+ Implicit Arguments Concatenable [ ].
+Open Scope string_scope.
+Open Scope type_scope.
+Close Scope list_scope.
+Notation "a +++ b" := (@concatenate _ _ a b) (at level 99).
+Instance ConcatenableString : Concatenable string := { concatenate := append }.
+
 
 (*******************************************************************************)
 (* Trees                                                                       *)
@@ -145,11 +153,10 @@ Lemma mapOptionTree_extensional {A}{B}(f g:A->B) : (forall a, f a = g a) -> (for
   simpl; rewrite IHt1; rewrite IHt2; auto.
   Qed.
 
-Open Scope string_scope.
 Fixpoint treeToString {T}{TT:ToString T}(t:Tree ??T) : string :=
 match t with
   | T_Leaf None => "[]"
-  | T_Leaf (Some s) => "["+++s+++"]"
+  | T_Leaf (Some s) => "["+++toString s+++"]"
   | T_Branch b1 b2 => treeToString b1 +++ ",," +++ treeToString b2
 end.
 Instance TreeToString {T}{TT:ToString T} : ToString (Tree ??T) := { toString := treeToString }.
@@ -725,10 +732,6 @@ Lemma extensionality_composes : forall t1 t2 t3 (f f':t1->t2) (g g':t2->t3),
 
 
 
-CoInductive Fresh A T :=
-{ next  : forall a:A, (T a * Fresh A T)
-; split : Fresh A T * Fresh A T
-}.
 
 
 
@@ -763,7 +766,6 @@ Definition orErrorBind {T:Type} (oe:OrError T) {Q:Type} (f:T -> OrError Q) :=
   end.
 Notation "a >>= b" := (@orErrorBind _ a _ b) (at level 20).
 
-Open Scope string_scope.
 Definition orErrorBindWithMessage {T:Type} (oe:OrError T) {Q:Type} (f:T -> OrError Q) err_msg :=
   match oe with
     | Error s => Error (err_msg +++ eol +++ "  " +++ s)
@@ -904,31 +906,116 @@ Lemma unleaves_injective : forall T (t1 t2:list T), unleaves t1 = unleaves t2 ->
   reflexivity.
   Qed.
 
+(* adapted from Adam Chlipala's posting to the coq-club list (thanks!) *)
+Definition openVec A n (v: vec A (S n)) : exists a, exists v0, v = a:::v0 :=
+  match v in vec _ N return match N return vec A N -> Prop with
+                              | O => fun _ => True
+                              | S n => fun v => exists a, exists v0, v = a:::v0
+                            end v with
+    | vec_nil => I
+    | a:::v0 => ex_intro _ a (ex_intro _ v0 (refl_equal _))
+  end.
+
+Definition nilVec A (v: vec A O) : v = vec_nil :=
+  match v in vec _ N return match N return vec A N -> Prop with
+                              | O   => fun v => v = vec_nil
+                              | S n => fun v => True
+                            end v with
+    | vec_nil => refl_equal _
+    | a:::v0  => I
+  end.
+
 Lemma fst_zip : forall T Q n (v1:vec T n)(v2:vec Q n), vec_map (@fst _ _) (vec_zip v1 v2) = v1.
-  admit.
-  Defined.
+  intros.
+  induction n.
+  set (nilVec _ v1) as v1'.
+  set (nilVec _ v2) as v2'.
+  subst.
+  simpl.
+  reflexivity.
+  set (openVec _ _ v1) as v1'.
+  set (openVec _ _ v2) as v2'.
+  destruct v1'.
+  destruct v2'.
+  destruct H.
+  destruct H0.
+  subst.
+  simpl.
+  rewrite IHn.
+  reflexivity.
+  Qed.
 
