Document the stdlib with new why3doc

theories/algebra.why

 
-(** Basic Algebra Theories *)
+(** {1 Basic Algebra Theories} *)
+
+(** {2 Associativity} *)
 
 theory Assoc
   type t
@@ -7,12 +9,16 @@ theory Assoc
   axiom Assoc : forall x y z : t. op (op x y) z = op x (op y z)
 end
 
+(** {2 Commutativity} *)
+
 theory Comm
   type t
   function op t t : t
   axiom Comm : forall x y : t. op x y = op y x
 end
 
+(** {2 Associativity and Commutativity} *)
+
 theory AC
   type t
   function op t t : t
@@ -21,6 +27,8 @@ theory AC
   meta AC function op (*, prop Assoc.Assoc, prop Comm.Comm*)
 end
 
+(** {2 Group theory} *)
+
 theory Group
   type t
 
@@ -35,18 +43,23 @@ theory Group
 
   axiom Inv_def : forall x:t. op x (inv x) = unit
 
-(*
+(***
   lemma Inv_unit : forall x y:t. op x (inv y) = unit -> x = y
 *)
 
 end
 
+(** {2 Commutative groups} *)
+
+
 theory CommutativeGroup
   clone export Group
   clone Comm with type t = t, function op = op
   meta AC function op (*, prop Assoc.Assoc, prop Comm.Comm*)
 end
 
+(** {2 Rings} *)
+
 theory Ring
   type t
   constant zero : t
@@ -66,12 +79,16 @@ theory Ring
   function (-) (x y : t) : t = x + -y
 end
 
+(** {2 Commutative Rings} *)
+
 theory CommutativeRing
   clone export Ring
   clone Comm with type t = t, function op = (*)
   meta AC function (*) (*, prop Assoc.Assoc, prop Comm.Comm*)
 end
 
+(** {2 Commutative Rings with Unit} *)
+
 theory UnitaryCommutativeRing
   clone export CommutativeRing
   constant one : t
@@ -79,6 +96,8 @@ theory UnitaryCommutativeRing
   axiom NonTrivialRing : zero <> one
 end
 
+(** {2 Ordered Commutative Rings} *)
+
 theory OrderedUnitaryCommutativeRing
   clone export UnitaryCommutativeRing
   predicate (<=) t t
@@ -93,6 +112,8 @@ theory OrderedUnitaryCommutativeRing
     forall x y z : t. x <= y -> zero <= z -> x * z <= y * z
 end
 
+(** {2 Field theory} *)
+
 theory Field
   clone export UnitaryCommutativeRing
   function inv t : t
@@ -113,6 +134,8 @@ theory Field
 
 end
 
+(** {2 Ordered Fields} *)
+
 theory OrderedField
   clone export Field
 
@@ -127,7 +150,8 @@ theory OrderedField
     forall x y z : t. x <= y -> zero <= z -> x * z <= y * z
 end
 
-(* to be discussed: should we add the following lemmas, and where
+(***
+ to be discussed: should we add the following lemmas, and where
 
   lemma InvMult : forall x y : t. (-x) * y = - (x * y) = x * (-y)
   lemma InvSquare : forall x : t. x * x = (-x) * (-x)

theories/bool.why

 
+(** {1 Booleans} *)
+
+(** {2 Basic theory of Booleans} *)
+
 theory Bool
 
   use export Bool (* built-in theory of Booleans *)
@@ -36,6 +40,8 @@ theory Bool
 
 end
 
+(** {2 Operator if-then-else} *)
+
 theory Ite
 
   use import Bool (* this is the previously declared local theory *)

theories/comparison.why

 
+(** {1 Comparison Operators, Order relations} *)
+
+(** {2 Absolute value} *)
+
 theory Abs
 
   type t
@@ -11,13 +15,15 @@ theory Abs
   axiom Pos: forall x:t. ge x zero -> abs x = x
   axiom Neg: forall x:t. not ge x zero -> abs x = neg x
 
-(*
+(***
   function abs(x : t) : t
   axiom Abs_def : if ge x zero then abs x = x else abs x = neg x
 *)
 end
 
 
+(** {2 minimum and maximum} *)
+
 theory MinMax
 
   type t
@@ -39,14 +45,14 @@ theory MinMax
   lemma Max_sym: forall x y:t. ge x y -> max x y = max y x
   lemma Min_sym: forall x y:t. ge x y -> min x y = min y x
 
-(*
+(***
   function min (x y : t) : t
   axiom Min_def : if ge x y then min x y = y else min x y = x
   function max (x y : t) : t
   axiom Max_def : if ge x y then max x y = x else max x y = y
 *)
 
