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feat(tests): Python AVM port rewrite + test harness, Go test harness

Browse source 
Python port rewritten to match spec:
- Added Q0_16, PUSH_Q0, PUSH_BOOL as separate opcodes
- Added V6 comparison (lt_q16_v6)
- Added floor division (Lean Int.ediv)
- Added stack depth limit (AVM_MAX_STACK = 1024)
- Added type checking in exec_prim
- All 10 tests passing

Go AVM port: added test_avm_test.go with 8 test cases

Milestone: Python → ✅, Go → 🔄
This commit is contained in:
allaun 2026-06-30 17:56:09 -05:00
parent 56b734cbc3
commit f6cbddcbf2
25 changed files with 2358 additions and 317 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

2
PORTING_MANIFEST.md
View file

@ -19,7 +19,7 @@ All other languages provide independent cross-validation.
| `CoreFormalism/Q16_16Numerics.lean` | — | — | ✅ | ✅ | | `CoreFormalism/Q16_16Numerics.lean` | — | — | ✅ | ✅ |
| `SilverSight/PIST/Spectral.lean` | — | — | ✅ | — | | `SilverSight/PIST/Spectral.lean` | — | — | ✅ | — |
| `SilverSight/PIST/Classify.lean` | — | — | — | — | | `SilverSight/PIST/Classify.lean` | — | — | — | — |
| `SilverSight/AVMIsa/Types.lean` (AVM) | ✅ | ✅ | ✅ | — | | `SilverSight/AVMIsa/Types.lean` (AVM) | ✅ | ✅ | ✅ | ✅ |
| `SilverSight/RRC/Emit.lean` | — | — | — | — | | `SilverSight/RRC/Emit.lean` | — | — | — | — |
| `python/nuvmap/projection_engine.py` | ✅ | ✅ | ✅ | — | | `python/nuvmap/projection_engine.py` | ✅ | ✅ | ✅ | — |

148
c/AVMIsa/avm.c Normal file
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@ -0,0 +1,148 @@
/* AVM ISA v1 — C Port (Strict Functional Execution) */
#include <stdint.h>
#include <stdbool.h>
#define Q16_SCALE 65536
#define AVM_Q0_MIN (-32767)
#define AVM_Q0_MAX 32767
#define AVM_Q16_MIN (-2147483648)
#define AVM_Q16_MAX 2147483647
/* ── Types ─────────────────────────────────────── */
typedef enum { VAL_Q0, VAL_Q16, VAL_BOOL } ValType;
typedef struct { ValType ty; int32_t val; } AvmVal;
AvmVal avm_q0(int32_t x) {
if (x < AVM_Q0_MIN) x = AVM_Q0_MIN;
if (x > AVM_Q0_MAX) x = AVM_Q0_MAX;
return (AvmVal){VAL_Q0, x};
}
AvmVal avm_q16(int32_t x) { return (AvmVal){VAL_Q16, x}; }
AvmVal avm_bool(bool x) { return (AvmVal){VAL_BOOL, x ? 1 : 0}; }
/* ── Primitives ─────────────────────────────────── */
typedef enum {
PRIM_ADD_Q16, PRIM_SUB_Q16, PRIM_MUL_Q16, PRIM_DIV_Q16,
PRIM_LT_Q16, PRIM_EQ_Q16, PRIM_AND, PRIM_OR, PRIM_NOT
} Prim;
typedef struct { AvmVal *data; int len, cap; } Stack;
typedef struct { AvmVal *data; int len; } Locals;
typedef struct State {
int pc;
Stack stack;
Locals locals;
int halted;
} State;
int64_t q16_mul(int32_t a, int32_t b) {
return (int64_t)a * (int64_t)b / Q16_SCALE;
}
int64_t q16_div(int32_t a, int32_t b) {
if (b == 0) return AVM_Q16_MAX;
return (int64_t)a * Q16_SCALE / b;
}
/* ── Instr ──────────────────────────────────────── */
typedef enum {
INSTR_PUSH_Q16, INSTR_PUSH_BOOL, INSTR_POP, INSTR_DUP, INSTR_SWAP,
INSTR_LOAD, INSTR_STORE, INSTR_JUMP, INSTR_JUMP_IF, INSTR_PRIM, INSTR_HALT
} InstrOp;
typedef struct { InstrOp op; int32_t arg; int arg2; } Instr;
Instr i_push_q16(int32_t x) { return (Instr){INSTR_PUSH_Q16, x, 0}; }
Instr i_push_bool(int x) { return (Instr){INSTR_PUSH_BOOL, x, 0}; }
Instr i_pop(void) { return (Instr){INSTR_POP, 0, 0}; }
Instr i_dup(void) { return (Instr){INSTR_DUP, 0, 0}; }
Instr i_swap(void) { return (Instr){INSTR_SWAP, 0, 0}; }
Instr i_load(int i) { return (Instr){INSTR_LOAD, i, 0}; }
Instr i_store(int i) { return (Instr){INSTR_STORE, i, 0}; }
Instr i_jump(int t) { return (Instr){INSTR_JUMP, t, 0}; }
Instr i_jump_if(int t) { return (Instr){INSTR_JUMP_IF, t, 0}; }
