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[sledge] Uncurry ternary term constructors

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Reviewed By: bennostein

Differential Revision: D17665227

fbshipit-source-id: 56240d374
master
Josh Berdine 5 years ago committed by Facebook Github Bot
parent 167e489e24
commit 6805da9557
3 changed files with 65 additions and 58 deletions
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3
sledge/src/symbheap/sh.ml
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@ -389,8 +389,7 @@ let rec pure (e : Term.t) =
| Ap2 (Xor, arg, Integer {data}) when Z.is_true data -> eq_false arg | Ap2 (Xor, arg, Integer {data}) when Z.is_true data -> eq_false arg
| Ap2 (And, e1, e2) -> star (pure e1) (pure e2) | Ap2 (And, e1, e2) -> star (pure e1) (pure e2)
| Ap2 (Or, e1, e2) -> or_ (pure e1) (pure e2) | Ap2 (Or, e1, e2) -> or_ (pure e1) (pure e2)
| App {op= App {op= App {op= Conditional; arg= cnd}; arg= thn}; arg= els} | Ap3 (Conditional, cnd, thn, els) ->
->
or_ or_
(star (pure cnd) (pure thn)) (star (pure cnd) (pure thn))
(star (pure (Term.not_ cnd)) (pure els)) (star (pure (Term.not_ cnd)) (pure els))

115
sledge/src/symbheap/term.ml
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@ -44,8 +44,12 @@ module rec T : sig
| Ashr | Ashr
[@@deriving compare, equal, hash, sexp] [@@deriving compare, equal, hash, sexp]
type op3 = (* if-then-else *)
| Conditional
[@@deriving compare, equal, hash, sexp]
type t = type t =
(* nary: arithmetic, numeric and pointer *) (* nary arithmetic *)
| Add of qset | Add of qset
| Mul of qset | Mul of qset
(* pointer and memory constants and operations *) (* pointer and memory constants and operations *)
@ -59,9 +63,8 @@ module rec T : sig
(* application *) (* application *)
| Ap1 of op1 * t | Ap1 of op1 * t
| Ap2 of op2 * t * t | Ap2 of op2 * t * t
| Ap3 of op3 * t * t * t
| App of {op: t; arg: t} | App of {op: t; arg: t}
(* ternary: conditional *)
| Conditional
(* array/struct constants and operations *) (* array/struct constants and operations *)
| Record | Record
| Select | Select
@ -109,6 +112,8 @@ and T0 : sig
| Ashr | Ashr
[@@deriving compare, equal, hash, sexp] [@@deriving compare, equal, hash, sexp]
type op3 = Conditional [@@deriving compare, equal, hash, sexp]
type t = type t =
| Add of qset | Add of qset
| Mul of qset | Mul of qset
@ -120,8 +125,8 @@ and T0 : sig
| Label of {parent: string; name: string} | Label of {parent: string; name: string}
| Ap1 of op1 * t | Ap1 of op1 * t
| Ap2 of op2 * t * t | Ap2 of op2 * t * t
| Ap3 of op3 * t * t * t
| App of {op: t; arg: t} | App of {op: t; arg: t}
| Conditional
| Record | Record
| Select | Select
| Update | Update
@ -154,6 +159,8 @@ end = struct
| Ashr | Ashr
[@@deriving compare, equal, hash, sexp] [@@deriving compare, equal, hash, sexp]
type op3 = Conditional [@@deriving compare, equal, hash, sexp]
type t = type t =
| Add of qset | Add of qset
| Mul of qset | Mul of qset
@ -165,8 +172,8 @@ end = struct
| Label of {parent: string; name: string} | Label of {parent: string; name: string}
| Ap1 of op1 * t | Ap1 of op1 * t
| Ap2 of op2 * t * t | Ap2 of op2 * t * t
| Ap3 of op3 * t * t * t
| App of {op: t; arg: t} | App of {op: t; arg: t}
| Conditional
| Record | Record
| Select | Select
| Update | Update
@ -261,12 +268,7 @@ let rec pp ?is_x fs term =
| Ap2 (Shl, x, y) -> pf "(%a@ shl %a)" pp x pp y | Ap2 (Shl, x, y) -> pf "(%a@ shl %a)" pp x pp y
| Ap2 (Lshr, x, y) -> pf "(%a@ lshr %a)" pp x pp y | Ap2 (Lshr, x, y) -> pf "(%a@ lshr %a)" pp x pp y
| Ap2 (Ashr, x, y) -> pf "(%a@ ashr %a)" pp x pp y | Ap2 (Ashr, x, y) -> pf "(%a@ ashr %a)" pp x pp y
| Conditional -> pf "(_?_:_)" | Ap3 (Conditional, cnd, thn, els) ->
| App {op= Conditional; arg= cnd} -> pf "(%a@ ? _:_)" pp cnd
| App {op= App {op= Conditional; arg= cnd}; arg= thn} ->
pf "(%a@ ? %a@ : _)" pp cnd pp thn
| App {op= App {op= App {op= Conditional; arg= cnd}; arg= thn}; arg= els}
->
pf "(%a@ ? %a@ : %a)" pp cnd pp thn pp els pf "(%a@ ? %a@ : %a)" pp cnd pp thn pp els
| Select -> pf "_[_]" | Select -> pf "_[_]"
| App {op= Select; arg= rcd} -> pf "%a[_]" pp rcd | App {op= Select; arg= rcd} -> pf "%a[_]" pp rcd
@ -397,7 +399,8 @@ let invariant ?(partial = false) e =
| _ -> () ) | _ -> () )
| Memory _ -> assert true | Memory _ -> assert true
| Select -> assert_arity 2 | Select -> assert_arity 2
| Conditional | Update -> assert_arity 3 | Ap3 (Conditional, _, _, _) -> assert true
| Update -> assert_arity 3
| Record -> assert (partial || not (List.is_empty args)) | Record -> assert (partial || not (List.is_empty args))
| Struct_rec {elts} -> | Struct_rec {elts} ->
assert (not (Vector.is_empty elts)) ; assert (not (Vector.is_empty elts)) ;
@ -519,24 +522,25 @@ module Var = struct
end end
let fold_terms e ~init ~f = let fold_terms e ~init ~f =
let fold_terms_ fold_terms_ e z = let fold_terms_ fold_terms_ e s =
let z = let s =
match e with match e with
| Ap1 (_, x) -> fold_terms_ x z | Ap1 (_, x) -> fold_terms_ x s
| Ap2 (_, x, y) -> fold_terms_ y (fold_terms_ x z) | Ap2 (_, x, y) -> fold_terms_ y (fold_terms_ x s)
| Ap3 (_, x, y, z) -> fold_terms_ z (fold_terms_ y (fold_terms_ x s))
| App {op= x; arg= y} | App {op= x; arg= y}
|Splat {byt= x; siz= y} |Splat {byt= x; siz= y}
|Memory {siz= x; arr= y} -> |Memory {siz= x; arr= y} ->
fold_terms_ y (fold_terms_ x z) fold_terms_ y (fold_terms_ x s)
| Add args | Mul args -> | Add args | Mul args ->
Qset.fold args ~init:z ~f:(fun arg _ z -> fold_terms_ arg z) Qset.fold args ~init:s ~f:(fun arg _ s -> fold_terms_ arg s)
| Concat {args} | Struct_rec {elts= args} -> | Concat {args} | Struct_rec {elts= args} ->
Vector.fold args ~init:z ~f:(fun z elt -> fold_terms_ elt z) Vector.fold args ~init:s ~f:(fun s elt -> fold_terms_ elt s)
| _ -> z | _ -> s
in in
f z e f s e
in in
fix fold_terms_ (fun _ z -> z) e init fix fold_terms_ (fun _ s -> s) e init
let iter_terms e ~f = fold_terms e ~init:() ~f:(fun () e -> f e) let iter_terms e ~f = fold_terms e ~init:() ~f:(fun () e -> f e)
@ -741,8 +745,7 @@ let simp_cond cnd thn els =
| Integer {data} when Z.is_true data -> thn | Integer {data} when Z.is_true data -> thn
(* ¬(false ? t : e) ==> e *) (* ¬(false ? t : e) ==> e *)
| Integer {data} when Z.is_false data -> els | Integer {data} when Z.is_false data -> els
| _ -> | _ -> Ap3 (Conditional, cnd, thn, els)
App {op= App {op= App {op= Conditional; arg= cnd}; arg= thn}; arg= els}
let rec simp_and x y = let rec simp_and x y =
match (x, y) with match (x, y) with
@ -755,8 +758,7 @@ let rec simp_and x y =
when Z.is_false data -> when Z.is_false data ->
f f
(* e && (c ? t : f) ==> (c ? e && t : e && f) *) (* e && (c ? t : f) ==> (c ? e && t : e && f) *)
| e, App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f} | e, Ap3 (Conditional, c, t, f) | Ap3 (Conditional, c, t, f), e ->
|App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f}, e ->
simp_cond c (simp_and e t) (simp_and e f) simp_cond c (simp_and e t) (simp_and e f)
(* e && e ==> e *) (* e && e ==> e *)
| _ when equal x y -> x | _ when equal x y -> x
@ -773,8 +775,7 @@ let rec simp_or x y =
(* e || false ==> e *) (* e || false ==> e *)
| (Integer {data}, e | e, Integer {data}) 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 || (c ? t : f) ==> (c ? e || t : e || f) *)
| e, App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f} | e, Ap3 (Conditional, c, t, f) | Ap3 (Conditional, c, t, f), e ->
|App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f}, e ->
simp_cond c (simp_or e t) (simp_or e f) simp_cond c (simp_or e t) (simp_or e f)
(* e || e ==> e *) (* e || e ==> e *)
| _ when equal x y -> x | _ when equal x y -> x
@ -785,7 +786,7 @@ let rec is_boolean = function
|Ap2 ((Eq | Dq | Lt | Le), _, _) -> |Ap2 ((Eq | Dq | Lt | Le), _, _) ->
true true
| Ap2 ((Div | Rem | And | Or | Xor | Shl | Lshr | Ashr), x, y) | Ap2 ((Div | Rem | And | Or | Xor | Shl | Lshr | Ashr), x, y)
|App {op= App {op= App {op= Conditional}; arg= x}; arg= y} -> |Ap3 (Conditional, _, x, y) ->
is_boolean x || is_boolean y is_boolean x || is_boolean y
| _ -> false | _ -> false
@ -808,8 +809,7 @@ let rec simp_not term =
(* ¬(a ∨ b) ==> ¬a ∧ ¬b *) (* ¬(a ∨ b) ==> ¬a ∧ ¬b *)
| Ap2 (Or, x, y) -> simp_and (simp_not x) (simp_not y) | Ap2 (Or, x, y) -> simp_and (simp_not x) (simp_not y)
(* ¬(c ? t : e) ==> c ? ¬t : ¬e *) (* ¬(c ? t : e) ==> c ? ¬t : ¬e *)
| App {op= App {op= App {op= Conditional; arg= cnd}; arg= thn}; arg= els} | Ap3 (Conditional, cnd, thn, els) ->
->
simp_cond cnd (simp_not thn) (simp_not els) simp_cond cnd (simp_not thn) (simp_not els)
(* ¬i ==> -i-1 *) (* ¬i ==> -i-1 *)
| Integer {data} -> integer (Z.lognot data) | Integer {data} -> integer (Z.lognot data)
@ -827,8 +827,7 @@ and simp_eq x y =
| b, Integer {data} when Z.is_true data && is_boolean b -> b | b, Integer {data} when Z.is_true data && is_boolean b -> b
| Integer {data}, b when Z.is_true data && is_boolean b -> b | Integer {data}, b when Z.is_true data && is_boolean b -> b
(* e = (c ? t : f) ==> (c ? e = t : e = f) *) (* e = (c ? t : f) ==> (c ? e = t : e = f) *)
| e, App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f} | e, Ap3 (Conditional, c, t, f) | Ap3 (Conditional, c, t, f), e ->
|App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f}, e ->
simp_cond c (simp_eq e t) (simp_eq e f) simp_cond c (simp_eq e t) (simp_eq e f)
(* e = e ==> true *) (* e = e ==> true *)
| x, y when equal x y -> bool true | x, y when equal x y -> bool true
@ -837,8 +836,7 @@ and simp_eq x y =
and simp_dq x y = and simp_dq x y =
match (x, y) with match (x, y) with
(* e ≠ (c ? t : f) ==> (c ? e ≠ t : e ≠ f) *) (* e ≠ (c ? t : f) ==> (c ? e ≠ t : e ≠ f) *)
| e, App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f} | e, Ap3 (Conditional, c, t, f) | Ap3 (Conditional, c, t, f), e ->
