From 3003a8e6469aa41e9a65ac793d7c8bc6977bb392 Mon Sep 17 00:00:00 2001
From: Josh Berdine <jjb@fb.com>
Date: Wed, 9 Oct 2019 08:36:49 -0700
Subject: [PATCH] [sledge] NFC minor cleanups

Reviewed By: jvillard

Differential Revision: D17665255

fbshipit-source-id: 0f18e5777
---
 sledge/src/control.ml             |   2 +-
 sledge/src/domain/used_globals.ml |   3 +-
 sledge/src/llair/exp.ml           |  82 +++---
 sledge/src/llair/exp.mli          |  24 +-
 sledge/src/llair/frontend.ml      |   4 +-
 sledge/src/llair/term.ml          | 438 +++++++++++++++---------------
 sledge/src/llair/term.mli         |  99 ++++---
 7 files changed, 348 insertions(+), 304 deletions(-)

diff --git a/sledge/src/control.ml b/sledge/src/control.ml
index 45b4c8d59..a5075bf4e 100644
--- a/sledge/src/control.ml
+++ b/sledge/src/control.ml
@@ -248,7 +248,7 @@ module Make (Dom : Domain_sig.Dom) = struct
       | None -> [%Trace.info "queue empty"] ; ()
   end
 
-  let used_globals : exec_opts -> Reg.reg -> Reg.Set.t =
+  let used_globals : exec_opts -> Reg.t -> Reg.Set.t =
    fun opts fn ->
     [%Trace.call fun {pf} -> pf "%a" Reg.pp fn]
     ;
diff --git a/sledge/src/domain/used_globals.ml b/sledge/src/domain/used_globals.ml
index 479733b09..99e2f9e47 100644
--- a/sledge/src/domain/used_globals.ml
+++ b/sledge/src/domain/used_globals.ml
@@ -14,8 +14,7 @@ let report_fmt_thunk = Fn.flip pp
 let empty = Reg.Set.empty
 
 let init globals =
-  [%Trace.info
-    "pgm globals: {%a}" (Vector.pp ", " Llair_.Global.pp) globals] ;
+  [%Trace.info "pgm globals: {%a}" (Vector.pp ", " Global.pp) globals] ;
   empty
 
 let join l r = Some (Set.union l r)
diff --git a/sledge/src/llair/exp.ml b/sledge/src/llair/exp.ml
index 2666af1f7..e3d228d68 100644
--- a/sledge/src/llair/exp.ml
+++ b/sledge/src/llair/exp.ml
@@ -186,10 +186,6 @@ and pp_record fs elts =
       elts]
   [@@warning "-9"]
 
-type exp = t
-
-let pp_exp = pp
-
 (** Invariant *)
 
 let valid_idx idx elts = 0 <= idx && idx < Vector.length elts
@@ -288,6 +284,10 @@ and typ_of exp =
 
 let typ = typ_of
 
+type exp = t
+
+let pp_exp = pp
+
 (** Registers are the expressions constructed by [Reg] *)
 module Reg = struct
   include T
@@ -371,31 +371,14 @@ module Reg = struct
     |> check invariant
 end
 
-(** Access *)
-
-let fold_exps e ~init ~f =
-  let fold_exps_ fold_exps_ e z =
-    let z =
-      match e.desc with
-      | Ap1 (_, _, x) -> fold_exps_ x z
-      | Ap2 (_, _, x, y) -> fold_exps_ y (fold_exps_ x z)
-      | Ap3 (_, _, w, x, y) -> fold_exps_ w (fold_exps_ y (fold_exps_ x z))
-      | ApN (_, _, xs) ->
-          Vector.fold xs ~init:z ~f:(fun z elt -> fold_exps_ elt z)
-      | _ -> z
-    in
-    f z e
-  in
-  fix fold_exps_ (fun _ z -> z) e init
-
-let fold_regs e ~init ~f =
-  fold_exps e ~init ~f:(fun z x ->
-      match x.desc with Reg _ -> f z (x :> Reg.t) | _ -> z )
-
 (** Construct *)
 
+(* registers *)
+
 let reg x = x
 
+(* constants *)
+
 let nondet typ msg =
   {desc= Nondet {msg; typ}; term= Term.nondet msg} |> check invariant
 
@@ -412,6 +395,8 @@ let bool b = integer Typ.bool (Z.of_bool b)
 let float typ data =
   {desc= Float {data; typ}; term= Term.float data} |> check invariant
 
+(* type conversions *)
+
 let convert ?(unsigned = false) ~dst ~src exp =
   ( if (not unsigned) && Typ.equal dst src then exp
   else
@@ -419,9 +404,7 @@ let convert ?(unsigned = false) ~dst ~src exp =
     ; term= Term.convert ~unsigned ~dst ~src exp.term } )
   |> check invariant
 
-let select typ rcd idx =
-  {desc= Ap1 (Select idx, typ, rcd); term= Term.select ~rcd:rcd.term ~idx}
-  |> check invariant
+(* comparisons *)
 
 let unsigned typ op x y =
   let bits = Option.value_exn (Typ.prim_bit_size_of typ) in
@@ -477,6 +460,8 @@ let uno typ x y =
   {desc= Ap2 (Uno, typ, x, y); term= Term.uno x.term y.term}
   |> check invariant
 
+(* arithmetic *)
+
 let add typ x y =
   {desc= Ap2 (Add, typ, x, y); term= Term.add x.term y.term}
   |> check invariant
@@ -505,6 +490,8 @@ let urem typ x y =
   {desc= Ap2 (Urem, typ, x, y); term= unsigned typ Term.rem x.term y.term}
   |> check invariant
 
+(* boolean / bitwise *)
+
 let and_ typ x y =
   {desc= Ap2 (And, typ, x, y); term= Term.and_ x.term y.term}
   |> check invariant
@@ -513,6 +500,8 @@ let or_ typ x y =
   {desc= Ap2 (Or, typ, x, y); term= Term.or_ x.term y.term}
   |> check invariant
 
+(* bitwise *)
+
 let xor typ x y =
   {desc= Ap2 (Xor, typ, x, y); term= Term.xor x.term y.term}
   |> check invariant
@@ -529,21 +518,29 @@ let ashr typ x y =
   {desc= Ap2 (Ashr, typ, x, y); term= Term.ashr x.term y.term}
   |> check invariant
 
-let update typ ~rcd idx ~elt =
-  { desc= Ap2 (Update idx, typ, rcd, elt)
-  ; term= Term.update ~rcd:rcd.term ~idx ~elt:elt.term }
-  |> check invariant
+(* if-then-else *)
 
 let conditional typ ~cnd ~thn ~els =
   { desc= Ap3 (Conditional, typ, cnd, thn, els)
   ; term= Term.conditional ~cnd:cnd.term ~thn:thn.term ~els:els.term }
   |> check invariant
 
+(* records (struct / array values) *)
+
 let record typ elts =
   { desc= ApN (Record, typ, elts)
   ; term= Term.record (Vector.map ~f:(fun elt -> elt.term) elts) }
   |> check invariant
 
+let select typ rcd idx =
+  {desc= Ap1 (Select idx, typ, rcd); term= Term.select ~rcd:rcd.term ~idx}
+  |> check invariant
+
+let update typ ~rcd idx ~elt =
+  { desc= Ap2 (Update idx, typ, rcd, elt)
+  ; term= Term.update ~rcd:rcd.term ~idx ~elt:elt.term }
+  |> check invariant
+
 let struct_rec key =
   let memo_id = Hashtbl.create key in
   let rec_app = (Staged.unstage (Term.rec_app key)) Term.Record in
@@ -569,6 +566,27 @@ let struct_rec key =
          forcing the recursive thunks also updates this value. *)
       {desc= ApN (Struct_rec, typ, elts); term= rec_app ~id Vector.empty}
 
+(** Traverse *)
+
+let fold_exps e ~init ~f =
+  let fold_exps_ fold_exps_ e z =
+    let z =
+      match e.desc with
+      | Ap1 (_, _, x) -> fold_exps_ x z
+      | Ap2 (_, _, x, y) -> fold_exps_ y (fold_exps_ x z)
+      | Ap3 (_, _, w, x, y) -> fold_exps_ w (fold_exps_ y (fold_exps_ x z))
+      | ApN (_, _, xs) ->
+          Vector.fold xs ~init:z ~f:(fun z elt -> fold_exps_ elt z)
+      | _ -> z
+    in
+    f z e
+  in
+  fix fold_exps_ (fun _ z -> z) e init
+
+let fold_regs e ~init ~f =
+  fold_exps e ~init ~f:(fun z x ->
+      match x.desc with Reg _ -> f z (x :> Reg.t) | _ -> z )
+
 (** Query *)
 
 let is_true e =
diff --git a/sledge/src/llair/exp.mli b/sledge/src/llair/exp.mli
index c2a760a74..99c35ba29 100644
--- a/sledge/src/llair/exp.mli
+++ b/sledge/src/llair/exp.mli
@@ -125,13 +125,21 @@ end
 
 (** Construct *)
 
+(* registers *)
 val reg : Reg.t -> t
+
+(* constants *)
 val nondet : Typ.t -> string -> t
 val label : parent:string -> name:string -> t
 val null : t
 val bool : bool -> t
 val integer : Typ.t -> Z.t -> t
 val float : Typ.t -> string -> t
+
+(* type conversions *)
+val convert : ?unsigned:bool -> dst:Typ.t -> src:Typ.t -> t -> t
+
+(* comparisons *)
 val eq : Typ.t -> t -> t -> t
 val dq : Typ.t -> t -> t -> t
 val gt : Typ.t -> t -> t -> t
@@ -144,6 +152,8 @@ val ult : Typ.t -> t -> t -> t
 val ule : Typ.t -> t -> t -> t
 val ord : Typ.t -> t -> t -> t
 val uno : Typ.t -> t -> t -> t
+
+(* arithmetic *)
 val add : Typ.t -> t -> t -> t
 val sub : Typ.t -> t -> t -> t
 val mul : Typ.t -> t -> t -> t
@@ -151,13 +161,21 @@ val div : Typ.t -> t -> t -> t
 val rem : Typ.t -> t -> t -> t
 val udiv : Typ.t -> t -> t -> t
 val urem : Typ.t -> t -> t -> t
+
+(* boolean / bitwise *)
 val and_ : Typ.t -> t -> t -> t
 val or_ : Typ.t -> t -> t -> t
+
+(* bitwise *)
 val xor : Typ.t -> t -> t -> t
 val shl : Typ.t -> t -> t -> t
 val lshr : Typ.t -> t -> t -> t
 val ashr : Typ.t -> t -> t -> t
+
+(* if-then-else *)
 val conditional : Typ.t -> cnd:t -> thn:t -> els:t -> t
+
+(* records (struct / array values) *)
 val record : Typ.t -> t vector -> t
 val select : Typ.t -> t -> int -> t
 val update : Typ.t -> rcd:t -> int -> elt:t -> t
@@ -173,15 +191,13 @@ val struct_rec :
     one point on each cycle. Failure to obey these requirements will lead to
     stack overflow. *)
 
-val convert : ?unsigned:bool -> dst:Typ.t -> src:Typ.t -> t -> t
-
-(** Access *)
+(** Traverse *)
 
 val fold_regs : t -> init:'a -> f:('a -> Reg.t -> 'a) -> 'a
 
 (** Query *)
 
 val term : t -> Term.t
+val typ : t -> Typ.t
 val is_true : t -> bool
 val is_false : t -> bool
-val typ : t -> Typ.t
diff --git a/sledge/src/llair/frontend.ml b/sledge/src/llair/frontend.ml
index b7c731389..e4b8d4b38 100644
--- a/sledge/src/llair/frontend.ml
+++ b/sledge/src/llair/frontend.ml
@@ -714,7 +714,7 @@ let exception_typs =
     the PHIs of [dst] translated to a move. *)
 let xlate_jump :
        x
-    -> ?reg_exps:(Reg.reg * Exp.t) list
+    -> ?reg_exps:(Reg.t * Exp.t) list
     -> Llvm.llvalue
     -> Llvm.llbasicblock
     -> Loc.t
@@ -859,7 +859,7 @@ let xlate_instr :
         | ConstantExpr -> (
           match Llvm.constexpr_opcode maybe_llfunc with
           | BitCast -> Llvm.operand maybe_llfunc 0
-          | IntToPtr -> todo "maybe handle calls with inttoptr" ()
+          | IntToPtr -> todo "calls with inttoptr" ()
           | _ ->
               fail "Unknown value in a call instruction %a" pp_llvalue
                 maybe_llfunc () )
diff --git a/sledge/src/llair/term.ml b/sledge/src/llair/term.ml
index 109f6544c..1d25009c1 100644
--- a/sledge/src/llair/term.ml
+++ b/sledge/src/llair/term.ml
@@ -7,6 +7,8 @@
 
 (** Terms *)
 
+[@@@warning "+9"]
+
 module Z = struct
   include Z
 
@@ -19,63 +21,48 @@ module rec T : sig
   type qset = Qset.M(T).t [@@deriving compare, equal, hash, sexp]
 
   type op1 =
-    (* conversion *)
     | Extract of {unsigned: bool; bits: int}
     | Convert of {unsigned: bool; dst: Typ.t; src: Typ.t}
-    (* array/struct *)
     | Select of int
   [@@deriving compare, equal, hash, sexp]
 
   type op2 =
-    (* memory *)
-    | Splat
-    | Memory
-    (* comparison *)
     | Eq
     | Dq
     | Lt
     | Le
     | Ord
     | Uno
-    (* arithmetic *)
     | Div
     | Rem
-    (* boolean / bitwise *)
     | And
     | Or
     | Xor
     | Shl
     | Lshr
     | Ashr
-    (* array/struct *)
+    | Splat
+    | Memory
     | Update of int
   [@@deriving compare, equal, hash, sexp]
 
-  type op3 = (* if-then-else *)
-    | Conditional
-  [@@deriving compare, equal, hash, sexp]
-
+  type op3 = Conditional [@@deriving compare, equal, hash, sexp]
   type opN = Concat | Record [@@deriving compare, equal, hash, sexp]
   type recN = Record [@@deriving compare, equal, hash, sexp]
 
   type t =
-    (* nary arithmetic *)
     | Add of qset
     | Mul of qset
-    (* nullary *)
     | Var of {id: int; name: string}
-    | Nondet of {msg: string}
-    | Label of {parent: string; name: string}
-    (* application *)
     | Ap1 of op1 * t
     | Ap2 of op2 * t * t
     | Ap3 of op3 * t * t * t
     | ApN of opN * t vector
-    (* recursive application *)
     | RecN of recN * t vector  (** NOTE: cyclic *)
-    (* numeric constants *)
     | Integer of {data: Z.t}
     | Float of {data: string}
+    | Nondet of {msg: string}
+    | Label of {parent: string; name: string}
   [@@deriving compare, equal, hash, sexp]
 
   (* Note: solve (and invariant) requires Qset.min_elt to return a
@@ -100,8 +87,6 @@ and T0 : sig
   [@@deriving compare, equal, hash, sexp]
 
   type op2 =
-    | Splat
-    | Memory
     | Eq
     | Dq
     | Lt
@@ -116,6 +101,8 @@ and T0 : sig
     | Shl
     | Lshr
     | Ashr
+    | Splat
+    | Memory
     | Update of int
   [@@deriving compare, equal, hash, sexp]
 
@@ -127,8 +114,6 @@ and T0 : sig
     | Add of qset
     | Mul of qset
     | Var of {id: int; name: string}
-    | Nondet of {msg: string}
-    | Label of {parent: string; name: string}
     | Ap1 of op1 * t
     | Ap2 of op2 * t * t
     | Ap3 of op3 * t * t * t
@@ -136,6 +121,8 @@ and T0 : sig
     | RecN of recN * t vector
     | Integer of {data: Z.t}
     | Float of {data: string}
+    | Nondet of {msg: string}
+    | Label of {parent: string; name: string}
   [@@deriving compare, equal, hash, sexp]
 end = struct
   type qset = Qset.M(T).t [@@deriving compare, equal, hash, sexp]
@@ -147,8 +134,6 @@ end = struct
   [@@deriving compare, equal, hash, sexp]
 
   type op2 =
-    | Splat
-    | Memory
     | Eq
     | Dq
     | Lt
@@ -163,6 +148,8 @@ end = struct
     | Shl
     | Lshr
     | Ashr
+    | Splat
+    | Memory
     | Update of int
   [@@deriving compare, equal, hash, sexp]
 
@@ -174,8 +161,6 @@ end = struct
     | Add of qset
     | Mul of qset
     | Var of {id: int; name: string}
-    | Nondet of {msg: string}
-    | Label of {parent: string; name: string}
     | Ap1 of op1 * t
     | Ap2 of op2 * t * t
     | Ap3 of op3 * t * t * t
@@ -183,6 +168,8 @@ end = struct
     | RecN of recN * t vector
     | Integer of {data: Z.t}
     | Float of {data: string}
+    | Nondet of {msg: string}
+    | Label of {parent: string; name: string}
   [@@deriving compare, equal, hash, sexp]
 end
 