Instr i_prim(Prim p) { return (Instr){INSTR_PRIM, p, 0}; }
Instr i_halt(void) { return (Instr){INSTR_HALT, 0, 0}; }
/* ── Step ───────────────────────────────────────── */
int step(State *s, Instr *prog, int prog_len) {
if (s->halted) return -1;
if (s->pc < 0 || s->pc >= prog_len) { s->halted = 1; return 0; }
Instr instr = prog[s->pc];
s->pc++;
AvmVal a, b;
switch (instr.op) {
case INSTR_PUSH_Q16:
s->stack.data[s->stack.len++] = avm_q16(instr.arg);
break;
case INSTR_PUSH_BOOL:
s->stack.data[s->stack.len++] = avm_bool(instr.arg);
break;
case INSTR_POP: s->stack.len--; break;
case INSTR_DUP:
s->stack.data[s->stack.len] = s->stack.data[s->stack.len - 1];
s->stack.len++;
break;
case INSTR_SWAP: {
AvmVal t = s->stack.data[s->stack.len - 1];
s->stack.data[s->stack.len - 1] = s->stack.data[s->stack.len - 2];
s->stack.data[s->stack.len - 2] = t;
break;
}
case INSTR_LOAD:
s->stack.data[s->stack.len++] = s->locals.data[instr.arg];
break;
case INSTR_STORE:
s->locals.data[instr.arg] = s->stack.data[--s->stack.len];
break;
case INSTR_JUMP: s->pc = instr.arg; break;
case INSTR_JUMP_IF:
if (s->stack.data[--s->stack.len].val) s->pc = instr.arg;
break;
case INSTR_PRIM: {
int arity = (instr.arg == PRIM_NOT) ? 1 : 2;
if (arity == 2) b = s->stack.data[--s->stack.len];
a = s->stack.data[--s->stack.len];
switch (instr.arg) {
case PRIM_ADD_Q16:
s->stack.data[s->stack.len++] = avm_q16(a.val + b.val);
break;
case PRIM_SUB_Q16:
s->stack.data[s->stack.len++] = avm_q16(a.val - b.val);
break;
case PRIM_MUL_Q16:
s->stack.data[s->stack.len++] = avm_q16(q16_mul(a.val, b.val));
break;
case PRIM_DIV_Q16:
s->stack.data[s->stack.len++] = avm_q16(q16_div(a.val, b.val));
break;
case PRIM_LT_Q16:
s->stack.data[s->stack.len++] = avm_bool(a.val < b.val);
break;
case PRIM_EQ_Q16:
s->stack.data[s->stack.len++] = avm_bool(a.val == b.val);
break;
case PRIM_AND:
s->stack.data[s->stack.len++] = avm_bool(a.val && b.val);
break;
case PRIM_OR:
s->stack.data[s->stack.len++] = avm_bool(a.val || b.val);
break;
case PRIM_NOT:
s->stack.data[s->stack.len++] = avm_bool(!a.val);
break;
}
break;
}
case INSTR_HALT: s->halted = 1; break;
}
return 0;
}
int run(State *s, Instr *prog, int prog_len, int fuel) {
for (int i = 0; i < fuel && !s->halted; i++)
if (step(s, prog, prog_len)) return -1;
return 0;
}

7
coq/AVMIsa/.avm.aux Normal file
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@ -0,0 +1,7 @@
COQAUX1 3a6af8bd9f0880063607a37ee751b817 /home/allaun/SilverSight/coq/AVMIsa/avm.v
0 0 VernacProof "tac:no using:no"
4413 4417 proof_build_time "0.001"
0 0 step_halted "0.001"
4376 4412 context_used ""
4413 4417 proof_check_time "0.001"
0 0 vo_compile_time "0.141"

62
coq/AVMIsa/.q16_16.aux Normal file
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@ -0,0 +1,62 @@
COQAUX1 674cb8319be2cff2e3564b20efcaccb5 /home/allaun/SilverSight/coq/AVMIsa/q16_16.v
0 0 VernacProof "tac:no using:no"
164 168 proof_build_time "0.002"
0 0 le_neg2147483648_2147483647 "0.002"
159 163 context_used ""
164 168 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
226 230 proof_build_time "0.000"
0 0 le_0_2147483647 "0.000"
221 225 context_used ""
226 230 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
292 296 proof_build_time "0.000"
0 0 le_neg2147483648_0 "0.000"
287 291 context_used ""
292 296 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
373 377 proof_build_time "0.000"
0 0 le_2147483647_2147483647 "0.000"
368 372 context_used ""
373 377 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
1220 1224 proof_build_time "0.002"
0 0 clamp_bounded "0.002"
1183 1217 context_used ""
1220 1224 proof_check_time "0.001"
0 0 VernacProof "tac:no using:no"
1560 1564 proof_build_time "0.001"
0 0 clamp_idempotent "0.001"
1545 1557 context_used ""
1560 1564 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2259 2263 proof_build_time "0.000"
0 0 add_comm "0.000"
2214 2258 context_used ""
2259 2263 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2445 2449 proof_build_time "0.000"
0 0 add_in_range "0.000"
2396 2442 context_used ""
2445 2449 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2708 2712 proof_build_time "0.001"
0 0 sub_self "0.001"
2647 2705 context_used ""
2708 2712 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2818 2822 proof_build_time "0.000"
0 0 mul_comm "0.000"
2773 2817 context_used ""
2818 2822 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2973 2977 proof_build_time "0.000"
0 0 in_range_zero "0.000"
2914 2972 context_used ""
2973 2977 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
3127 3131 proof_build_time "0.000"
0 0 in_range_one "0.000"
3068 3126 context_used ""
3127 3131 proof_check_time "0.000"
0 0 vo_compile_time "0.143"

446
coq/AVMIsa/avm.glob Normal file
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@ -0,0 +1,446 @@
DIGEST 3a6af8bd9f0880063607a37ee751b817
Favm
R54:59 Stdlib.ZArith.ZArith <> <> lib
R61:64 Stdlib.Lists.List <> <> lib
mod 101:103 <> AVM
def 119:127 AVM q16_scale
R131:131 Corelib.Numbers.BinNums <> Z ind
ind 156:160 AVM AvmTy
constr 171:175 AVM Q0_16
constr 179:184 AVM Q16_16
constr 188:191 AVM Bool
scheme 156:160 AVM AvmTy_rect
scheme 156:160 AVM AvmTy_ind
scheme 156:160 AVM AvmTy_rec
scheme 156:160 AVM AvmTy_sind
ind 207:212 AVM AvmVal
constr 223:225 AVM Vq0
constr 237:240 AVM Vq16
constr 252:256 AVM Vbool
R232:232 Corelib.Numbers.BinNums <> Z ind
binder 228:228 <> x:5
R247:247 Corelib.Numbers.BinNums <> Z ind
binder 243:243 <> x:6
R263:266 Corelib.Init.Datatypes <> bool ind
binder 259:259 <> b:7
scheme 207:212 AVM AvmVal_rect
scheme 207:212 AVM AvmVal_ind
scheme 207:212 AVM AvmVal_rec
scheme 207:212 AVM AvmVal_sind
ind 283:286 AVM Prim
constr 301:306 AVM AddQ16
constr 310:315 AVM SubQ16
constr 319:324 AVM MulQ16
constr 328:333 AVM DivQ16
constr 337:341 AVM LtQ16
constr 345:349 AVM EqQ16
constr 353:355 AVM And
constr 359:360 AVM Or
constr 364:366 AVM Not
scheme 283:286 AVM Prim_rect
scheme 283:286 AVM Prim_ind
scheme 283:286 AVM Prim_rec
scheme 283:286 AVM Prim_sind
ind 382:386 AVM Instr
constr 401:408 AVM Push_q16
constr 420:428 AVM Push_bool
constr 443:445 AVM Pop
constr 449:451 AVM Dup
constr 455:458 AVM Swap
constr 464:467 AVM Load
constr 481:485 AVM Store
constr 499:502 AVM Jump
constr 516:522 AVM Jump_if
constr 538:544 AVM Prim_op
constr 559:562 AVM Halt
R415:415 Corelib.Numbers.BinNums <> Z ind
binder 411:411 <> x:12
R435:438 Corelib.Init.Datatypes <> bool ind
binder 431:431 <> b:13
R474:476 Corelib.Init.Datatypes <> nat ind
binder 470:470 <> i:14
R492:494 Corelib.Init.Datatypes <> nat ind
binder 488:488 <> i:15
R509:511 Corelib.Init.Datatypes <> nat ind
binder 505:505 <> t:16
R529:531 Corelib.Init.Datatypes <> nat ind
binder 525:525 <> t:17
R551:554 avm AVM Prim ind
binder 547:547 <> p:18
scheme 382:386 AVM Instr_rect
scheme 382:386 AVM Instr_ind
scheme 382:386 AVM Instr_rec
scheme 382:386 AVM Instr_sind
rec 575:579 AVM State
proj 604:605 AVM pc
proj 614:618 AVM stack
proj 635:640 AVM locals
proj 666:671 AVM halted
R609:611 Corelib.Init.Datatypes <> nat ind
R622:625 Corelib.Init.Datatypes <> list ind
R627:632 avm AVM AvmVal ind
R644:647 Corelib.Init.Datatypes <> list ind
R650:655 Corelib.Init.Datatypes <> option ind
R657:662 avm AVM AvmVal ind
R675:678 Corelib.Init.Datatypes <> bool ind
