WhyML: tuple terms/expressions do not require parentheses

This makes the syntax cleaner and brings us closer to OCaml.

One incompatibility with the previous grammar is that "ghost"
binds stronger than the left arrow of assignment, and thus
ghost assignments have to be written as "ghost (x.f <- v)".

This is unavoidable, because assignment has to be weaker than
the tuple comma (think "x.f, y.g <- y.g, x.f" or "a[i] <- u,v"),
and "ghost" has to be stronger than comma, for consistency with
our patterns and our return types.

The "return" construction is weaker than comma, for "return a,b".
It is also weaker than assignment, though "return x.f <- b" does
not make much sense either way.

This change does not concern type expressions, where a tuple
type must always have its clothes^Wparentheses on: (int, int).
It might be nice to write "constant pair: int, bool", but on
the other hand this would break casts like "42: int, true".

examples/add_list.mlw

@@ -33,12 +33,12 @@ let rec sum (l: list or_integer_float) : (int, real) =
     variant { l }
     returns { si, sf -> si = add_int l /\ sf = add_real l }
   match l with
-  | Nil -> (0, 0.0)
+  | Nil -> 0, 0.0
   | Cons h t ->
-      let (a,b) = sum t in
+      let a,b = sum t in
       match h with
-      | Integer n -> (n + a,b)
-      | Real x -> (a,x +. b)
+      | Integer n -> n + a, b
+      | Real x -> a, x +. b
       end
   end
 
@@ -47,7 +47,7 @@ let main () =
     Cons (Integer 5) (Cons (Real 3.3) (Cons (Integer 8)
       (Cons (Real 1.4) (Cons (Integer 9) Nil))))
   in
-  let (s,f) = sum l in
+  let s,f = sum l in
   assert { s = 22 };
   assert { f = 4.7 }
 
@@ -69,7 +69,7 @@ let sum (l: list or_integer_float) : (int, real) =
                 !sf +. add_real !ll = add_real l }
     variant { !ll }
      match !ll with
-     | Nil -> return (!si, !sf)
+     | Nil -> return !si, !sf
      | Cons (Integer n) t ->
          si := !si + n; ll := t
      | Cons (Real x) t ->
@@ -84,7 +84,7 @@ let main () =
     Cons (Integer 5) (Cons (Real 3.3) (Cons (Integer 8)
       (Cons (Real 1.4) (Cons (Integer 9) Nil))))
   in
-  let (s,f) = sum l in
+  let s,f = sum l in
   assert { s = 22 };
   assert { f = 4.7 }
 

examples/assigning_meanings_to_programs.mlw

@@ -46,6 +46,6 @@ module Division
       r := !r - y;
       q := !q + 1
     done;
-    (!q, !r)
+    !q, !r
 
 end

examples/balance.mlw

@@ -116,18 +116,18 @@ module Puzzle12
       match balance (balls[0] + balls[8]) (balls[9] + balls[10]) with
       | Equal -> (* 0,8 = 9,10 *)
          match balance balls[0] balls[11] with
-         | Right -> (11, False) | _ -> (11, True) end
+         | Right -> 11, False | _ -> 11, True end
       | Right -> (* 0,8 < 9,10 *)
          match balance balls[9] balls[10] with
-         | Equal -> (8, True)
-         | Right -> (10,  False)
-         | Left  -> (9, False)
+         | Equal -> 8, True
+         | Right -> 10,  False
+         | Left  -> 9, False
          end
       | Left -> (* 0,8 > 9,10 *)
          match balance balls[9] balls[10] with
-         | Equal -> (8, False)
-         | Right -> (9,  True)
-         | Left  -> (10, True)
+         | Equal -> 8, False
+         | Right -> 9,  True
+         | Left  -> 10, True
          end
       end
    | Right -> (* 0,1,2,3 < 4,5,6,7 *)
@@ -135,20 +135,20 @@ module Puzzle12
                     (balls[2] + balls[5] + balls[8]) with
       | Equal -> (* 0,1,4 = 2,5,8 *)
          match balance balls[6] balls[7] with
-         | Equal -> (3, True)
-         | Right -> (7, False)
-         | Left -> (6, False)
+         | Equal -> 3, True
+         | Right -> 7, False
+         | Left -> 6, False
          end
       | Right -> (* 0,1,4 < 2,5,8 *)
          match balance balls[0] balls[1] with
-         | Equal -> (5, False)
-         | Right -> (0, True)
-         | Left -> (1, True)
+         | Equal -> 5, False
+         | Right -> 0, True
+         | Left -> 1, True
          end
       | Left -> (* 0,1,4 > 2,5,8 *)
          match balance balls[4] balls[8] with
-         | Equal -> (2, True)
-         | _     -> (4, False)
+         | Equal -> 2, True
+         | _     -> 4, False
          end
       end
    | Left -> (* 0,1,2,3 > 4,5,6,7 *)
@@ -156,21 +156,21 @@ module Puzzle12
                     (balls[2] + balls[5] + balls[8]) with
       | Equal -> (* 0,1,4 = 2,5,8 *)
          match balance balls[6] balls[7] with
-         | Equal -> (3, False)
-         | Right -> (6, True)
-         | Left -> (7, True)
+         | Equal -> 3, False
+         | Right -> 6, True
+         | Left -> 7, True
          end
       | Right -> (* 0,1,4 < 2,5,8 *)
          match balance balls[2] balls[5] with
-         | Equal -> (4, True)
-         | Right -> (5, False)
-         | Left -> (2, False)
+         | Equal -> 4, True
+         | Right -> 5, False
+         | Left -> 2, False
          end
       | Left -> (* 0,1,4 > 2,5,8 *)
          match balance balls[0] balls[1] with
-         | Equal -> (5, True)
-         | Right -> (1, False)
-         | Left -> (0, False)
+         | Equal -> 5, True
+         | Right -> 1, False
+         | Left -> 0, False
          end
       end
     end

examples/binomial_heap.mlw

@@ -257,7 +257,7 @@ module BinomialHeap
     requires { inv k h }
     requires { h <> Nil }
     variant  { h }
-    ensures  { let (t, h') = result in
+    ensures  { let t, h' = result in
                heaps (Cons t Nil) && heaps h' && inv k h' &&
                le_roots t.elem h && binomial_tree t &&
                forall x. occ x h = occ x (Cons t Nil) + occ x h' }
@@ -266,10 +266,10 @@ module BinomialHeap
     | Nil ->
         absurd
     | Cons t Nil ->
-        (t, Nil)
+        t, Nil
     | Cons t tl ->
-        let (t', tl') = extract_min_tree (rank t + 1) tl in
-        if le t.elem t'.elem then (t, tl) else (t', Cons t tl')
+        let t', tl' = extract_min_tree (rank t + 1) tl in
+        if le t.elem t'.elem then t, tl else t', Cons t tl'
     end
 
   let rec extract_min (h: heap) : (elt, heap)
@@ -277,13 +277,13 @@ module BinomialHeap
     requires { inv 0 h }
     requires { h <> Nil }
     variant  { h }
-    ensures  { let (e, h') = result in
+    ensures  { let e, h' = result in
                heaps h' && inv 0 h' &&
                occ e h' = occ e h - 1 &&
                forall x. x <> e -> occ x h' = occ x h }
     =
-    let (t, h') = extract_min_tree 0 h in
-    (t.elem, merge 0 (reverse t.children) h')
+    let t, h' = extract_min_tree 0 h in
+    t.elem, merge 0 (reverse t.children) h'
 
   (** Complexity analysis. *)
 

examples/braun_trees.mlw

@@ -100,7 +100,7 @@ module BraunHeaps
      requires { inv t }
      requires { 0 < size t }
      variant  { t }
-     ensures  { let (e, t') = result in
+     ensures  { let e, t' = result in
                 heap t' && inv t' && size t' = size t - 1 &&
                 occ e t' = occ e t - 1 &&
                 forall x. x <> e -> occ x t' = occ x t }
@@ -110,10 +110,10 @@ module BraunHeaps
         absurd
     | Node Empty y r ->
         assert { r = Empty };
-        (y, Empty)
+        y, Empty
     | Node l y r ->
-        let (x, l) = extract l in
-        (x, Node r y l)
+        let x, l = extract l in
+        x, Node r y l
     end
 
   let rec replace_min (x: elt) (t: tree elt)
@@ -162,7 +162,7 @@ module BraunHeaps
         if le lx ly then
           Node r lx (merge ll lr)
         else
-          let (x, l) = extract l in
+          let x, l = extract l in
           Node (replace_min x r) ly l
     | Empty, _ ->
         absurd

examples/defunctionalization.mlw

@@ -115,11 +115,11 @@ let function interpret_0 (p:prog) : int = eval_0 p
 *)
 
 let test () =
-  (interpret_0 p0,
+   interpret_0 p0,
    interpret_0 p1,
    interpret_0 p2,
    interpret_0 p3,
-   interpret_0 p4)
+   interpret_0 p4
 
 
 constant v3 : int = eval_0 p3
@@ -269,11 +269,11 @@ let interpret_2 (p:prog) : int
   = eval_2 p I
 
 let test () =
-  (interpret_2 p0,
+   interpret_2 p0,
    interpret_2 p1,
    interpret_2 p2,
    interpret_2 p3,
-   interpret_2 p4)
+   interpret_2 p4
 
 end
 
@@ -379,11 +379,11 @@ let interpret_2 (p:prog) : int
   = eval_2 p I
 
 let test () =
-  (interpret_2 p0,
+   interpret_2 p0,
    interpret_2 p1,
    interpret_2 p2,
    interpret_2 p3,
-   interpret_2 p4)
+   interpret_2 p4
 
 end
 
@@ -715,11 +715,11 @@ let interpret_4 (p:prog) : value
 
 
 let test () =
-  (interpret_4 p0,
+   interpret_4 p0,
    interpret_4 p1,
    interpret_4 p2,
    interpret_4 p3,
-   interpret_4 p4)
+   interpret_4 p4
 
 end
 
@@ -902,7 +902,7 @@ lemma size_c_pos: forall c: context. size_c c >= 0
 
 let rec decompose_term (e:expr) (c:context) : (context, expr)
   variant { size_e e + size_c c }
-  ensures { let (c1,e1) = result in
+  ensures { let c1,e1 = result in
             recompose c1 e1 = recompose c e /\
             is_a_redex e1 }
   raises { Stuck -> is_empty_context c /\ is_a_value e }
@@ -915,7 +915,7 @@ let rec decompose_term (e:expr) (c:context) : (context, expr)
 
 with decompose_cont (c:context) (n:int) : (context, expr)
   variant { size_c c }
-  ensures { let (c1,e1) = result in
+  ensures { let c1,e1 = result in
             recompose c1 e1 = recompose c (Cte n)  /\
             is_a_redex e1 }
   raises { Stuck -> is_empty_context c }
@@ -924,11 +924,11 @@ with decompose_cont (c:context) (n:int) : (context, expr)
   match c with
   | Empty -> raise Stuck
   | Left c e -> decompose_term e (Right n c)
-  | Right n1 c -> (c, Sub (Cte n1) (Cte n))
+  | Right n1 c -> c, Sub (Cte n1) (Cte n)
   end
 
 let decompose (e:expr) : (context, expr)
-  ensures { let (c1,e1) = result in recompose c1 e1 = e  /\
+  ensures { let c1,e1 = result in recompose c1 e1 = e  /\
             is_a_redex e1 }
   raises { Stuck -> is_a_value e }
   =
@@ -961,7 +961,7 @@ let reduce (e:expr) : expr
   ensures { eval_0 result = eval_0 e }
   raises { Stuck -> is_a_value e }
   =
-  let (c,r) = decompose e in
+  let c,r = decompose e in
   recompose c (contract r)
 
 (**
@@ -1000,7 +1000,7 @@ let rec itere (e:expr) : int
 
 
 let refocus c e
-  ensures { let (c1,e1) = result in
+  ensures { let c1,e1 = result in
             recompose c1 e1 = recompose c e /\
             is_a_redex e1 }
   raises { Stuck -> is_empty_context c /\ is_a_value e }
@@ -1063,11 +1063,11 @@ let interpret p
 = eval_1 Empty p
 
 let test () =
-  (interpret p0,
+   interpret p0,
    interpret p1,
    interpret p2,
    interpret p3,
-   interpret p4)
+   interpret p4
 
 end
 
@@ -1164,11 +1164,11 @@ let interpret p
 = eval_1 Empty p
 
 let test () =
-  (interpret p0,
+   interpret p0,
    interpret p1,
    interpret p2,
    interpret p3,
-   interpret p4)
+   interpret p4
 
 
 end

examples/esterel.mlw

@@ -73,8 +73,8 @@ module Esterel
     in
     assert {
       forall x. mem x res.mdl ->
-        let (y,z) =
-          if mem x a.mdl then (x,min_elt b.mdl) else (min_elt a.mdl,x)
+        let y,z =
+          if mem x a.mdl then x, min_elt b.mdl else min_elt a.mdl, x
         in
           mem y a.mdl /\ mem z b.mdl /\ x = max y z };
     res

examples/fibonacci.mlw

@@ -145,7 +145,7 @@ module Zeckendorf
 
   let greatest_fib (x: int) : (int, int)
     requires { 0 < x }
-    ensures  { let (k, fk) = result in
+    ensures  { let k, fk = result in
                2 <= k /\ 1 <= fk = fib k <= x < fib (k + 1) }
   =
     let a = ref 1 in
@@ -160,7 +160,7 @@ module Zeckendorf
       b := f;
       k := !k + 1
    done;
-   (!k, !a)
+   !k, !a
 
   let zeckendorf (n: int) : list int
     requires { 0 <= n }
@@ -175,7 +175,7 @@ module Zeckendorf
       invariant { !x + sum !l = n }
       invariant { match !l with Nil -> true | Cons k _ -> !x < fib (k-1) end }
       variant   { !x }
-      let (k, fk) = greatest_fib !x in
+      let k, fk = greatest_fib !x in
       x := !x - fk;
       l := Cons k !l
     done;
@@ -239,19 +239,19 @@ module Zeckendorf
       requires { wf k lc }
       requires { k >= 2 /\ lc <> Nil }
       requires { 0 <= acc = sum lb - sum lc < fib (k-1) }
-      returns { (x,p) -> fib x <= sum lb = acc + fib x + sum p < fib (x+1) }
-      returns { (x,p) -> wf k p /\ x >= k /\ lc = snoc p x }
+      returns { x,p -> fib x <= sum lb = acc + fib x + sum p < fib (x+1) }
+      returns { x,p -> wf k p /\ x >= k /\ lc = snoc p x }
       variant { lc }
     = match lc with
       | Nil -> absurd
-      | Cons x Nil -> (x,Nil)
-      | Cons x q -> let (y,p) = decomp (x+2) (acc+fib x) q lb in (y,Cons x p)
+      | Cons x Nil -> x,Nil
+      | Cons x q -> let y,p = decomp (x+2) (acc+fib x) q lb in y,Cons x p
       end in
     match l1 , l2 with
     | Nil , Nil -> ()
     | Nil , l | l , Nil -> let _ = decomp 2 0 l l in absurd
-    | _ , _ -> let (_,q1) = decomp 2 0 l1 l1 in
-      let (_,q2) = decomp 2 0 l2 l2 in
+    | _ , _ -> let _,q1 = decomp 2 0 l1 l1 in
+      let _,q2 = decomp 2 0 l2 l2 in
       zeckendorf_unique q1 q2
     end
 