@@ -226,13 +213,18 @@ let rec pp ?is_x fs term =
         Trace.pp_styled (get_var_style var) "%%%s" fs name
     | Var {name; id} as var ->
         Trace.pp_styled (get_var_style var) "%%%s_%d" fs name id
-    | Nondet {msg} -> pf "nondet \"%s\"" msg
-    | Label {name} -> pf "%s" name
-    | Ap2 (Splat, byt, siz) -> pf "%a^%a" pp byt pp siz
-    | Ap2 (Memory, siz, arr) -> pf "@<1>⟨%a,%a@<1>⟩" pp siz pp arr
-    | ApN (Concat, args) -> pf "%a" (Vector.pp "@,^" pp) args
     | Integer {data} -> Trace.pp_styled `Magenta "%a" fs Z.pp data
     | Float {data} -> pf "%s" data
+    | Nondet {msg} -> pf "nondet \"%s\"" msg
+    | Label {name} -> pf "%s" name
+    | Ap1 (Extract {unsigned; bits}, arg) ->
+        pf "(%s%i)@ %a" (if unsigned then "u" else "i") bits pp arg
+    | Ap1 (Convert {dst; unsigned= true; src= Integer {bits}}, arg) ->
+        pf "((%a)(u%i)@ %a)" Typ.pp dst bits pp arg
+    | Ap1 (Convert {unsigned= true; dst= Integer {bits}; src}, arg) ->
+        pf "((u%i)(%a)@ %a)" bits Typ.pp src pp arg
+    | Ap1 (Convert {dst; src}, arg) ->
+        pf "((%a)(%a)@ %a)" Typ.pp dst Typ.pp src pp arg
     | Ap2 (Eq, x, y) -> pf "(%a@ = %a)" pp x pp y
     | Ap2 (Dq, x, y) -> pf "(%a@ @<2>≠ %a)" pp x pp y
     | Ap2 (Lt, x, y) -> pf "(%a@ < %a)" pp x pp y
@@ -266,21 +258,17 @@ let rec pp ?is_x fs term =
     | Ap2 (Ashr, x, y) -> pf "(%a@ ashr %a)" pp x pp y
     | Ap3 (Conditional, cnd, thn, els) ->
         pf "(%a@ ? %a@ : %a)" pp cnd pp thn pp els
+    | Ap2 (Splat, byt, siz) -> pf "%a^%a" pp byt pp siz
+    | Ap2 (Memory, siz, arr) -> pf "@<1>⟨%a,%a@<1>⟩" pp siz pp arr
+    | ApN (Concat, args) -> pf "%a" (Vector.pp "@,^" pp) args
+    | ApN (Record, elts) -> pf "{%a}" pp_record elts
+    | RecN (Record, elts) -> pf "{|%a|}" (Vector.pp ",@ " pp) elts
     | Ap1 (Select idx, rcd) -> pf "%a[%i]" pp rcd idx
     | Ap2 (Update idx, rcd, elt) ->
         pf "[%a@ @[| %i → %a@]]" pp rcd idx pp elt
-    | ApN (Record, elts) -> pf "{%a}" pp_record elts
-    | RecN (Record, elts) -> pf "{|%a|}" (Vector.pp ",@ " pp) elts
-    | Ap1 (Extract {unsigned; bits}, arg) ->
-        pf "(%s%i)@ %a" (if unsigned then "u" else "i") bits pp arg
-    | Ap1 (Convert {dst; unsigned= true; src= Integer {bits}}, arg) ->
-        pf "((%a)(u%i)@ %a)" Typ.pp dst bits pp arg
-    | Ap1 (Convert {unsigned= true; dst= Integer {bits}; src}, arg) ->
-        pf "((u%i)(%a)@ %a)" bits Typ.pp src pp arg
-    | Ap1 (Convert {dst; src}, arg) ->
-        pf "((%a)(%a)@ %a)" Typ.pp dst Typ.pp src pp arg
   in
   fix_flip pp_ (fun _ _ -> ()) fs term
+  [@@warning "-9"]
 
 and pp_record fs elts =
   [%Trace.fprintf
@@ -356,28 +344,15 @@ let invariant e =
   Invariant.invariant [%here] e [%sexp_of: t]
   @@ fun () ->
   match e with
-  | Var _ | Nondet _ | Label _ | Integer _ | Float _ -> ()
-  | Ap1 (Extract _, _) -> ()
-  | Ap1 (Convert {dst; src}, _) -> assert (Typ.convertible src dst)
   | Add _ -> assert_polynomial e |> Fn.id
   | Mul _ -> assert_monomial e |> Fn.id
-  | Ap2
-      ( ( Eq | Dq | Lt | Le | Ord | Uno | Div | Rem | And | Or | Xor | Shl
-        | Lshr | Ashr )
-      , _
-      , _ ) ->
-      ()
-  | ApN (Concat, args) -> assert (Vector.length args <> 1)
-  | Ap2 (Splat, _, siz) -> (
-    match siz with
-    | Integer {data} -> assert (not (Z.equal Z.zero data))
-    | _ -> () )
-  | Ap2 (Memory, _, _) -> ()
-  | Ap1 (Select _, _) -> ()
-  | Ap3 (Conditional, _, _, _) -> ()
-  | Ap2 (Update _, _, _) -> ()
+  | Ap2 (Splat, _, Integer {data}) -> assert (not (Z.equal Z.zero data))
+  | ApN (Concat, mems) -> assert (Vector.length mems <> 1)
   | ApN (Record, elts) | RecN (Record, elts) ->
       assert (not (Vector.is_empty elts))
+  | Ap1 (Convert {dst; src}, _) -> assert (Typ.convertible src dst)
+  | _ -> ()
+  [@@warning "-9"]
 
 (** Variables are the terms constructed by [Var] *)
 module Var = struct
@@ -415,8 +390,8 @@ module Var = struct
     Invariant.invariant [%here] x [%sexp_of: t]
     @@ fun () -> match x with Var _ -> invariant x | _ -> assert false
 
-  let id = function Var {id} -> id | x -> violates invariant x
-  let name = function Var {name} -> name | x -> violates invariant x
+  let id = function Var v -> v.id | x -> violates invariant x
+  let name = function Var v -> v.name | x -> violates invariant x
 
   let of_term = function
     | Var _ as v -> Some (v |> check invariant)
@@ -490,34 +465,14 @@ module Var = struct
   end
 end
 
-let fold_terms e ~init ~f =
-  let fold_terms_ fold_terms_ e s =
-    let s =
-      match e with
-      | Ap1 (_, x) -> fold_terms_ x s
-      | Ap2 (_, x, y) -> fold_terms_ y (fold_terms_ x s)
-      | Ap3 (_, x, y, z) -> fold_terms_ z (fold_terms_ y (fold_terms_ x s))
-      | ApN (_, xs) | RecN (_, xs) ->
-          Vector.fold ~f:(fun s x -> fold_terms_ x s) xs ~init:s
-      | Add args | Mul args ->
-          Qset.fold args ~init:s ~f:(fun arg _ s -> fold_terms_ arg s)
-      | _ -> s
-    in
-    f s e
-  in
-  fix fold_terms_ (fun _ s -> s) e init
+(** Construct *)
 
-let fold_vars e ~init ~f =
-  fold_terms e ~init ~f:(fun z -> function
-    | Var _ as v -> f z (v :> Var.t) | _ -> z )
+(* variables *)
 
-let fv e = fold_vars e ~f:Set.add ~init:Var.Set.empty
+let var x = x
 
-(** Construct *)
+(* constants *)
 
-let var x = x
-let nondet msg = Nondet {msg} |> check invariant
-let label ~parent ~name = Label {parent; name} |> check invariant
 let integer data = Integer {data} |> check invariant
 let null = integer Z.zero
 let zero = integer Z.zero
@@ -527,6 +482,10 @@ let bool b = integer (Z.of_bool b)
 let true_ = bool true
 let false_ = bool false
 let float data = Float {data} |> check invariant
+let nondet msg = Nondet {msg} |> check invariant
+let label ~parent ~name = Label {parent; name} |> check invariant
+
+(* type conversions *)
 
 let simp_extract ~unsigned bits arg =
   match arg with
@@ -541,47 +500,7 @@ let simp_convert ~unsigned dst src arg =
         integer (Z.extract ~unsigned (min m n) data)
     | _ -> Ap1 (Convert {unsigned; dst; src}, arg)
 
-let simp_record elts = ApN (Record, elts)
-let simp_select idx rcd = Ap1 (Select idx, rcd)
-let simp_update idx rcd elt = Ap2 (Update idx, rcd, elt)
-
-let simp_concat xs =
-  if Vector.length xs = 1 then Vector.get xs 0
-  else
-    let args =
-      if
-        Vector.for_all xs ~f:(function
-          | ApN (Concat, _) -> false
-          | _ -> true )
-      then xs
-      else
-        Vector.concat
-          (Vector.fold_right xs ~init:[] ~f:(fun x s ->
-               match x with
-               | ApN (Concat, args) -> args :: s
-               | x -> Vector.of_array [|x|] :: s ))
-    in
-    ApN (Concat, args)
-
-let simp_splat byt siz =
-  match siz with
-  | Integer {data} when Z.equal Z.zero data -> simp_concat Vector.empty
-  | _ -> Ap2 (Splat, byt, siz)
-
-let simp_memory siz arr = Ap2 (Memory, siz, arr)
-
-let simp_lt x y =
-  match (x, y) with
-  | Integer {data= i}, Integer {data= j} -> bool (Z.lt i j)
-  | _ -> Ap2 (Lt, x, y)
-
-let simp_le x y =
-  match (x, y) with
-  | Integer {data= i}, Integer {data= j} -> bool (Z.leq i j)
-  | _ -> Ap2 (Le, x, y)
-
-let simp_ord x y = Ap2 (Ord, x, y)
-let simp_uno x y = Ap2 (Uno, x, y)
+(* arithmetic *)
 
 let sum_mul_const const sum =
   assert (not (Q.equal Q.zero const)) ;
@@ -731,6 +650,8 @@ let simp_sub x y =
   (* x - y ==> x + (-1 * y) *)
   | _ -> simp_add2 x (simp_negate y)
 
+(* if-then-else *)
+
 let simp_cond cnd thn els =
   match cnd with
   (* ¬(true ? t : e) ==> t *)
@@ -739,6 +660,17 @@ let simp_cond cnd thn els =
   | Integer {data} when Z.is_false data -> els
   | _ -> Ap3 (Conditional, cnd, thn, els)
 
+(* boolean / bitwise *)
+
+let rec is_boolean = function
+  | Ap1 ((Extract {bits= 1; _} | Convert {dst= Integer {bits= 1; _}; _}), _)
+   |Ap2 ((Eq | Dq | Lt | Le), _, _) ->
+      true
+  | Ap2 ((Div | Rem | And | Or | Xor | Shl | Lshr | Ashr), x, y)
+   |Ap3 (Conditional, _, x, y) ->
+      is_boolean x || is_boolean y
+  | _ -> false
+
 let rec simp_and x y =
   match (x, y) with
   (* i && j *)
@@ -773,42 +705,22 @@ let rec simp_or x y =
   | _ when equal x y -> x
   | _ -> Ap2 (Or, x, y)
 
-let rec is_boolean = function
-  | Ap1 ((Extract {bits= 1} | Convert {dst= Integer {bits= 1}}), _)
-   |Ap2 ((Eq | Dq | Lt | Le), _, _) ->
-      true
-  | Ap2 ((Div | Rem | And | Or | Xor | Shl | Lshr | Ashr), x, y)
-   |Ap3 (Conditional, _, x, y) ->
-      is_boolean x || is_boolean y
-  | _ -> false
+(* comparison *)
 
-let rec simp_not term =
-  match term with
-  (* ¬(x = y) ==> x ≠ y *)
-  | Ap2 (Eq, x, y) -> simp_dq x y
-  (* ¬(x ≠ y) ==> x = y *)
-  | Ap2 (Dq, x, y) -> simp_eq x y
-  (* ¬(x < y) ==> y <= x *)
-  | Ap2 (Lt, x, y) -> simp_le y x
-  (* ¬(x <= y) ==> y < x *)
-  | Ap2 (Le, x, y) -> simp_lt y x
-  (* ¬(x ≠ nan ∧ y ≠ nan) ==> x = nan ∨ y = nan *)
-  | Ap2 (Ord, x, y) -> simp_uno x y
-  (* ¬(x = nan ∨ y = nan) ==> x ≠ nan ∧ y ≠ nan *)
-  | Ap2 (Uno, x, y) -> simp_ord x y
-  (* ¬(a ∧ b) ==> ¬a ∨ ¬b *)
-  | Ap2 (And, x, y) -> simp_or (simp_not x) (simp_not y)
-  (* ¬(a ∨ b) ==> ¬a ∧ ¬b *)
-  | Ap2 (Or, x, y) -> simp_and (simp_not x) (simp_not y)
-  (* ¬(c ? t : e) ==> c ? ¬t : ¬e *)
-  | Ap3 (Conditional, cnd, thn, els) ->
-      simp_cond cnd (simp_not thn) (simp_not els)
-  (* ¬i ==> -i-1 *)
-  | Integer {data} -> integer (Z.lognot data)
-  (* ¬e ==> true xor e *)
-  | e -> Ap2 (Xor, true_, e)
+let simp_lt x y =
+  match (x, y) with
+  | Integer {data= i}, Integer {data= j} -> bool (Z.lt i j)
+  | _ -> Ap2 (Lt, x, y)
 
-and simp_eq x y =
+let simp_le x y =
+  match (x, y) with
+  | Integer {data= i}, Integer {data= j} -> bool (Z.leq i j)
+  | _ -> Ap2 (Le, x, y)
+
+let simp_ord x y = Ap2 (Ord, x, y)
+let simp_uno x y = Ap2 (Uno, x, y)
+
+let rec simp_eq x y =
   match (x, y) with
   (* i = j *)
   | Integer {data= i}, Integer {data= j} -> bool (Z.equal i j)
@@ -835,6 +747,35 @@ and simp_dq x y =
     | Ap2 (Eq, x, y) -> Ap2 (Dq, x, y)
     | b -> simp_not b )
 