def 699:709 AVM empty_state
R713:717 avm AVM State rec
R722:728 avm AVM mkState constr
R732:734 Corelib.Init.Datatypes <> nil constr
R736:738 Corelib.Init.Datatypes <> nil constr
R740:744 Corelib.Init.Datatypes <> false constr
def 761:769 AVM get_local
R776:780 avm AVM State rec
binder 772:772 <> s:24
R788:790 Corelib.Init.Datatypes <> nat ind
binder 784:784 <> i:25
R795:800 Corelib.Init.Datatypes <> option ind
R802:807 avm AVM AvmVal ind
R822:835 Stdlib.Lists.List <> nth_error def
R848:848 avm <> i:25 var
R840:845 avm AVM locals proj
R837:837 avm <> s:24 var
R861:864 Corelib.Init.Datatypes <> Some constr
R867:870 Corelib.Init.Datatypes <> Some constr
R878:881 Corelib.Init.Datatypes <> Some constr
R892:895 Corelib.Init.Datatypes <> None constr
def 920:926 AVM q16_mul
R935:935 Corelib.Numbers.BinNums <> Z ind
binder 929:929 <> a:26
binder 931:931 <> b:27
R940:940 Corelib.Numbers.BinNums <> Z ind
R945:949 Stdlib.ZArith.BinInt Z div def
R953:955 Stdlib.ZArith.BinInt <> ::Z_scope:x_'*'_x not
R952:952 avm <> a:26 var
R956:956 avm <> b:27 var
R959:967 avm AVM q16_scale def
def 983:989 AVM q16_div
R998:998 Corelib.Numbers.BinNums <> Z ind
binder 992:992 <> a:28
binder 994:994 <> b:29
R1003:1003 Corelib.Numbers.BinNums <> Z ind
R1015:1019 Stdlib.ZArith.BinInt Z eqb def
R1021:1021 avm <> b:29 var
R1045:1049 Stdlib.ZArith.BinInt Z div def
R1053:1055 Stdlib.ZArith.BinInt <> ::Z_scope:x_'*'_x not
R1052:1052 avm <> a:28 var
R1056:1064 avm AVM q16_scale def
R1067:1067 avm <> b:29 var
R1030:1038 avm AVM q16_scale def
def 1084:1092 AVM exec_prim
R1099:1102 avm AVM Prim ind
binder 1095:1095 <> p:30
R1112:1117 Corelib.Init.Datatypes <> option ind
R1119:1124 avm AVM AvmVal ind
binder 1106:1106 <> a:31
binder 1108:1108 <> b:32
R1129:1134 Corelib.Init.Datatypes <> option ind
R1136:1141 avm AVM AvmVal ind
R1162:1162 avm <> b:32 var
R1159:1159 avm <> a:31 var
R1156:1156 avm <> p:30 var
R1175:1180 avm AVM AddQ16 constr
R1183:1186 Corelib.Init.Datatypes <> Some constr
R1189:1192 avm AVM Vq16 constr
R1198:1201 Corelib.Init.Datatypes <> Some constr
R1204:1207 avm AVM Vq16 constr
R1215:1218 Corelib.Init.Datatypes <> Some constr
R1221:1224 avm AVM Vq16 constr
R1228:1230 Stdlib.ZArith.BinInt <> ::Z_scope:x_'+'_x not
R1241:1246 avm AVM SubQ16 constr
R1249:1252 Corelib.Init.Datatypes <> Some constr
R1255:1258 avm AVM Vq16 constr
R1264:1267 Corelib.Init.Datatypes <> Some constr
R1270:1273 avm AVM Vq16 constr
R1281:1284 Corelib.Init.Datatypes <> Some constr
R1287:1290 avm AVM Vq16 constr
R1294:1296 Stdlib.ZArith.BinInt <> ::Z_scope:x_'-'_x not
R1307:1312 avm AVM MulQ16 constr
R1315:1318 Corelib.Init.Datatypes <> Some constr
R1321:1324 avm AVM Vq16 constr
R1330:1333 Corelib.Init.Datatypes <> Some constr
R1336:1339 avm AVM Vq16 constr
R1347:1350 Corelib.Init.Datatypes <> Some constr
R1353:1356 avm AVM Vq16 constr
R1359:1365 avm AVM q16_mul def
R1379:1384 avm AVM DivQ16 constr
R1387:1390 Corelib.Init.Datatypes <> Some constr
R1393:1396 avm AVM Vq16 constr
R1402:1405 Corelib.Init.Datatypes <> Some constr
R1408:1411 avm AVM Vq16 constr
R1419:1422 Corelib.Init.Datatypes <> Some constr
R1425:1428 avm AVM Vq16 constr
R1431:1437 avm AVM q16_div def
R1451:1455 avm AVM LtQ16 constr
R1458:1461 Corelib.Init.Datatypes <> Some constr
R1464:1467 avm AVM Vq16 constr
R1473:1476 Corelib.Init.Datatypes <> Some constr
R1479:1482 avm AVM Vq16 constr
R1490:1493 Corelib.Init.Datatypes <> Some constr
R1496:1500 avm AVM Vbool constr
R1503:1507 Stdlib.ZArith.BinInt Z ltb def
R1521:1525 avm AVM EqQ16 constr
R1528:1531 Corelib.Init.Datatypes <> Some constr
R1534:1537 avm AVM Vq16 constr
R1543:1546 Corelib.Init.Datatypes <> Some constr
R1549:1552 avm AVM Vq16 constr
R1560:1563 Corelib.Init.Datatypes <> Some constr
R1566:1570 avm AVM Vbool constr
R1573:1577 Stdlib.ZArith.BinInt Z eqb def
R1591:1593 avm AVM And constr
R1596:1599 Corelib.Init.Datatypes <> Some constr
R1602:1606 avm AVM Vbool constr
R1612:1615 Corelib.Init.Datatypes <> Some constr
R1618:1622 avm AVM Vbool constr
R1630:1633 Corelib.Init.Datatypes <> Some constr
R1636:1640 avm AVM Vbool constr
R1644:1647 Corelib.Init.Datatypes <> ::bool_scope:x_'&&'_x not
R1658:1659 avm AVM Or constr
R1662:1665 Corelib.Init.Datatypes <> Some constr
R1668:1672 avm AVM Vbool constr
R1678:1681 Corelib.Init.Datatypes <> Some constr
R1684:1688 avm AVM Vbool constr
R1696:1699 Corelib.Init.Datatypes <> Some constr
R1702:1706 avm AVM Vbool constr
R1710:1713 Corelib.Init.Datatypes <> ::bool_scope:x_'||'_x not
R1724:1726 avm AVM Not constr
R1729:1732 Corelib.Init.Datatypes <> Some constr
R1735:1739 avm AVM Vbool constr
R1745:1748 Corelib.Init.Datatypes <> None constr
R1753:1756 Corelib.Init.Datatypes <> Some constr
R1759:1763 avm AVM Vbool constr
R1766:1769 Corelib.Init.Datatypes <> negb def
R1792:1795 Corelib.Init.Datatypes <> None constr
def 1820:1823 AVM step
R1830:1834 avm AVM State rec
binder 1826:1826 <> s:36
R1845:1848 Corelib.Init.Datatypes <> list ind
R1850:1854 avm AVM Instr ind
binder 1838:1841 <> prog:37
R1859:1864 Corelib.Init.Datatypes <> option ind
R1866:1870 avm AVM State rec
R1885:1890 avm AVM halted proj
R1882:1882 avm <> s:36 var
R1918:1931 Stdlib.Lists.List <> nth_error def
R1941:1942 avm AVM pc proj
R1938:1938 avm <> s:36 var
R1933:1936 avm <> prog:37 var
R1956:1959 Corelib.Init.Datatypes <> None constr
R1964:1967 Corelib.Init.Datatypes <> Some constr
R1970:1976 avm AVM mkState constr
R1981:1982 avm AVM pc proj
R1978:1978 avm <> s:36 var
R1988:1992 avm AVM stack proj
R1985:1985 avm <> s:36 var
R1998:2003 avm AVM locals proj
R1995:1995 avm <> s:36 var
R2006:2009 Corelib.Init.Datatypes <> true constr
R2018:2021 Corelib.Init.Datatypes <> Some constr
R2052:2052 Corelib.Init.Datatypes <> S constr
R2057:2058 avm AVM pc proj
R2054:2054 avm <> s:36 var
binder 2042:2047 <> new_pc:38
binder 2079:2079 <> v:39
R2084:2087 Corelib.Init.Datatypes <> Some constr
R2090:2096 avm AVM mkState constr
R2098:2103 avm <> new_pc:38 var
R2107:2110 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2106:2106 avm <> v:39 var
R2114:2118 avm AVM stack proj
R2111:2111 avm <> s:36 var
R2125:2130 avm AVM locals proj
R2122:2122 avm <> s:36 var
R2133:2137 Corelib.Init.Datatypes <> false constr
binder 2074:2077 <> push:40
R2174:2181 avm AVM Push_q16 constr
R2188:2191 avm <> push:40 var
R2194:2197 avm AVM Vq16 constr
R2210:2218 avm AVM Push_bool constr
R2225:2228 avm <> push:40 var
R2231:2235 avm AVM Vbool constr
R2248:2250 avm AVM Pop constr
R2272:2276 avm AVM stack proj
R2269:2269 avm <> s:36 var
R2295:2298 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2307:2310 Corelib.Init.Datatypes <> Some constr
R2313:2319 avm AVM mkState constr
R2321:2326 avm <> new_pc:38 var
R2336:2341 avm AVM locals proj
R2333:2333 avm <> s:36 var
R2344:2348 Corelib.Init.Datatypes <> false constr
R2361:2363 Corelib.Init.Datatypes <> nil constr
R2368:2371 Corelib.Init.Datatypes <> None constr
R2393:2395 avm AVM Dup constr
R2417:2421 avm AVM stack proj
R2414:2414 avm <> s:36 var
R2440:2443 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2449:2452 avm <> push:40 var
R2458:2460 Corelib.Init.Datatypes <> nil constr
R2465:2468 Corelib.Init.Datatypes <> None constr
R2490:2493 avm AVM Swap constr
R2515:2519 avm AVM stack proj
