@ -276,13 +276,11 @@ let rec pp ?is_x fs term =
| And -> pf " && "
| Or -> pf " || "
| Xor -> pf " xor "
| App
{ op = App { op = Xor ; arg } ; arg = Integer { data ; typ = Integer { bits = 1 } } }
when Z . is_true data ->
| App { op = App { op = Xor ; arg } ; arg = Integer { data } } when Z . is_true data
->
pf " ¬%a " pp arg
| App
{ op = App { op = Xor ; arg = Integer { data ; typ = Integer { bits = 1 } } } ; arg }
when Z . is_true data ->
| App { op = App { op = Xor ; arg = Integer { data } } ; arg } when Z . is_true data
->
pf " ¬%a " pp arg
| Shl -> pf " shl "
| Lshr -> pf " lshr "
@ -860,9 +858,9 @@ let simp_sub typ x y =
let simp_cond cnd thn els =
match cnd with
(* ¬ ( true ? t : e ) ==> t *)
| Integer { data ; typ = Integer { bits = 1 } } when Z . is_true data -> thn
| Integer { data } when Z . is_true data -> thn
(* ¬ ( false ? t : e ) ==> e *)
| Integer { data ; typ = Integer { bits = 1 } } when Z . is_false data -> els
| Integer { data } when Z . is_false data -> els
| _ ->
App { op = App { op = App { op = Conditional ; arg = cnd } ; arg = thn } ; arg = els }
@ -871,13 +869,9 @@ let rec simp_and x y =
(* i && j *)
| Integer { data = i ; typ } , Integer { data = j } -> integer ( Z . logand i j ) typ
(* e && true ==> e *)
| Integer { data ; typ = Integer { bits = 1 } } , e
| e , Integer { data ; typ = Integer { bits = 1 } }
when Z . is_true data ->
e
| ( Integer { data } , e | e , Integer { data } ) when Z . is_true data -> e
(* e && false ==> 0 *)
| ( Integer { data ; typ = Integer { bits = 1 } } as f ) , _
| _ , ( Integer { data ; typ = Integer { bits = 1 } } as f )
| ( ( Integer { data } as f ) , _ | _ , ( Integer { data } as f ) )
when Z . is_false data ->
f
(* e && ( c ? t : f ) ==> ( c ? e && t : e && f ) *)
@ -893,15 +887,11 @@ let rec simp_or x y =
(* i || j *)
| Integer { data = i ; typ } , Integer { data = j } -> integer ( Z . logor i j ) typ
(* e || true ==> true *)
| ( Integer { data ; typ = Integer { bits = 1 } } as t ) , _
| _ , ( Integer { data ; typ = Integer { bits = 1 } } as t )
| ( ( Integer { data } as t ) , _ | _ , ( Integer { data } as t ) )
when Z . is_true data ->
t
(* e || false ==> e *)
| Integer { data ; typ = Integer { bits = 1 } } , e
| e , Integer { data ; typ = Integer { bits = 1 } }
when Z . is_false data ->
e
| ( Integer { data } , e | e , Integer { data } ) when Z . is_false data -> e
(* e || ( c ? t : f ) ==> ( c ? e || t : e || f ) *)
| e , App { op = App { op = App { op = Conditional ; arg = c } ; arg = t } ; arg = f }
| App { op = App { op = App { op = Conditional ; arg = c } ; arg = t } ; arg = f } , e ->
@ -911,46 +901,45 @@ let rec simp_or x y =
| _ -> App { op = App { op = Or ; arg = x } ; arg = y }
let rec simp_not ( typ : Typ . t ) term =
match ( term , typ ) with
match term with
(* ¬ ( x = y ) ==> x ≠ y *)
| App { op = App { op = Eq ; arg = x } ; arg = y } , _ -> simp_dq x y
| App { op = App { op = Eq ; arg = x } ; arg = y } -> simp_dq x y
(* ¬ ( x ≠ y ) ==> x = y *)
| App { op = App { op = Dq ; arg = x } ; arg = y } , _ -> simp_eq x y
| App { op = App { op = Dq ; arg = x } ; arg = y } -> simp_eq x y
(* ¬ ( x > y ) ==> x <= y *)
| App { op = App { op = Gt ; arg = x } ; arg = y } , _ -> simp_le x y
| App { op = App { op = Gt ; arg = x } ; arg = y } -> simp_le x y