-(*
+(***
   function min (x y : t) : t = if ge x y then y else x
   function max (x y : t) : t = if ge x y then x else y
 *)

theories/floating_point.why

@@ -36,6 +36,15 @@ theory SpecialValues
 
 end
 
+(** {2 Generic theory of floats}
+
+The theory is parametrized by the real constant [max] which denotes
+the maximal representable number, and the integer constant
+[max_representable_integer] which is the maximal integer [n] such that
+every integer between [0] and [n] are representable.
+
+*) 
+
 theory GenFloat
 
   use import Rounding
@@ -95,6 +104,11 @@ theory GenFloat
 
 end
 
+(** {2 single precision floats}
+
+a.k.a 32-bits floats
+ *)
+
 theory Single
 
   type single
@@ -111,6 +125,10 @@ end
 
 
 
+(** {2 Double precision floats}
+
+a.k.a 64-bits floats
+ *)
 theory Double
 
   type double
@@ -126,6 +144,11 @@ theory Double
 end
 
 
+(** {2 Generic Full theory of floats}
+
+this theory extends the generic theory above by adding the special values
+
+ *)
 
 theory GenFloatFull
 
@@ -194,7 +217,7 @@ theory GenFloatFull
 end
 
 
-
+(** {2 Full theory of single precision floats} *)
 
 theory SingleFull
 
@@ -211,6 +234,7 @@ theory SingleFull
 end
 
 
+(** {2 Full theory of double precision floats} *)
 
 theory DoubleFull
 

theories/list.why

 
+(** {1 Polymorphic Lists} *)
+
+(** {2 Basic theory of polymorphic lists} *)
+
 theory List
 
   type list 'a = Nil | Cons 'a (list 'a)
 
 end
 
+(** {2 Length of a list} *)
+
 theory Length
   use import int.Int
   use import List
@@ -21,6 +27,8 @@ theory Length
 
 end
 
+(** {2 Membership in a list} *)
+
 theory Mem
   use export List
 
@@ -31,6 +39,8 @@ theory Mem
 
 end
 
+(** {2 Nth element of a list} *)
+
 theory Nth
   use export List
   use export option.Option
@@ -43,7 +53,9 @@ theory Nth
 
 end
 
-theory HdTl "head and tail"
+(** {2 Head and tail} *)
+
+theory HdTl 
 
   use export List
   use export option.Option
@@ -60,6 +72,8 @@ theory HdTl "head and tail"
 
 end
 
+(** {2 Relation between head, tail and nth} *)
+
 theory NthHdTl
 
   use import int.Int
@@ -75,6 +89,7 @@ theory NthHdTl
 
 end
 
+(** {2 Appending two lists} *)
 
 theory Append
   use export List
@@ -109,6 +124,8 @@ theory Append
 
 end
 
+(** {2 Rerversing a list} *)
+
 theory Reverse
 
   use export List
@@ -133,6 +150,8 @@ theory Reverse
 
 end
 
+(** {2 Sorted lists for some order as parameter} *)
+
 theory Sorted
 
   use export List
@@ -157,6 +176,8 @@ theory Sorted
 
 end
 
+(** {2 Sorted lists of integers} *)
+
 theory SortedInt
 
   use import int.Int
@@ -164,6 +185,8 @@ theory SortedInt
 
 end
 
+(** {2 Number of occurrences in a list} *)
+
 theory NumOcc
 
   use import int.Int
@@ -189,6 +212,8 @@ theory NumOcc
 
 end
 
+(** {2 Permutation of lists} *)
+
 theory Permut
 
   use import NumOcc
@@ -241,6 +266,8 @@ theory Permut
 
 end
 
+(** {2 List with pairwise distinct elements} *)
+
 theory Distinct
 
   use import List
@@ -262,6 +289,8 @@ theory Distinct
 
 end
 
+(** {2 Induction on lists} *)
+
 theory Induction
   use import List
 
@@ -276,6 +305,8 @@ theory Induction
 
 end
 
+(** {2 Maps as lists of pairs} *)
+
 theory Map
   use import List
 
@@ -290,6 +321,8 @@ theory Map
     end
 end
 
+(** {2 Generic recursors on lists} *)
+
 theory FoldLeft
   use import List
 
@@ -318,6 +351,8 @@ theory FoldRight
     end
 end
 
+(** {2 Importation of all list theories in one} *)
+
 theory ListRich
   use export List
   use export Length
@@ -332,7 +367,7 @@ theory ListRich
   use export Permut
 end
 
-(*
+(***
 Local Variables:
 compile-command: "make -C .. theories/list"
 End: