diff --git a/std/arith.asm b/std/arith.asm
index 9a06cd6fa..ab5296aaa 100644
--- a/std/arith.asm
+++ b/std/arith.asm
@@ -14,7 +14,7 @@ use std::prover::Query;
 // Currently only supports "Equation 0", i.e., 256-Bit addition and multiplication.
 machine Arith(CLK32_31, operation_id){
     
-    // The operation ID will be bit-decomosed to yield selEq[], controlling which equations are activated.
+    // The operation ID will be bit-decomposed to yield selEq[], controlling which equations are activated.
     col witness operation_id;
 
     // Computes x1 * y1 + x2, where all inputs / outputs are 256-bit words (represented as 32-Bit limbs in little-endian order).
@@ -29,7 +29,10 @@ machine Arith(CLK32_31, operation_id){
     // Performs elliptic curve doubling of point (x1, y2).
     // Operation ID is 12 = 0b1100, i.e., we activate equations 2, 3, and 4.
     operation ec_double<12> x1c[0], x1c[1], x1c[2], x1c[3], x1c[4], x1c[5], x1c[6], x1c[7], y1c[0], y1c[1], y1c[2], y1c[3], y1c[4], y1c[5], y1c[6], y1c[7] -> x3c[0], x3c[1], x3c[2], x3c[3], x3c[4], x3c[5], x3c[6], x3c[7], y3c[0], y3c[1], y3c[2], y3c[3], y3c[4], y3c[5], y3c[6], y3c[7];
-    
+
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     let BYTE: col = |i| i & 0xff;
     let BYTE2: col = |i| i & 0xffff;
 
diff --git a/std/binary.asm b/std/binary.asm
index 21c0ec634..dbd0e9e18 100644
--- a/std/binary.asm
+++ b/std/binary.asm
@@ -12,13 +12,16 @@ machine Binary(latch, operation_id) {
 
     operation xor<2> A, B -> C;
 
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     col witness operation_id;
     unchanged_until(operation_id, latch);
 
     col fixed latch(i) { if (i % 4) == 3 { 1 } else { 0 } };
     col fixed FACTOR(i) { 1 << (((i + 1) % 4) * 8) };
 
-    // TOOD would be nice with destructuring assignment for arrays.
+    // TODO would be nice with destructuring assignment for arrays.
     let inputs: (int -> int)[] = cross_product([256, 256, 3]);
     let a = inputs[0];
     let b = inputs[1];
diff --git a/std/hash/poseidon_bn254.asm b/std/hash/poseidon_bn254.asm
index 9ca71cff0..74799afde 100644
--- a/std/hash/poseidon_bn254.asm
+++ b/std/hash/poseidon_bn254.asm
@@ -14,6 +14,9 @@ machine PoseidonBN254(FIRSTBLOCK, operation_id) {
     // hash functions.
     operation poseidon_permutation<0> state[0], state[1], state[2] -> output[0];
 
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     col witness operation_id;
 
     // Using parameters from https://eprint.iacr.org/2019/458.pdf
diff --git a/std/hash/poseidon_gl.asm b/std/hash/poseidon_gl.asm
index 84fd8105c..5ba1b8dde 100644
--- a/std/hash/poseidon_gl.asm
+++ b/std/hash/poseidon_gl.asm
@@ -11,6 +11,9 @@ machine PoseidonGL(FIRSTBLOCK, operation_id) {
     // hash functions.
     operation poseidon_permutation<0> state[0], state[1], state[2], state[3], state[4], state[5], state[6], state[7], state[8], state[9], state[10], state[11] -> output[0], output[1], output[2], output[3];
 
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     col witness operation_id;
 
     // Ported from:
diff --git a/std/shift.asm b/std/shift.asm
index 38b4db66d..cd71289ec 100644
--- a/std/shift.asm
+++ b/std/shift.asm
@@ -9,6 +9,9 @@ machine Shift(latch, operation_id) {
 
     operation shr<1> A, B -> C;
 
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     col witness operation_id;
     unchanged_until(operation_id, latch);
 
diff --git a/std/split/split_bn254.asm b/std/split/split_bn254.asm
index 9b340be41..3f4b3e1e6 100644
--- a/std/split/split_bn254.asm
+++ b/std/split/split_bn254.asm
@@ -6,6 +6,9 @@ machine SplitBN254(RESET, _) {
 
     operation split in_acc -> o1, o2, o3, o4, o5, o6, o7, o8;
 
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     // Latch and operation ID
     col fixed RESET(i) { if i % 32 == 31 { 1 } else { 0 } };
 
diff --git a/std/split/split_gl.asm b/std/split/split_gl.asm
index 15112f773..5c1fe8ffe 100644
--- a/std/split/split_gl.asm
+++ b/std/split/split_gl.asm
@@ -6,6 +6,9 @@ machine SplitGL(RESET, _) {
 
     operation split in_acc -> output_low, output_high;
 
+    // Allow this machine to be connected via a permutation
+    call_selectors sel;
+
     // Latch and operation ID
     col fixed RESET(i) { if i % 8 == 7 { 1 } else { 0 } };
 
diff --git a/test_data/std/arith_test.asm b/test_data/std/arith_test.asm
index bcf9942e3..d742d143e 100644
--- a/test_data/std/arith_test.asm
+++ b/test_data/std/arith_test.asm
@@ -72,9 +72,9 @@ machine Main{
 
     Arith arith;
 