+(* negation-normal form *)
+and simp_not term =
+  match term with
+  (* ¬(x = y) ==> x ≠ y *)
+  | Ap2 (Eq, x, y) -> simp_dq x y
+  (* ¬(x ≠ y) ==> x = y *)
+  | Ap2 (Dq, x, y) -> simp_eq x y
+  (* ¬(x < y) ==> y <= x *)
+  | Ap2 (Lt, x, y) -> simp_le y x
+  (* ¬(x <= y) ==> y < x *)
+  | Ap2 (Le, x, y) -> simp_lt y x
+  (* ¬(x ≠ nan ∧ y ≠ nan) ==> x = nan ∨ y = nan *)
+  | Ap2 (Ord, x, y) -> simp_uno x y
+  (* ¬(x = nan ∨ y = nan) ==> x ≠ nan ∧ y ≠ nan *)
+  | Ap2 (Uno, x, y) -> simp_ord x y
+  (* ¬(a ∧ b) ==> ¬a ∨ ¬b *)
+  | Ap2 (And, x, y) -> simp_or (simp_not x) (simp_not y)
+  (* ¬(a ∨ b) ==> ¬a ∧ ¬b *)
+  | Ap2 (Or, x, y) -> simp_and (simp_not x) (simp_not y)
+  (* ¬(c ? t : e) ==> c ? ¬t : ¬e *)
+  | Ap3 (Conditional, cnd, thn, els) ->
+      simp_cond cnd (simp_not thn) (simp_not els)
+  (* ¬i ==> -i-1 *)
+  | Integer {data} -> integer (Z.lognot data)
+  (* ¬e ==> true xor e *)
+  | e -> Ap2 (Xor, true_, e)
+
+(* bitwise *)
+
 let simp_xor x y =
   match (x, y) with
   (* i xor j *)
@@ -871,26 +812,62 @@ let simp_ashr x y =
   | e, Integer {data} when Z.equal Z.zero data -> e
   | _ -> Ap2 (Ashr, x, y)
 
-(** Access *)
+(* memory *)
 
-let iter e ~f =
-  match e with
-  | Ap1 (_, x) -> f x
-  | Ap2 (_, x, y) -> f x ; f y
-  | Ap3 (_, x, y, z) -> f x ; f y ; f z
-  | ApN (_, xs) | RecN (_, xs) -> Vector.iter ~f xs
-  | Add args | Mul args -> Qset.iter ~f:(fun arg _ -> f arg) args
-  | _ -> ()
+let simp_concat xs =
+  if Vector.length xs = 1 then Vector.get xs 0
+  else
+    let args =
+      if
+        Vector.for_all xs ~f:(function
+          | ApN (Concat, _) -> false
+          | _ -> true )
+      then xs
+      else
+        Vector.concat
+          (Vector.fold_right xs ~init:[] ~f:(fun x s ->
+               match x with
+               | ApN (Concat, args) -> args :: s
+               | x -> Vector.of_array [|x|] :: s ))
+    in
+    ApN (Concat, args)
 
-let fold e ~init:s ~f =
-  match e with
-  | Ap1 (_, x) -> f x s
-  | Ap2 (_, x, y) -> f y (f x s)
-  | Ap3 (_, x, y, z) -> f z (f y (f x s))
-  | ApN (_, xs) | RecN (_, xs) ->
-      Vector.fold ~f:(fun s x -> f x s) xs ~init:s
-  | Add args | Mul args -> Qset.fold ~f:(fun e _ s -> f e s) args ~init:s
-  | _ -> s
+let simp_splat byt siz =
+  match siz with
+  | Integer {data} when Z.equal Z.zero data -> simp_concat Vector.empty
+  | _ -> Ap2 (Splat, byt, siz)
+
+let simp_memory siz arr = Ap2 (Memory, siz, arr)
+
+(* records *)
+
+let simp_record elts = ApN (Record, elts)
+let simp_select idx rcd = Ap1 (Select idx, rcd)
+let simp_update idx rcd elt = Ap2 (Update idx, rcd, elt)
+
+let rec_app key =
+  let memo_id = Hashtbl.create key in
+  let dummy = null in
+  Staged.stage
+  @@ fun ~id op elt_thks ->
+  match Hashtbl.find memo_id id with
+  | None ->
+      (* Add placeholder to prevent computing [elts] in calls to [rec_app]
+         from [elt_thks] for recursive occurrences of [id]. *)
+      let elta = Array.create ~len:(Vector.length elt_thks) dummy in
+      let elts = Vector.of_array elta in
+      Hashtbl.set memo_id ~key:id ~data:elts ;
+      Vector.iteri elt_thks ~f:(fun i (lazy elt) -> elta.(i) <- elt) ;
+      RecN (op, elts) |> check invariant
+  | Some elts ->
+      (* Do not check invariant as invariant will be checked above after the
+         thunks are forced, before which invariant-checking may spuriously
+         fail. Note that it is important that the value constructed here
+         shares the array in the memo table, so that the update after
+         forcing the recursive thunks also updates this value. *)
+      RecN (op, elts)
+
+(* dispatching for normalization and invariant checking *)
 
 let norm1 op x =
   ( match op with
@@ -927,63 +904,43 @@ let normN op xs =
   (match op with Concat -> simp_concat xs | Record -> simp_record xs)
   |> check invariant
 
-let addN args = simp_add args |> check invariant
-let mulN args = simp_mul args |> check invariant
-let concat xs = normN Concat (Vector.of_array xs)
-let splat ~byt ~siz = norm2 Splat byt siz
-let memory ~siz ~arr = norm2 Memory siz arr
+(* exposed interface *)
+
+let extract ?(unsigned = false) ~bits term =
+  norm1 (Extract {unsigned; bits}) term
+
+let convert ?(unsigned = false) ~dst ~src term =
+  norm1 (Convert {unsigned; dst; src}) term
+
 let eq = norm2 Eq
 let dq = norm2 Dq
 let lt = norm2 Lt
 let le = norm2 Le
 let ord = norm2 Ord
 let uno = norm2 Uno
-let neg = simp_negate
-let add = simp_add2
-let sub = simp_sub
-let mul = simp_mul2
+let neg e = simp_negate e |> check invariant
+let add e f = simp_add2 e f |> check invariant
+let addN args = simp_add args |> check invariant
+let sub e f = simp_sub e f |> check invariant
+let mul e f = simp_mul2 e f |> check invariant
+let mulN args = simp_mul args |> check invariant
 let div = norm2 Div
 let rem = norm2 Rem
 let and_ = norm2 And
 let or_ = norm2 Or
+let not_ e = simp_not e |> check invariant
 let xor = norm2 Xor
-let not_ = simp_not
 let shl = norm2 Shl
 let lshr = norm2 Lshr
 let ashr = norm2 Ashr
 let conditional ~cnd ~thn ~els = norm3 Conditional cnd thn els
+let splat ~byt ~siz = norm2 Splat byt siz
+let memory ~siz ~arr = norm2 Memory siz arr
+let concat xs = normN Concat (Vector.of_array xs)
 let record elts = normN Record elts
 let select ~rcd ~idx = norm1 (Select idx) rcd
 let update ~rcd ~idx ~elt = norm2 (Update idx) rcd elt
 