 Lemma snd_zip : forall T Q n (v1:vec T n)(v2:vec Q n), vec_map (@snd _ _) (vec_zip v1 v2) = v2.
-  admit.
-  Defined.
+  intros.
+  induction n.
+  set (nilVec _ v1) as v1'.
+  set (nilVec _ v2) as v2'.
+  subst.
+  simpl.
+  reflexivity.
+  set (openVec _ _ v1) as v1'.
+  set (openVec _ _ v2) as v2'.
+  destruct v1'.
+  destruct v2'.
+  destruct H.
+  destruct H0.
+  subst.
+  simpl.
+  rewrite IHn.
+  reflexivity.
+  Qed.
+
+Fixpoint mapM {M}{mon:Monad M}{T}(ml:list (M T)) : M (list T) :=
+  match ml with
+    | nil  => return nil
+    | a::b => bind a' = a ; bind b' = mapM b ; return a'::b'
+  end.
+
+Fixpoint list_to_ilist {T}{F}(f:forall t:T, F t) (l:list T) : IList T F l :=
+  match l as L return IList T F L with
+  | nil  => INil
+  | a::b => ICons a b (f a) (list_to_ilist f b)
+  end.
+
+Fixpoint treeM {T}{M}{MT:Monad M}(t:Tree ??(M T)) : M (Tree ??T) :=
+  match t with
+    | T_Leaf None     => return []
+    | T_Leaf (Some x) => bind x' = x ; return [x']
+    | T_Branch b1 b2  => bind b1' = treeM b1 ; bind b2' = treeM b2 ; return (b1',,b2')
+  end.
+
 
 (* escapifies any characters which might cause trouble for LaTeX *)
 Variable sanitizeForLatex    : string      -> string.
    Extract Inlined Constant sanitizeForLatex      => "sanitizeForLatex".
-Inductive Latex : Type := latex : string -> Latex.
-Instance LatexToString : ToString Latex := { toString := fun x => match x with latex s => s end }.
-Class ToLatex (T:Type) := { toLatex : T -> Latex }.
-Instance StringToLatex : ToLatex string := { toLatex := fun x => latex (sanitizeForLatex x) }.
-Instance LatexToLatex  : ToLatex Latex  := { toLatex := fun x => x }.
-Definition concatLatex {T1}{T2}(l1:T1)(l2:T2){L1:ToLatex T1}{L2:ToLatex T2} : Latex :=
-  match toLatex l1 with
-    latex s1 =>
-  match toLatex l2 with
-    latex s2 =>
-    latex (s1 +++ s2)
-    end
-    end.
-Notation "a +=+ b" := (concatLatex a b) (at level 60, right associativity).
-
-
+Inductive Latex     : Type := rawLatex     : string -> Latex.
+Inductive LatexMath : Type := rawLatexMath : string -> LatexMath.
 
+Class ToLatex (T:Type) := { toLatex : T -> Latex }.
+Instance ConcatenableLatex : Concatenable Latex :=
+  { concatenate := fun l1 l2 => match l1 with rawLatex l1' => match l2 with rawLatex l2' => rawLatex (l1'+++l2') end end }.
+Instance LatexToString : ToString Latex := { toString := fun x => match x with rawLatex s => s end }.
+
+Class ToLatexMath (T:Type) := { toLatexMath : T -> LatexMath }.
+Instance ConcatenableLatexMath : Concatenable LatexMath :=
+  { concatenate := fun l1 l2 =>
+    match l1 with rawLatexMath l1' =>
+      match l2 with rawLatexMath l2' => rawLatexMath (l1'+++l2')
+      end end }.
+Instance LatexMathToString : ToString LatexMath := { toString := fun x => match x with rawLatexMath s => s end }.
+
+Instance ToLatexLatexMath : ToLatex LatexMath := { toLatex     := fun l => rawLatex     ("$"+++toString l+++"$") }.
+Instance ToLatexMathLatex : ToLatexMath Latex := { toLatexMath := fun l => rawLatexMath ("\text{"+++toString l+++"}") }.
+
+Instance StringToLatex     : ToLatex string := { toLatex := fun x => rawLatex (sanitizeForLatex x) }.
+Instance StringToLatexMath : ToLatexMath  string := { toLatexMath := fun x => toLatexMath (toLatex x) }.
+Instance LatexToLatex          : ToLatex     Latex      := { toLatex := fun x => x }.
+Instance LatexMathToLatexMath  : ToLatexMath LatexMath  := { toLatexMath := fun x => x }.
+
+Fixpoint treeToLatexMath {V}{ToLatexV:ToLatexMath V}(t:Tree ??V) : LatexMath :=
+  match t with
+    | T_Leaf None     => rawLatexMath "\langle\rangle"
+    | T_Leaf (Some x) => (rawLatexMath "\langle")+++toLatexMath x+++(rawLatexMath "\rangle")
+    | T_Branch b1 b2  => (rawLatexMath "\langle")+++treeToLatexMath b1+++(rawLatexMath " , ")
+      +++treeToLatexMath b2+++(rawLatexMath "\rangle")
+  end.