|App {op= App {op= App {op= Conditional; arg= c}; arg= t}; arg= f}, e ->
simp_cond c (simp_dq e t) (simp_dq e f) simp_cond c (simp_dq e t) (simp_dq e f)
| _ -> ( | _ -> (
match simp_eq x y with match simp_eq x y with
@ -887,6 +885,7 @@ let iter e ~f =
match e with match e with
| Ap1 (_, x) -> f x | Ap1 (_, x) -> f x
| Ap2 (_, x, y) -> f x ; f y | Ap2 (_, x, y) -> f x ; f y
| Ap3 (_, x, y, z) -> f x ; f y ; f z
| App {op= x; arg= y} | Splat {byt= x; siz= y} | Memory {siz= x; arr= y} | App {op= x; arg= y} | Splat {byt= x; siz= y} | Memory {siz= x; arr= y}
-> ->
f x ; f y f x ; f y
@ -898,6 +897,7 @@ let fold e ~init:s ~f =
match e with match e with
| Ap1 (_, x) -> f x s | Ap1 (_, x) -> f x s
| Ap2 (_, x, y) -> f y (f x s) | Ap2 (_, x, y) -> f y (f x s)
| Ap3 (_, x, y, z) -> f z (f y (f x s))
| App {op= x; arg= y} | Splat {byt= x; siz= y} | Memory {siz= x; arr= y} | App {op= x; arg= y} | Splat {byt= x; siz= y} | Memory {siz= x; arr= y}
-> ->
f y (f x s) f y (f x s)
@ -936,25 +936,23 @@ let norm2 op x y =
| Ashr -> simp_ashr x y ) | Ashr -> simp_ashr x y )
|> check invariant |> check invariant
let norm3 op x y z =
(match op with Conditional -> simp_cond x y z) |> check invariant
let app1 ?(partial = false) op arg = let app1 ?(partial = false) op arg =
( match (op, arg) with App {op; arg}
| App {op= App {op= Conditional; arg= x}; arg= y}, z -> simp_cond x y z
| _ -> App {op; arg} )
|> check (invariant ~partial) |> check (invariant ~partial)
|> check (fun e -> |> check (fun e ->
(* every App subterm of output appears in input *) (* every App subterm of output appears in input *)
match e with iter e ~f:(function
| App {op= App {op= App {op= Conditional}}} -> () | App _ as a ->
| _ -> assert (
iter e ~f:(function is_subterm ~sub:a ~sup:op
| App _ as a -> || is_subterm ~sub:a ~sup:arg
assert ( || Trace.fail
is_subterm ~sub:a ~sup:op "simplifying %a %a@ yields %a@ with new subterm %a" pp
|| is_subterm ~sub:a ~sup:arg op pp arg pp e pp a )
|| Trace.fail | _ -> () ) )
"simplifying %a %a@ yields %a@ with new subterm %a"
pp op pp arg pp e pp a )
| _ -> () ) )
let app2 op x y = app1 (app1 ~partial:true op x) y let app2 op x y = app1 (app1 ~partial:true op x) y
let app3 op x y z = app1 (app1 ~partial:true (app1 ~partial:true op x) y) z let app3 op x y z = app1 (app1 ~partial:true (app1 ~partial:true op x) y) z
@ -1005,7 +1003,7 @@ let not_ = simp_not
let shl = norm2 Shl let shl = norm2 Shl
let lshr = norm2 Lshr let lshr = norm2 Lshr
let ashr = norm2 Ashr let ashr = norm2 Ashr
let conditional ~cnd ~thn ~els = app3 Conditional cnd thn els let conditional ~cnd ~thn ~els = norm3 Conditional cnd thn els
let record elts = List.fold ~f:app1 ~init:Record elts let record elts = List.fold ~f:app1 ~init:Record elts
let select ~rcd ~idx = app2 Select rcd idx let select ~rcd ~idx = app2 Select rcd idx
let update ~rcd ~elt ~idx = app3 Update rcd elt idx let update ~rcd ~elt ~idx = app3 Update rcd elt idx
@ -1109,6 +1107,12 @@ let map e ~f =
let y' = f y in let y' = f y in
if x' == x && y' == y then e else norm2 op x' y' if x' == x && y' == y then e else norm2 op x' y'
in in
let map3 op ~f x y z =
let x' = f x in
let y' = f y in
let z' = f z in
if x' == x && y' == y && z' == z then e else norm3 op x' y' z'
in