R2512:2512 avm <> s:36 var
R2538:2541 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2543:2546 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2555:2558 Corelib.Init.Datatypes <> Some constr
R2561:2567 avm AVM mkState constr
R2569:2574 avm <> new_pc:38 var
R2578:2581 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2583:2586 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2596:2601 avm AVM locals proj
R2593:2593 avm <> s:36 var
R2604:2608 Corelib.Init.Datatypes <> false constr
R2626:2629 Corelib.Init.Datatypes <> None constr
R2651:2654 avm AVM Load constr
R2675:2683 avm AVM get_local def
R2685:2685 avm <> s:36 var
R2704:2707 Corelib.Init.Datatypes <> Some constr
R2714:2717 avm <> push:40 var
R2723:2726 Corelib.Init.Datatypes <> None constr
R2731:2734 Corelib.Init.Datatypes <> None constr
R2756:2760 avm AVM Store constr
R2784:2788 avm AVM stack proj
R2781:2781 avm <> s:36 var
R2807:2810 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2829:2832 Corelib.Init.Datatypes <> Some constr
R2835:2841 avm AVM mkState constr
R2843:2848 avm <> new_pc:38 var
R2892:2895 Corelib.Init.Datatypes <> ::list_scope:x_'++'_x not
R2868:2878 Stdlib.Lists.List <> firstn abbrev
R2885:2890 avm AVM locals proj
R2882:2882 avm <> s:36 var
R2902:2905 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R2896:2899 Corelib.Init.Datatypes <> Some constr
R2906:2915 Stdlib.Lists.List <> skipn abbrev
R2926:2931 avm AVM locals proj
R2923:2923 avm <> s:36 var
R2918:2918 Corelib.Init.Datatypes <> S constr
R2935:2939 Corelib.Init.Datatypes <> false constr
R2952:2954 Corelib.Init.Datatypes <> nil constr
R2959:2962 Corelib.Init.Datatypes <> None constr
R2984:2987 avm AVM Jump constr
R2994:2997 Corelib.Init.Datatypes <> Some constr
R3000:3006 avm AVM mkState constr
R3013:3017 avm AVM stack proj
R3010:3010 avm <> s:36 var
R3023:3028 avm AVM locals proj
R3020:3020 avm <> s:36 var
R3031:3035 Corelib.Init.Datatypes <> false constr
R3046:3052 avm AVM Jump_if constr
R3076:3080 avm AVM stack proj
R3073:3073 avm <> s:36 var
R3108:3111 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3098:3102 avm AVM Vbool constr
R3104:3107 Corelib.Init.Datatypes <> true constr
R3120:3123 Corelib.Init.Datatypes <> Some constr
R3126:3132 avm AVM mkState constr
R3144:3149 avm AVM locals proj
R3141:3141 avm <> s:36 var
R3152:3156 Corelib.Init.Datatypes <> false constr
R3180:3183 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3169:3173 avm AVM Vbool constr
R3175:3179 Corelib.Init.Datatypes <> false constr
R3192:3195 Corelib.Init.Datatypes <> Some constr
R3198:3204 avm AVM mkState constr
R3206:3211 avm <> new_pc:38 var
R3221:3226 avm AVM locals proj
R3218:3218 avm <> s:36 var
R3229:3233 Corelib.Init.Datatypes <> false constr
R3247:3250 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3256:3259 Corelib.Init.Datatypes <> None constr
R3263:3265 Corelib.Init.Datatypes <> nil constr
R3270:3273 Corelib.Init.Datatypes <> None constr
R3295:3301 avm AVM Prim_op constr
R3340:3342 avm AVM Not constr
R3366:3370 avm AVM stack proj
R3363:3363 avm <> s:36 var
R3391:3394 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3421:3429 avm AVM exec_prim def
R3434:3437 Corelib.Init.Datatypes <> Some constr
R3442:3445 Corelib.Init.Datatypes <> None constr
R3466:3469 Corelib.Init.Datatypes <> Some constr
R3476:3479 Corelib.Init.Datatypes <> Some constr
R3482:3488 avm AVM mkState constr
R3490:3495 avm <> new_pc:38 var
R3499:3502 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3512:3517 avm AVM locals proj
R3509:3509 avm <> s:36 var
R3520:3524 Corelib.Init.Datatypes <> false constr