@@ -299,7 +299,7 @@ module FibonacciLogarithmic
     ensures  { let a, b = result in
       power m1110 n = { a11 = a+b; a12 = b; a21 = b; a22 = a } }
   = if n = 0 then
-      (1, 0)
+      1, 0
     else begin
       assert { 0 <= div n 2 };
       let a, b = logfib (div n 2) in
@@ -307,12 +307,12 @@ module FibonacciLogarithmic
       if mod n 2 = 0 then
         begin
         assert { 2 * (div n 2) = (div n 2) + (div n 2) };
-        (a*a+ b*b, b*(a + c))
+        a*a+ b*b, b*(a + c)
         end
       else
         begin
         assert { 2 * (div n 2) + 1 = (div n 2) + (div n 2) + 1 };
-        (b*(a + c), c*c + b*b)
+        b*(a + c), c*c + b*b
         end
     end
 

examples/finger_trees.mlw

 
 module FingerTrees
-  
+
   use import int.Int
   use import list.List
   use import list.Length
   use import list.Append
-  
+
   type digit 'a =
    | One 'a
    | Two 'a 'a
    | Three 'a 'a 'a
    | Four 'a 'a 'a 'a
-  
+
   function d_m (b:digit 'a) : list 'a = match b with
     | One x -> Cons x Nil
     | Two y x -> Cons y (Cons x Nil)
     | Three z y x -> Cons z (Cons y (Cons x Nil))
     | Four u z y x -> Cons u (Cons z (Cons y (Cons x Nil)))
     end
-  
+
   type node 'a =
     | Node2 'a 'a
     | Node3 'a 'a 'a
-  
+
   function node_cons (nd:node 'a) (l:list 'a) : list 'a = match nd with
     | Node2 x y -> Cons x (Cons y l)
     | Node3 x y z -> Cons x (Cons y (Cons z l))
     end
-  
+
   let lemma node_cons_app (nd:node 'a) (p q:list 'a)
     ensures { node_cons nd (p++q) = node_cons nd p ++ q }
   = match nd with Node2 _ _ -> "keep_on_simp" () | _ -> () end
-  
+
   function flatten (l:list (node 'a)) : list 'a = match l with
     | Nil -> Nil
     | Cons nd q -> node_cons nd (flatten q)
     end
-  
+
   type t 'a =
     | Empty
     | Single (digit 'a)
     | Deep (digit 'a) (t (node 'a)) (digit 'a)
-  
+
   function t_m (t:t 'a) : list 'a = match t with
     | Empty -> Nil
     | Single x -> d_m x
     | Deep l m r -> d_m l ++ flatten (t_m m) ++ d_m r
     end
-  
+
   let d_cons (x:'a) (d:digit 'a) : (digit 'a,list (node 'a))
-    returns { (b,o) -> Cons x (d_m d) = d_m b ++ flatten o /\ length o <= 1 }
+    returns { b,o -> Cons x (d_m d) = d_m b ++ flatten o /\ length o <= 1 }
   = match d with
-    | One y -> (Two x y , Nil)
-    | Two y z -> (Three x y z , Nil)
-    | Three y z t -> (Four x y z t , Nil)
-    | Four y z t u -> (Two x y , Cons (Node3 z t u) Nil)
+    | One y -> Two x y , Nil
+    | Two y z -> Three x y z , Nil
+    | Three y z t -> Four x y z t , Nil
+    | Four y z t u -> Two x y , Cons (Node3 z t u) Nil
     end
-  
+
   let rec cons (x:'a) (t:t 'a) : t 'a
     ensures { t_m result = Cons x (t_m t) }
     variant { t }
   = match t with
     | Empty -> Single (One x)
     | Single d -> Deep (One x) Empty d
-    | Deep lf md rg -> let (lf2 , rem) = d_cons x lf in
+    | Deep lf md rg -> let lf2 , rem = d_cons x lf in
       match rem with
       | Nil -> Deep lf2 md rg
       | Cons x q -> assert { q = Nil };
         Deep lf2 (cons x md) rg
       end
     end
-  
+
 end
 

examples/in_progress/simple_queue.mlw

@@ -102,6 +102,6 @@ module SimpleQueue
 *)
     q.data[q.n] <- x;
     q.n <- q.n + 1;
-    ghost q.contents <- q.contents ++ Cons x Nil
+    ghost (q.contents <- q.contents ++ Cons x Nil)
 