let map_bin mk ~f x y = let map_bin mk ~f x y =
let x' = f x in let x' = f x in
let y' = f y in let y' = f y in
@ -1132,6 +1136,7 @@ let map e ~f =
| Struct_rec {elts= args} -> Struct_rec {elts= Vector.map args ~f:map_} | Struct_rec {elts= args} -> Struct_rec {elts= Vector.map args ~f:map_}
| Ap1 (op, x) -> map1 op ~f x | Ap1 (op, x) -> map1 op ~f x
| Ap2 (op, x, y) -> map2 op ~f x y | Ap2 (op, x, y) -> map2 op ~f x y
| Ap3 (op, x, y, z) -> map3 op ~f x y z
| _ -> e | _ -> e
in in
fix map_ (fun e -> e) e fix map_ (fun e -> e) e
@ -1150,14 +1155,14 @@ let is_true = function Integer {data} -> Z.is_true data | _ -> false
let is_false = function Integer {data} -> Z.is_false data | _ -> false let is_false = function Integer {data} -> Z.is_false data | _ -> false
let rec is_constant e = let rec is_constant e =
let is_constant_bin x y = is_constant x && is_constant y in
match e with match e with
| Var _ | Nondet _ -> false | Var _ | Nondet _ -> false
| Ap1 (_, x) -> is_constant x | Ap1 (_, x) -> is_constant x
| Ap2 (_, x, y) -> is_constant_bin x y | Ap2 (_, x, y) -> is_constant x && is_constant y
| Ap3 (_, x, y, z) -> is_constant x && is_constant y && is_constant z
| App {op= x; arg= y} | Splat {byt= x; siz= y} | Memory {siz= x; arr= y} | App {op= x; arg= y} | Splat {byt= x; siz= y} | Memory {siz= x; arr= y}
-> ->
is_constant_bin x y is_constant x && is_constant y
| Add args | Mul args -> | Add args | Mul args ->
Qset.for_all ~f:(fun arg _ -> is_constant arg) args Qset.for_all ~f:(fun arg _ -> is_constant arg) args
| Concat {args} | Struct_rec {elts= args} -> | Concat {args} | Struct_rec {elts= args} ->
@ -1167,7 +1172,7 @@ let rec is_constant e =
let classify = function let classify = function
| Add _ | Mul _ -> `Interpreted | Add _ | Mul _ -> `Interpreted
| Ap2 ((Eq | Dq), _, _) -> `Simplified | Ap2 ((Eq | Dq), _, _) -> `Simplified
| Ap1 _ | Ap2 _ | App _ -> `Uninterpreted | Ap1 _ | Ap2 _ | Ap3 _ | App _ -> `Uninterpreted
| _ -> `Atomic | _ -> `Atomic
let solve e f = let solve e f =

5
sledge/src/symbheap/term.mli
Unescape View File

@ -47,6 +47,9 @@ type op2 =
| Ashr (** Arithmetic shift right, bitwise *) | Ashr (** Arithmetic shift right, bitwise *)
[@@deriving compare, equal, hash, sexp] [@@deriving compare, equal, hash, sexp]
type op3 = Conditional (** If-then-else *)
[@@deriving compare, equal, hash, sexp]
type qset = (t, comparator_witness) Qset.t type qset = (t, comparator_witness) Qset.t
and t = private and t = private
@ -64,9 +67,9 @@ and t = private
(** Address of named code block within parent function *) (** Address of named code block within parent function *)
| Ap1 of op1 * t | Ap1 of op1 * t
| Ap2 of op2 * t * t | Ap2 of op2 * t * t
| Ap3 of op3 * t * t * t
| App of {op: t; arg: t} | App of {op: t; arg: t}
(** Application of function symbol to argument, curried *) (** Application of function symbol to argument, curried *)
| Conditional (** If-then-else *)
| Record (** Record (array / struct) constant *) | Record (** Record (array / struct) constant *)
| Select (** Select an index from a record *) | Select (** Select an index from a record *)
| Update (** Constant record with updated index *) | Update (** Constant record with updated index *)

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