fix: Fix completeness bug of recurse_or_return

The Jump Stack Table did not know that instruction `recurse_or_return`
could return. Consequently, proving correct execution of programs
making use of instruction `recurse_or_return` was not possible (except
for a few specific cases).

specification/src/arithmetization-overview.md

@@ -15,9 +15,9 @@
 | [CascadeTable](cascade-table.md)           |          6 |         2 |          12 |
 | [LookupTable](lookup-table.md)             |          4 |         2 |          10 |
 | [U32Table](u32-table.md)                   |         10 |         1 |          13 |
-| DegreeLowering                             |        200 |        36 |         308 |
+| DegreeLowering                             |        201 |        36 |         309 |
 | Randomizers                                |          0 |         1 |           3 |
-| **TOTAL**                                  |    **349** |    **86** |     **607** |
+| **TOTAL**                                  |    **350** |    **86** |     **608** |
 <!-- auto-gen info stop table_overview -->
 
 ## Constraints
@@ -37,7 +37,7 @@ Before automatic degree lowering:
 | [ProcessorTable](processor-table.md)           |       29 |           10 |          41 |         1 |         19 |
 | [OpStackTable](operational-stack-table.md)     |        3 |            0 |           5 |         0 |          4 |
 | [RamTable](random-access-memory-table.md)      |        7 |            0 |          12 |         1 |          5 |
-| [JumpStackTable](jump-stack-table.md)          |        6 |            0 |           6 |         0 |          4 |
+| [JumpStackTable](jump-stack-table.md)          |        6 |            0 |           6 |         0 |          5 |
 | [HashTable](hash-table.md)                     |       22 |           45 |          47 |         2 |          9 |
 | [CascadeTable](cascade-table.md)               |        2 |            1 |           3 |         0 |          4 |
 | [LookupTable](lookup-table.md)                 |        3 |            1 |           4 |         1 |          3 |
@@ -53,13 +53,13 @@ After automatically lowering degree to 4:
 | [ProcessorTable](processor-table.md)           |       31 |           10 |         207 |         1 |
 | [OpStackTable](operational-stack-table.md)     |        3 |            0 |           5 |         0 |
 | [RamTable](random-access-memory-table.md)      |        7 |            0 |          13 |         1 |
-| [JumpStackTable](jump-stack-table.md)          |        6 |            0 |           6 |         0 |
+| [JumpStackTable](jump-stack-table.md)          |        6 |            0 |           7 |         0 |
 | [HashTable](hash-table.md)                     |       22 |           52 |          84 |         2 |
 | [CascadeTable](cascade-table.md)               |        2 |            1 |           3 |         0 |
 | [LookupTable](lookup-table.md)                 |        3 |            1 |           4 |         1 |
 | [U32Table](u32-table.md)                       |        1 |           26 |          34 |         2 |
 | [Grand Cross-Table Argument](table-linking.md) |        0 |            0 |           0 |        14 |
-| **TOTAL**                                      |   **81** |       **94** |     **366** |    **23** |
+| **TOTAL**                                      |   **81** |       **94** |     **367** |    **23** |
 <!-- auto-gen info stop constraints_overview -->
 
 
@@ -71,5 +71,5 @@ In order to gauge the runtime cost for this step, the following table provides e
 <!-- auto-gen info start tasm_air_evaluation_cost -->
 | Processor | Op Stack |   RAM |
 |----------:|---------:|------:|
-|     34469 |    63967 | 22617 |
+|     34477 |    63981 | 22620 |
 <!-- auto-gen info stop tasm_air_evaluation_cost -->

specification/src/jump-stack-table.md

@@ -164,16 +164,17 @@ None.
 1. The jump stack pointer `jsp` increases by 1, *or*
 1. (`jsp` does not change and `jso` does not change and `jsd` does not change and the cycle counter `clk` increases by 1), *or*
 1. (`jsp` does not change and `jso` does not change and `jsd` does not change and the current instruction `ci` is `call`), *or*
-1. (`jsp` does not change and the current instruction `ci` is `return`).
+1. (`jsp` does not change and the current instruction `ci` is `return`), *or*
+1. (`jsp` does not change and the current instruction `ci` is `recurse_or_return`).
 1. The running product for the permutation argument `rppa` absorbs the next row  with respect to challenges 🍇, 🍅, 🍌, 🍏, and 🍐 and indeterminate 🧴.
 1. If the jump stack pointer `jsp` does not change, then the logarithmic derivative for the clock jump difference lookup `ClockJumpDifferenceLookupClientLogDerivative` accumulates a factor `(clk' - clk)` relative to indeterminate 🪞.
   Otherwise, it remains the same.
 
 Written as Disjunctive Normal Form, the same constraints can be expressed as:
 1. The jump stack pointer `jsp` increases by 1 or the jump stack pointer `jsp` does not change
-1. The jump stack pointer `jsp` increases by 1 or the jump stack origin `jso` does not change or current instruction `ci` is `return`
-1. The jump stack pointer `jsp` increases by 1 or the jump stack destination `jsd` does not change or current instruction `ci` is `return`
-1. The jump stack pointer `jsp` increases by 1 or the cycle count `clk` increases by 1 or current instruction `ci` is `call` or current instruction `ci` is `return`
+1. The jump stack pointer `jsp` increases by 1 or the jump stack origin `jso` does not change or current instruction `ci` is `return` or `recurse_or_return`
+1. The jump stack pointer `jsp` increases by 1 or the jump stack destination `jsd` does not change or current instruction `ci` is `return` or `recurse_or_return`
+1. The jump stack pointer `jsp` increases by 1 or the cycle count `clk` increases by 1 or current instruction `ci` is `call` or current instruction `ci` is `return` or `recurse_or_return`
 1. `rppa' - rppa·(🧴 - 🍇·clk' - 🍅·ci' - 🍌·jsp' - 🍏·jso' - 🍐·jsd')`
 1. - the `jsp` changes or the logarithmic derivative accumulates a summand, and
    - the `jsp` does not change or the logarithmic derivative does not change.