-    instr affine_256 A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7, C0, C1, C2, C3, C4, C5, C6, C7 -> D0, D1, D2, D3, D4, D5, D6, D7, E0, E1, E2, E3, E4, E5, E6, E7 = arith.affine_256;
-    instr ec_add A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7, C0, C1, C2, C3, C4, C5, C6, C7, D0, D1, D2, D3, D4, D5, D6, D7 -> E0, E1, E2, E3, E4, E5, E6, E7, F0, F1, F2, F3, F4, F5, F6, F7 = arith.ec_add;
-    instr ec_double A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7 -> E0, E1, E2, E3, E4, E5, E6, E7, F0, F1, F2, F3, F4, F5, F6, F7 = arith.ec_double;
+    instr affine_256 A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7, C0, C1, C2, C3, C4, C5, C6, C7 -> D0, D1, D2, D3, D4, D5, D6, D7, E0, E1, E2, E3, E4, E5, E6, E7 ~ arith.affine_256;
+    instr ec_add A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7, C0, C1, C2, C3, C4, C5, C6, C7, D0, D1, D2, D3, D4, D5, D6, D7 -> E0, E1, E2, E3, E4, E5, E6, E7, F0, F1, F2, F3, F4, F5, F6, F7 ~ arith.ec_add;
+    instr ec_double A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7 -> E0, E1, E2, E3, E4, E5, E6, E7, F0, F1, F2, F3, F4, F5, F6, F7 ~ arith.ec_double;
 
     instr assert_eq A0, A1, A2, A3, A4, A5, A6, A7, B0, B1, B2, B3, B4, B5, B6, B7 {
         A0 = B0,
diff --git a/test_data/std/binary_test.asm b/test_data/std/binary_test.asm
index 7d820adcd..ee9da6940 100644
--- a/test_data/std/binary_test.asm
+++ b/test_data/std/binary_test.asm
@@ -12,9 +12,9 @@ machine Main {
 
     Binary binary;
 
-    instr and X0, X1 -> X2 = binary.and;
-    instr or X0, X1 -> X2 = binary.or;
-    instr xor X0, X1 -> X2 = binary.xor;
+    instr and X0, X1 -> X2 ~ binary.and;
+    instr or X0, X1 -> X2 ~ binary.or;
+    instr xor X0, X1 -> X2 ~ binary.xor;
 
     instr assert_eq X0, X1 {
         X0 = X1
diff --git a/test_data/std/poseidon_bn254_test.asm b/test_data/std/poseidon_bn254_test.asm
index cc35e82ed..b8b582519 100644
--- a/test_data/std/poseidon_bn254_test.asm
+++ b/test_data/std/poseidon_bn254_test.asm
@@ -12,7 +12,7 @@ machine Main {
 
     PoseidonBN254 poseidon;
 
-    instr poseidon X0, X1, X2 -> X3 = poseidon.poseidon_permutation;
+    instr poseidon X0, X1, X2 -> X3 ~ poseidon.poseidon_permutation;
 
     instr assert_eq X0, X1 {
         X0 = X1
diff --git a/test_data/std/poseidon_gl_test.asm b/test_data/std/poseidon_gl_test.asm
index dfd1819f3..6183e2f6e 100644
--- a/test_data/std/poseidon_gl_test.asm
+++ b/test_data/std/poseidon_gl_test.asm
@@ -27,7 +27,7 @@ machine Main {
 
     PoseidonGL poseidon;
 
-    instr poseidon X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11 -> X12, X13, X14, X15 = poseidon.poseidon_permutation;
+    instr poseidon X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11 -> X12, X13, X14, X15 ~ poseidon.poseidon_permutation;
 
     instr assert_eq X0, X1 {
         X0 = X1
diff --git a/test_data/std/shift_test.asm b/test_data/std/shift_test.asm
index 89ff6350b..71118530f 100644
--- a/test_data/std/shift_test.asm
+++ b/test_data/std/shift_test.asm
@@ -12,8 +12,8 @@ machine Main {
 
     Shift shift;
 
-    instr shl X0, X1 -> X2 = shift.shl;
-    instr shr X0, X1 -> X2 = shift.shr;
+    instr shl X0, X1 -> X2 ~ shift.shl;
+    instr shr X0, X1 -> X2 ~ shift.shr;
 
     instr assert_eq X0, X1 {
         X0 = X1
diff --git a/test_data/std/split_bn254_test.asm b/test_data/std/split_bn254_test.asm
index 645334c96..739c98da9 100644
--- a/test_data/std/split_bn254_test.asm
+++ b/test_data/std/split_bn254_test.asm
@@ -25,7 +25,7 @@ machine Main {
 
     SplitBN254 split_machine;
 
-    instr split X0 -> X1, X2, X3, X4, X5, X6, X7, X8 = split_machine.split;
+    instr split X0 -> X1, X2, X3, X4, X5, X6, X7, X8 ~ split_machine.split;
 
     instr assert_eq X0, X1 {
         X0 = X1
diff --git a/test_data/std/split_gl_test.asm b/test_data/std/split_gl_test.asm
index 1ef2355fd..81fb8d207 100644
--- a/test_data/std/split_gl_test.asm
+++ b/test_data/std/split_gl_test.asm
@@ -13,7 +13,7 @@ machine Main {
 
     SplitGL split_machine;
 
-    instr split X0 -> X1, X2 = split_machine.split;
+    instr split X0 -> X1, X2 ~ split_machine.split;
 
     instr assert_eq X0, X1 {
         X0 = X1