 end

examples/mergesort_list.mlw

@@ -88,7 +88,7 @@ module Mergesort
 
   let split (l0: list 'a) : (list 'a, list 'a)
     requires { length l0 >= 2 }
-    ensures  { let (l1, l2) = result in
+    ensures  { let l1, l2 = result in
       1 <= length l1 /\ 1 <= length l2 /\ permut l0 (l1 ++ l2) }
   = let rec split_aux (l1 l2 l: list 'a) : (list 'a, list 'a)
       requires { length l2 = length l1 \/ length l2 = length l1 + 1 }
@@ -97,7 +97,7 @@ module Mergesort
         permut (r1 ++ r2) (l1 ++ (l2 ++ l)) }
       variant { length l }
     = match l with
-      | Nil -> (l1, l2)
+      | Nil -> l1, l2
       | Cons x r -> split_aux l2 (Cons x l1) r
       end
     in

examples/patience.mlw

@@ -267,7 +267,7 @@ module PatienceAbstract
            0 <= s.stacks[i][j] < s.num_elts)
          (** contents of stacks are valid card indexes *)
   /\ (forall i. 0 <= i < s.num_elts ->
-       let (is,ip) = s.positions[i] in
+       let is,ip = s.positions[i] in
        0 <= is < s.num_stacks &&
        let st = s.stacks[is] in
          0 <= ip < s.stack_sizes[is] &&
@@ -296,7 +296,7 @@ module PatienceAbstract
        (** the predecessor is a valid index or [-1] *)
        pred < i /\
        (** predecessor is always a smaller index *)
-       let (is,_ip) = s.positions[i] in
+       let is,_ip = s.positions[i] in
        if pred < 0 then is = 0
          (** if predecessor is [-1] then [i] is in leftmost stack *)
        else
@@ -304,7 +304,7 @@ module PatienceAbstract
          (** if predecessor is not [-1], it denotes a card with smaller value... *)
          is > 0 &&
          (** ...the card is not on the leftmost stack... *)
-         let (ps,_pp) = s.positions[pred] in
+         let ps,_pp = s.positions[pred] in
          ps = is - 1)
          (** ...and predecessor is in the stack on the immediate left *)
 
@@ -333,7 +333,7 @@ module PatienceAbstract
         !pred = top_stack_im1 /\
         c > s.values[!pred]  /\
         0 <= !pred < s.num_elts /\
-        let (ps,_pp) = s.positions[!pred] in
+        let ps,_pp = s.positions[!pred] in
         ps = i - 1
       }
       let stack_i = s.stacks[i] in
@@ -341,7 +341,7 @@ module PatienceAbstract
       let top_stack_i = stack_i[stack_i_size - 1] in
       if c <= s.values[top_stack_i] then raise (Return i);
       assert { 0 <= top_stack_i < s.num_elts };
-      assert { let (is,ip) = s.positions[top_stack_i] in
+      assert { let is,ip = s.positions[top_stack_i] in
         0 <= is < s.num_stacks &&
         0 <= ip < s.stack_sizes[is] &&
         s.stacks[is][ip] = top_stack_i &&
@@ -359,7 +359,7 @@ module PatienceAbstract
     s.num_stacks <- s.num_stacks + 1;
     s.stack_sizes <- s.stack_sizes[i <- 1];
     s.stacks <- s.stacks[i <- new_stack_i];
-    s.positions <- s.positions[idx <- (i,0)];
+    s.positions <- s.positions[idx <- i,0];
     s.preds <- s.preds[idx <- !pred]
   with Return i ->
          let stack_i = s.stacks[i] in
@@ -372,7 +372,7 @@ module PatienceAbstract
          (* s.num_stacks unchanged *)
          s.stack_sizes <- s.stack_sizes[i <- stack_i_size + 1];
          s.stacks <- s.stacks[i <- new_stack_i];
-         s.positions <- s.positions[idx <- (i,stack_i_size)];
+         s.positions <- s.positions[idx <- i,stack_i_size];
          s.preds <- s.preds[idx <- !pred];
   end
 