-let rec_app key =
-  let memo_id = Hashtbl.create key in
-  let dummy = null in
-  Staged.stage
-  @@ fun ~id op elt_thks ->
-  match Hashtbl.find memo_id id with
-  | None ->
-      (* Add placeholder to prevent computing [elts] in calls to [rec_app]
-         from [elt_thks] for recursive occurrences of [id]. *)
-      let elta = Array.create ~len:(Vector.length elt_thks) dummy in
-      let elts = Vector.of_array elta in
-      Hashtbl.set memo_id ~key:id ~data:elts ;
-      Vector.iteri elt_thks ~f:(fun i (lazy elt) -> elta.(i) <- elt) ;
-      RecN (op, elts) |> check invariant
-  | Some elts ->
-      (* Do not check invariant as invariant will be checked above after the
-         thunks are forced, before which invariant-checking may spuriously
-         fail. Note that it is important that the value constructed here
-         shares the array in the memo table, so that the update after
-         forcing the recursive thunks also updates this value. *)
-      RecN (op, elts)
-
-let extract ?(unsigned = false) ~bits term =
-  norm1 (Extract {unsigned; bits}) term
-
-let convert ?(unsigned = false) ~dst ~src term =
-  norm1 (Convert {unsigned; dst; src}) term
-
 let size_of t =
   Option.bind (Typ.prim_bit_size_of t) ~f:(fun n ->
       if n % 8 = 0 then Some (integer (Z.of_int (n / 8))) else None )
@@ -1062,8 +1019,51 @@ let rename sub e =
     | Var _ as v -> Some (Var.Subst.apply sub v)
     | _ -> None )
 
+(** Traverse *)
+
+let iter e ~f =
+  match e with
+  | Ap1 (_, x) -> f x
+  | Ap2 (_, x, y) -> f x ; f y
+  | Ap3 (_, x, y, z) -> f x ; f y ; f z
+  | ApN (_, xs) | RecN (_, xs) -> Vector.iter ~f xs
+  | Add args | Mul args -> Qset.iter ~f:(fun arg _ -> f arg) args
+  | _ -> ()
+
+let fold e ~init:s ~f =
+  match e with
+  | Ap1 (_, x) -> f x s
+  | Ap2 (_, x, y) -> f y (f x s)
+  | Ap3 (_, x, y, z) -> f z (f y (f x s))
+  | ApN (_, xs) | RecN (_, xs) ->
+      Vector.fold ~f:(fun s x -> f x s) xs ~init:s
+  | Add args | Mul args -> Qset.fold ~f:(fun e _ s -> f e s) args ~init:s
+  | _ -> s
+
+let fold_terms e ~init ~f =
+  let fold_terms_ fold_terms_ e s =
+    let s =
+      match e with
+      | Ap1 (_, x) -> fold_terms_ x s
+      | Ap2 (_, x, y) -> fold_terms_ y (fold_terms_ x s)
+      | Ap3 (_, x, y, z) -> fold_terms_ z (fold_terms_ y (fold_terms_ x s))
+      | ApN (_, xs) | RecN (_, xs) ->
+          Vector.fold ~f:(fun s x -> fold_terms_ x s) xs ~init:s
+      | Add args | Mul args ->
+          Qset.fold args ~init:s ~f:(fun arg _ s -> fold_terms_ arg s)
+      | _ -> s
+    in
+    f s e
+  in
+  fix fold_terms_ (fun _ s -> s) e init
+
+let fold_vars e ~init ~f =
+  fold_terms e ~init ~f:(fun z -> function
+    | Var _ as v -> f z (v :> Var.t) | _ -> z )
+
 (** Query *)
 
+let fv e = fold_vars e ~f:Set.add ~init:Var.Set.empty
 let is_true = function Integer {data} -> Z.is_true data | _ -> false
 let is_false = function Integer {data} -> Z.is_false data | _ -> false
 
@@ -1082,7 +1082,7 @@ let classify = function
   | Add _ | Mul _ -> `Interpreted
   | Ap2 ((Eq | Dq), _, _) -> `Simplified
   | Ap1 _ | Ap2 _ | Ap3 _ | ApN _ -> `Uninterpreted
-  | RecN _ | Var _ | Nondet _ | Label _ | Integer _ | Float _ -> `Atomic
+  | RecN _ | Var _ | Integer _ | Float _ | Nondet _ | Label _ -> `Atomic
 
 let solve e f =
   [%Trace.call fun {pf} -> pf "%a@ %a" pp e pp f]
diff --git a/sledge/src/llair/term.mli b/sledge/src/llair/term.mli
index ec37fcf74..f91714cd0 100644
--- a/sledge/src/llair/term.mli
+++ b/sledge/src/llair/term.mli
@@ -8,13 +8,7 @@
 (** Terms
 
     Pure (heap-independent) terms are complex arithmetic, bitwise-logical,
-    etc. operations over literal values and variables.
-
-    Terms for operations that are uninterpreted in the analyzer are
-    represented in curried form, where [App] is an application of a function
-    symbol to an argument. This is done to simplify the definition of
-    'subterm' and make it explicit. The specific constructor functions
-    indicate and check the expected arity of the function symbols. *)
+    etc. operations over literal values and variables. *)
 
 type comparator_witness
 
@@ -32,8 +26,6 @@ type op1 =
 [@@deriving compare, equal, hash, sexp]
 
 type op2 =
-  | Splat  (** Iterated concatenation of a single byte *)
-  | Memory  (** Size-tagged byte-array *)
   | Eq  (** Equal test *)
   | Dq  (** Disequal test *)
   | Lt  (** Less-than test *)
@@ -48,6 +40,8 @@ type op2 =
   | Shl  (** Shift left, bitwise *)
   | Lshr  (** Logical shift right, bitwise *)
   | Ashr  (** Arithmetic shift right, bitwise *)
+  | Splat  (** Iterated concatenation of a single byte *)
+  | Memory  (** Size-tagged byte-array *)
   | Update of int  (** Constant record with updated index *)
 [@@deriving compare, equal, hash, sexp]
 