R3541:3544 Corelib.Init.Datatypes <> None constr
R3549:3552 Corelib.Init.Datatypes <> None constr
R3582:3584 Corelib.Init.Datatypes <> nil constr
R3589:3592 Corelib.Init.Datatypes <> None constr
R3642:3646 avm AVM stack proj
R3639:3639 avm <> s:36 var
R3667:3670 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3672:3675 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3702:3710 avm AVM exec_prim def
R3715:3718 Corelib.Init.Datatypes <> Some constr
R3724:3727 Corelib.Init.Datatypes <> Some constr
R3751:3754 Corelib.Init.Datatypes <> Some constr
R3761:3764 Corelib.Init.Datatypes <> Some constr
R3767:3773 avm AVM mkState constr
R3775:3780 avm <> new_pc:38 var
R3784:3787 Corelib.Init.Datatypes <> ::list_scope:x_'::'_x not
R3797:3802 avm AVM locals proj
R3794:3794 avm <> s:36 var
R3805:3809 Corelib.Init.Datatypes <> false constr
R3826:3829 Corelib.Init.Datatypes <> None constr
R3834:3837 Corelib.Init.Datatypes <> None constr
R3872:3875 Corelib.Init.Datatypes <> None constr
R3912:3915 avm AVM Halt constr
R3920:3923 Corelib.Init.Datatypes <> Some constr
R3926:3932 avm AVM mkState constr
R3937:3938 avm AVM pc proj
R3934:3934 avm <> s:36 var
R3944:3948 avm AVM stack proj
R3941:3941 avm <> s:36 var
R3954:3959 avm AVM locals proj
R3951:3951 avm <> s:36 var
R3962:3965 Corelib.Init.Datatypes <> true constr
R1898:1901 Corelib.Init.Datatypes <> None constr
def 3999:4001 AVM run
R4008:4012 avm AVM State rec
binder 4004:4004 <> s:43
R4023:4026 Corelib.Init.Datatypes <> list ind
R4028:4032 avm AVM Instr ind
binder 4016:4019 <> prog:44
R4043:4045 Corelib.Init.Datatypes <> nat ind
binder 4036:4039 <> fuel:45
R4064:4069 Corelib.Init.Datatypes <> option ind
R4071:4075 avm AVM State rec
R4090:4093 avm <> fuel:45 var
R4106:4106 Corelib.Init.Datatypes <> O constr
R4111:4114 Corelib.Init.Datatypes <> Some constr
R4116:4116 avm <> s:43 var
R4124:4124 Corelib.Init.Datatypes <> S constr
R4143:4148 avm AVM halted proj
R4140:4140 avm <> s:43 var
R4180:4183 avm AVM step def
R4185:4185 avm <> s:43 var
R4187:4190 avm <> prog:44 var
R4205:4208 Corelib.Init.Datatypes <> None constr
R4213:4216 Corelib.Init.Datatypes <> None constr
R4220:4223 Corelib.Init.Datatypes <> Some constr
R4231:4233 avm <> run:46 def
R4238:4241 avm <> prog:44 var
R4156:4159 Corelib.Init.Datatypes <> Some constr
R4161:4161 avm <> s:43 var
prf 4273:4283 AVM step_halted
R4290:4294 avm AVM State rec
binder 4286:4286 <> s:48
R4305:4308 Corelib.Init.Datatypes <> list ind
R4310:4314 avm AVM Instr ind
binder 4298:4301 <> prog:49
R4332:4334 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R4325:4330 avm AVM halted proj
R4322:4322 avm <> s:48 var
R4335:4338 Corelib.Init.Datatypes <> true constr
binder 4318:4318 <> h:50
R4358:4360 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R4347:4350 avm AVM step def
R4352:4352 avm <> s:48 var
R4354:4357 avm <> prog:49 var
R4361:4364 Corelib.Init.Datatypes <> None constr
R4383:4386 avm AVM step def
R4423:4425 avm AVM <> mod

275
coq/AVMIsa/avm.v
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@ -1,165 +1,130 @@
(* AVM ISA v1 — Coq Port (Strict Functional Execution) (* AVM ISA v1 — Coq Formalization *)
Mirrors formal/SilverSight/AVMIsa/Step.lean *) Require Import ZArith List.
Local Open Scope Z_scope.
Require Import ZArith. Module AVM.
Require Import List. Definition q16_scale : Z := 65536.
Import ListNotations.
(* ── Constants ──────────────────────────────────────────────────── *) Inductive AvmTy : Set := Q0_16 | Q16_16 | Bool.
Definition AVM_CLAMP_MIN : Z := -2147483647.
Definition AVM_CLAMP_MAX : Z := 2147483647.
Definition AVM_Q0_MIN : Z := -32767.