triton-vm/src/table/jump_stack_table.rs

@@ -82,6 +82,8 @@ impl ExtJumpStackTable {
         let call_opcode =
             circuit_builder.b_constant(Instruction::Call(BFieldElement::default()).opcode_b());
         let return_opcode = circuit_builder.b_constant(Instruction::Return.opcode_b());
+        let recurse_or_return_opcode =
+            circuit_builder.b_constant(Instruction::RecurseOrReturn.opcode_b());
 
         let clk = circuit_builder.input(CurrentBaseRow(CLK.master_base_table_index()));
         let ci = circuit_builder.input(CurrentBaseRow(CI.master_base_table_index()));
@@ -106,50 +108,30 @@ impl ExtJumpStackTable {
             ClockJumpDifferenceLookupClientLogDerivative.master_ext_table_index(),
         ));
 
-        // 1. The jump stack pointer jsp increases by 1
-        //      or the jump stack pointer jsp does not change
         let jsp_inc_or_stays =
             (jsp_next.clone() - jsp.clone() - one()) * (jsp_next.clone() - jsp.clone());
 
-        // 2. The jump stack pointer jsp increases by 1
-        //      or current instruction ci is return
-        //      or the jump stack origin jso does not change
-        let jsp_inc_by_one_or_ci_is_return =
-            (jsp_next.clone() - jsp.clone() - one()) * (ci.clone() - return_opcode.clone());
-        let jsp_inc_or_jso_stays_or_ci_is_ret =
-            jsp_inc_by_one_or_ci_is_return.clone() * (jso_next.clone() - jso);
-
-        // 3. The jump stack pointer jsp increases by 1
-        //      or current instruction ci is return
-        //      or the jump stack destination jsd does not change
-        let jsp_inc_or_jsd_stays_or_ci_ret =
-            jsp_inc_by_one_or_ci_is_return * (jsd_next.clone() - jsd);
-
-        // 4. The jump stack pointer jsp increases by 1
-        //      or the cycle count clk increases by 1
-        //      or current instruction ci is call
-        //      or current instruction ci is return
-        let jsp_inc_or_clk_inc_or_ci_call_or_ci_ret = (jsp_next.clone() - jsp.clone() - one())
+        let jsp_inc_by_one_or_ci_can_return = (jsp_next.clone() - jsp.clone() - one())
+            * (ci.clone() - return_opcode)
+            * (ci.clone() - recurse_or_return_opcode);
+        let jsp_inc_or_jso_stays_or_ci_can_ret =
+            jsp_inc_by_one_or_ci_can_return.clone() * (jso_next.clone() - jso);
+
+        let jsp_inc_or_jsd_stays_or_ci_can_ret =
+            jsp_inc_by_one_or_ci_can_return.clone() * (jsd_next.clone() - jsd);
+
+        let jsp_inc_or_clk_inc_or_ci_call_or_ci_can_ret = jsp_inc_by_one_or_ci_can_return
             * (clk_next.clone() - clk.clone() - one())
-            * (ci.clone() - call_opcode)
-            * (ci - return_opcode);
+            * (ci.clone() - call_opcode);
 
-        // The running product for the permutation argument `rppa` accumulates one row in each
-        // row, relative to weights `a`, `b`, `c`, `d`, `e`, and indeterminate `α`.
         let compressed_row = circuit_builder.challenge(JumpStackClkWeight) * clk_next.clone()
             + circuit_builder.challenge(JumpStackCiWeight) * ci_next
             + circuit_builder.challenge(JumpStackJspWeight) * jsp_next.clone()
             + circuit_builder.challenge(JumpStackJsoWeight) * jso_next
             + circuit_builder.challenge(JumpStackJsdWeight) * jsd_next;
-
         let rppa_updates_correctly =
             rppa_next - rppa * (circuit_builder.challenge(JumpStackIndeterminate) - compressed_row);
 
-        // The running sum of the logarithmic derivative for the clock jump difference Lookup
-        // Argument accumulates a summand of `clk_diff` if and only if the `jsp` does not change.
-        // Expressed differently:
-        // - the `jsp` changes or the log derivative accumulates a summand, and
-        // - the `jsp` does not change or the log derivative does not change.
         let log_derivative_remains =
             clock_jump_diff_log_derivative_next.clone() - clock_jump_diff_log_derivative.clone();
         let clk_diff = clk_next - clk;
@@ -163,9 +145,9 @@ impl ExtJumpStackTable {
 
         vec![
             jsp_inc_or_stays,
-            jsp_inc_or_jso_stays_or_ci_is_ret,
-            jsp_inc_or_jsd_stays_or_ci_ret,
-            jsp_inc_or_clk_inc_or_ci_call_or_ci_ret,
+            jsp_inc_or_jso_stays_or_ci_can_ret,
+            jsp_inc_or_jsd_stays_or_ci_can_ret,
+            jsp_inc_or_clk_inc_or_ci_call_or_ci_can_ret,
             rppa_updates_correctly,
             log_derivative_updates_correctly,
         ]