@@ -59,42 +53,38 @@ type opN =
   | Record  (** Record (array / struct) constant *)
 [@@deriving compare, equal, hash, sexp]
 
-type recN =
-  | Record
-      (** Record constant that may recursively refer to itself
-          (transitively) from its args. NOTE: represented by cyclic values. *)
+type recN = Record  (** Recursive record (array / struct) constant *)
 [@@deriving compare, equal, hash, sexp]
 
 type qset = (t, comparator_witness) Qset.t
 
 and t = private
-  | Add of qset  (** Addition *)
-  | Mul of qset  (** Multiplication *)
+  | Add of qset  (** Sum of terms with rational coefficients *)
+  | Mul of qset  (** Product of terms with rational exponents *)
   | Var of {id: int; name: string}  (** Local variable / virtual register *)
+  | Ap1 of op1 * t  (** Unary application *)
+  | Ap2 of op2 * t * t  (** Binary application *)
+  | Ap3 of op3 * t * t * t  (** Ternary application *)
+  | ApN of opN * t vector  (** N-ary application *)
+  | RecN of recN * t vector
+      (** Recursive n-ary application, may recursively refer to itself
+          (transitively) from its args. NOTE: represented by cyclic values. *)
+  | Integer of {data: Z.t}  (** Integer constant *)
+  | Float of {data: string}  (** Floating-point constant *)
   | Nondet of {msg: string}
       (** Anonymous local variable with arbitrary value, representing
           non-deterministic approximation of value described by [msg] *)
   | Label of {parent: string; name: string}
       (** Address of named code block within parent function *)
-  | Ap1 of op1 * t
-  | Ap2 of op2 * t * t
-  | Ap3 of op3 * t * t * t
-  | ApN of opN * t vector
-  | RecN of recN * t vector
-  | Integer of {data: Z.t}
-      (** Integer constant, or if [typ] is a [Pointer], null pointer value
-          that never refers to an object *)
-  | Float of {data: string}  (** Floating-point constant *)
 [@@deriving compare, equal, hash, sexp]
 
 val comparator : (t, comparator_witness) Comparator.t
-
-type term = t
-
-val pp_full : ?is_x:(term -> bool) -> t pp
+val pp_full : ?is_x:(t -> bool) -> t pp
 val pp : t pp
 val invariant : t -> unit
 
+type term = t
+
 (** Term.Var is re-exported as Var *)
 module Var : sig
   type t = private term [@@deriving compare, equal, hash, sexp]
@@ -140,65 +130,86 @@ end
 
 (** Construct *)
 
+(* variables *)
 val var : Var.t -> t
+
+(* constants *)
 val nondet : string -> t
 val label : parent:string -> name:string -> t
+val null : t
+val bool : bool -> t
 val true_ : t
 val false_ : t
-val null : t
+val integer : Z.t -> t
 val zero : t
 val one : t
 val minus_one : t
-val splat : byt:t -> siz:t -> t
-val memory : siz:t -> arr:t -> t
-val concat : t array -> t
-val bool : bool -> t
-val integer : Z.t -> t
 val rational : Q.t -> t
 val float : string -> t
+
+(* type conversions *)
+val extract : ?unsigned:bool -> bits:int -> t -> t
+val convert : ?unsigned:bool -> dst:Typ.t -> src:Typ.t -> t -> t
+
+(* comparisons *)
 val eq : t -> t -> t
 val dq : t -> t -> t
 val lt : t -> t -> t
 val le : t -> t -> t
 val ord : t -> t -> t
 val uno : t -> t -> t
+
+(* arithmetic *)
 val neg : t -> t
 val add : t -> t -> t
 val sub : t -> t -> t
 val mul : t -> t -> t
 val div : t -> t -> t
 val rem : t -> t -> t
+
+(* boolean / bitwise *)
 val and_ : t -> t -> t
 val or_ : t -> t -> t
-val xor : t -> t -> t
 val not_ : t -> t
+
+(* bitwise *)
+val xor : t -> t -> t
 val shl : t -> t -> t
 val lshr : t -> t -> t
 val ashr : t -> t -> t
+
+(* if-then-else *)
 val conditional : cnd:t -> thn:t -> els:t -> t
+
+(* memory contents *)
+val splat : byt:t -> siz:t -> t
+val memory : siz:t -> arr:t -> t
+val concat : t array -> t
+
+(* records (struct / array values) *)
 val record : t vector -> t
 val select : rcd:t -> idx:int -> t
 val update : rcd:t -> idx:int -> elt:t -> t
-val extract : ?unsigned:bool -> bits:int -> t -> t
-val convert : ?unsigned:bool -> dst:Typ.t -> src:Typ.t -> t -> t
-val size_of : Typ.t -> t option
 
+(* recursive n-ary application *)
 val rec_app :
      (module Hashtbl.Key with type t = 'id)
   -> (id:'id -> recN -> t lazy_t vector -> t) Staged.t
 
-(** Access *)
-
-val iter : t -> f:(t -> unit) -> unit
-val fold_vars : t -> init:'a -> f:('a -> Var.t -> 'a) -> 'a
-val fold_terms : t -> init:'a -> f:('a -> t -> 'a) -> 'a
-val fold : t -> init:'a -> f:(t -> 'a -> 'a) -> 'a
+val size_of : Typ.t -> t option
 
 (** Transform *)
 
 val map : t -> f:(t -> t) -> t
 val rename : Var.Subst.t -> t -> t
 
+(** Traverse *)
+
+val iter : t -> f:(t -> unit) -> unit
+val fold : t -> init:'a -> f:(t -> 'a -> 'a) -> 'a
+val fold_vars : t -> init:'a -> f:('a -> Var.t -> 'a) -> 'a
+val fold_terms : t -> init:'a -> f:('a -> t -> 'a) -> 'a
+
 (** Query *)
 
 val fv : t -> Var.Set.t