(* ¬ ( x >= y ) ==> x < y *)
| App { op = App { op = Ge ; arg = x } ; arg = y } , _ -> simp_lt x y
| App { op = App { op = Ge ; arg = x } ; arg = y } -> simp_lt x y
(* ¬ ( x < y ) ==> x >= y *)
| App { op = App { op = Lt ; arg = x } ; arg = y } , _ -> simp_ge x y
| App { op = App { op = Lt ; arg = x } ; arg = y } -> simp_ge x y
(* ¬ ( x <= y ) ==> x > y *)
| App { op = App { op = Le ; arg = x } ; arg = y } , _ -> simp_gt x y
| App { op = App { op = Le ; arg = x } ; arg = y } -> simp_gt x y
(* ¬ ( x u> y ) ==> x u<= y *)
| App { op = App { op = Ugt ; arg = x } ; arg = y } , _ -> simp_ule x y
| App { op = App { op = Ugt ; arg = x } ; arg = y } -> simp_ule x y
(* ¬ ( x u>= y ) ==> x u< y *)
| App { op = App { op = Uge ; arg = x } ; arg = y } , _ -> simp_ult x y
| App { op = App { op = Uge ; arg = x } ; arg = y } -> simp_ult x y
(* ¬ ( x u< y ) ==> x u>= y *)
| App { op = App { op = Ult ; arg = x } ; arg = y } , _ -> simp_uge x y
| App { op = App { op = Ult ; arg = x } ; arg = y } -> simp_uge x y
(* ¬ ( x u<= y ) ==> x u> y *)
| App { op = App { op = Ule ; arg = x } ; arg = y } , _ -> simp_ugt x y
| App { op = App { op = Ule ; arg = x } ; arg = y } -> simp_ugt x y
(* ¬ ( x ≠ nan ∧ y ≠ nan ) ==> x = nan ∨ y = nan *)
| App { op = App { op = Ord ; arg = x } ; arg = y } , _ -> simp_uno x y
| App { op = App { op = Ord ; arg = x } ; arg = y } -> simp_uno x y
(* ¬ ( x = nan ∨ y = nan ) ==> x ≠ nan ∧ y ≠ nan *)
| App { op = App { op = Uno ; arg = x } ; arg = y } , _ -> simp_ord x y
| App { op = App { op = Uno ; arg = x } ; arg = y } -> simp_ord x y
(* ¬ ( a ∧ b ) ==> ¬a ∨ ¬b *)
| App { op = App { op = And ; arg = x } ; arg = y } , Integer { bits = 1 } ->
| App { op = App { op = And ; arg = x } ; arg = y } ->
simp_or ( simp_not typ x ) ( simp_not typ y )
(* ¬ ( a ∨ b ) ==> ¬a ∧ ¬b *)
| App { op = App { op = Or ; arg = x } ; arg = y } , Integer { bits = 1 } ->
| App { op = App { op = Or ; arg = x } ; arg = y } ->
simp_and ( simp_not typ x ) ( simp_not typ y )
(* ¬ ( c ? t : e ) ==> c ? ¬t : ¬e *)
| ( App { op = App { op = App { op = Conditional ; arg = cnd } ; arg = thn } ; arg = els }
, Integer { bits = 1 } ) ->
| App { op = App { op = App { op = Conditional ; arg = cnd } ; arg = thn } ; arg = els }
->
simp_cond cnd ( simp_not typ thn ) ( simp_not typ els )
(* ¬ false ==> true ¬true ==> false *)
| Integer { data }, Integer { bits = 1 } -> bool ( Z . is_false data )
(* ¬ i ==> -i-1 *)
| Integer { data ; typ } -> integer ( Z . lognot data ) typ
(* ¬e ==> true xor e *)
| e , _ ->
App { op = App { op = Xor ; arg = integer ( Z . of_bool true ) typ } ; arg = e }
| e -> App { op = App { op = Xor ; arg = integer ( Z . of_bool true ) typ } ; arg = e }
and simp_eq x y =
match ( x , y ) with
@ -1297,13 +1286,8 @@ let rename sub e =
(* * Query *)
let is_true = function
| Integer { data ; typ = Integer { bits = 1 } } -> Z . is_true data
| _ -> false
let is_false = function
| Integer { data ; typ = Integer { bits = 1 } } -> Z . is_false data
| _ -> false
let is_true = function Integer { data } -> Z . is_true data | _ -> false
let is_false = function Integer { data } -> Z . is_false data | _ -> false
let rec is_constant e =
let is_constant_bin x y = is_constant x && is_constant y in