@@ -471,7 +471,7 @@ module PatienceAbstract
     for i = ns-1 downto 0 do
        invariant { -1 <= !idx < s.num_elts }
        invariant { i >= 0 -> !idx >= 0 &&
-         let (is,_) = s.positions[!idx] in is = i }
+         let is,_ = s.positions[!idx] in is = i }
        invariant { i+1 < ns -> !idx < !seq[i+1] }
        invariant { 0 <= i < ns-1 -> s.values[!idx] < s.values[!seq[i+1]] }
        invariant { forall j. i < j < ns -> 0 <= !seq[j] < s.num_elts }
@@ -496,7 +496,7 @@ module PatienceAbstract
         increasing_subsequence sigma input /\ sigma.seqlen > s.num_stacks ->
         let f = fun i ->
           let si = sigma.seqval[i] in
-          let (stack_i,_) = s.positions[si] in
+          let stack_i,_ = s.positions[si] in
           stack_i
         in range f sigma.seqlen s.num_stacks &&
            not (injective f sigma.seqlen s.num_stacks)
@@ -509,8 +509,8 @@ module PatienceAbstract
           0 <= i < j < sigma.seqlen &&
           let si = sigma.seqval[i] in
           let sj = sigma.seqval[j] in
-          let (stack_i,_pi) = s.positions[si] in
-          let (stack_j,_pj) = s.positions[sj] in
+          let stack_i,_pi = s.positions[si] in
+          let stack_j,_pj = s.positions[sj] in
           stack_i = stack_j
     };
     assert { (* contradiction from non-injectivity *)
@@ -520,8 +520,8 @@ module PatienceAbstract
           0 <= i < j < sigma.seqlen ->
           let si = sigma.seqval[i] in
           let sj = sigma.seqval[j] in
-          let (stack_i,pi) = s.positions[si] in
-          let (stack_j,pj) = s.positions[sj] in
+          let stack_i,pi = s.positions[si] in
+          let stack_j,pj = s.positions[sj] in
           stack_i = stack_j ->
           si < sj && pi < pj && s.values[si] < s.values[sj]
     };
@@ -596,7 +596,7 @@ module PatienceFull
         !pred = top_stack_im1 /\
         c > state.values[!pred]  /\
         0 <= !pred < state.num_elts /\
-        let (ps,_pp) = state.positions[!pred] in
+        let ps,_pp = state.positions[!pred] in
         ps = !i - 1
       }
       invariant { old_stacks = rev_append !acc !rem_stacks }
@@ -626,7 +626,7 @@ module PatienceFull
              let ghost stack_i_size = state.stack_sizes[!i] in
              let ghost top_stack_i = stack_i[stack_i_size - 1] in
              assert { 0 <= top_stack_i < state.num_elts };
-             assert { let (is,ip) = state.positions[top_stack_i] in
+             assert { let is,ip = state.positions[top_stack_i] in
                0 <= is < state.num_stacks &&
                0 <= ip < state.stack_sizes[is] &&
                state.stacks[is][ip] = top_stack_i &&
@@ -648,7 +648,7 @@ module PatienceFull
     state.num_stacks <- state.num_stacks + 1;
     state.stack_sizes <- state.stack_sizes[i <- 1];
     state.stacks <- state.stacks[i <- new_stack_i];
-    state.positions <- state.positions[idx <- (i,0)];
+    state.positions <- state.positions[idx <- i,0];
     state.preds <- state.preds[idx <- !pred];
     (* we put card [c] in a new stack *)
     rev_append (Cons (Cons c Nil) !acc) Nil
@@ -665,7 +665,7 @@ module PatienceFull
          (* state.num_stacks unchanged *)
          state.stack_sizes <- state.stack_sizes[!i <- stack_i_size + 1];
          state.stacks <- state.stacks[!i <- new_stack_i];
-         state.positions <- state.positions[idx <- (!i,stack_i_size)];
+         state.positions <- state.positions[idx <- !i,stack_i_size];
          state.preds <- state.preds[idx <- !pred];
          (* card is placed on the leftmost stack where its card
             value is no greater than the topmost card on that
@@ -824,7 +824,7 @@ module PatienceFull
     for i = ns-1 downto 0 do
        invariant { -1 <= !idx < state.num_elts }
        invariant { i >= 0 -> !idx >= 0 &&
-         let (is,_) = state.positions[!idx] in is = i }
+         let is,_ = state.positions[!idx] in is = i }
        invariant { i+1 < ns -> !idx < !seq[i+1] }