Definition AVM_Q0_MAX : Z := 32767.
Definition Q16_SCALE : Z := 65536.
Definition avm_clamp (x : Z) : Z := Inductive AvmVal : Set := Vq0 (x : Z) | Vq16 (x : Z) | Vbool (b : bool).
Z.min AVM_CLAMP_MAX (Z.max AVM_CLAMP_MIN x).
Definition avm_q0_clamp (x : Z) : Z := Inductive Prim : Set :=
Z.min AVM_Q0_MAX (Z.max AVM_Q0_MIN x). AddQ16 | SubQ16 | MulQ16 | DivQ16 | LtQ16 | EqQ16 | And | Or | Not.
Definition lt_q16_v6 (a b : Z) : bool := Inductive Instr : Set :=
let sa := a <? 0 in Push_q16 (x : Z) | Push_bool (b : bool) | Pop | Dup | Swap
let sb := b <? 0 in | Load (i : nat) | Store (i : nat) | Jump (t : nat) | Jump_if (t : nat)
if Bool.eqb sa sb then a <? b else sa. | Prim_op (p : Prim) | Halt.
(* ── Types ──────────────────────────────────────────────────────── *) Record State : Set := mkState {
Inductive AvmTy : Type := pc : nat; stack : list AvmVal; locals : list (option AvmVal); halted : bool
| Q0_16 | Q16_16 | Bool. }.
(* ── Values ──────────────────────────────────────────────────────── *) Definition empty_state : State := mkState 0 nil nil false.
Inductive AvmVal : Type :=
| Vq0 : Z -> AvmVal
| Vq16 : Z -> AvmVal
| Vbool : bool -> AvmVal.
(* ── Primitives ──────────────────────────────────────────────────── *) Definition get_local (s : State) (i : nat) : option AvmVal :=
Inductive Prim : Type := match List.nth_error s.(locals) i with
| AddSatQ0 | SubSatQ0 | Some (Some v) => Some v | _ => None
| AddSatQ16 | SubSatQ16 | MulSatQ16 | DivSatQ16
| LtQ16 | EqQ16
| And | Or | Not.
(* ── Instructions ────────────────────────────────────────────────── *)
Inductive Instr : Type :=
| PushQ16 (x : Z) | PushBool (b : bool) | PushQ0 (x : Z)
| Pop | Dup | Swap
| Load (i : nat) | Store (i : nat)
| Jump (t : nat) | JumpIf (t : nat)
| Primitive (p : Prim)
| Halt.
(* ── State ───────────────────────────────────────────────────────── *)
Definition Local := option AvmVal.
Record State : Type := mkState {
pc : nat;
stack : list AvmVal;
locals : list Local;
halted : bool
}.
Definition init_state (n : nat) : State :=
mkState 0 [] (repeat None n) false.
(* ── Primitive execution ────────────────────────────────────────── *)
Definition div_floor (a b : Z) : Z :=
if b =? 0 then 0 else
let q := a / b in
let r := a mod b in
if (r <? 0) && (b <? 0) then q + 1
else if (r >? 0) && (b <? 0) then q - 1
else if (r <? 0) && (b >? 0) then q - 1
else q.
Definition exec_prim (p : Prim) (a b : AvmVal) : AvmVal :=
match p, a, b with
| AddSatQ0, Vq0 x, Vq0 y => Vq0 (avm_q0_clamp (x + y))
| SubSatQ0, Vq0 x, Vq0 y => Vq0 (avm_q0_clamp (x - y))
| AddSatQ16, Vq16 x, Vq16 y => Vq16 (avm_clamp (x + y))
| SubSatQ16, Vq16 x, Vq16 y => Vq16 (avm_clamp (x - y))
| MulSatQ16, Vq16 x, Vq16 y => Vq16 (avm_clamp (div_floor (x * y) Q16_SCALE))
| DivSatQ16, Vq16 x, Vq16 y => Vq16 (avm_clamp (div_floor (x * Q16_SCALE) y))
| LtQ16, Vq16 x, Vq16 y => Vbool (lt_q16_v6 x y)
| EqQ16, Vq16 x, Vq16 y => Vbool (x =? y)
| And, Vbool x, Vbool y => Vbool (x && y)
| Or, Vbool x, Vbool y => Vbool (x || y)
| Not, Vbool x, _ => Vbool (negb x)
| _, _, _ => Vbool false
end.
(* ── Step ────────────────────────────────────────────────────────── *)
Definition step (s : State) (prog : list Instr) : option State :=
if halted s then None else
if Nat.leb (length prog) (pc s) then
Some (mkState (pc s) (stack s) (locals s) true)
else
let instr := nth (pc s) prog Halt in
let stk := stack s in
let loc := locals s in
let npc := S (pc s) in
match instr with
| PushQ16 x => Some (mkState npc (Vq16 (avm_clamp x) :: stk) loc false)
| PushBool b => Some (mkState npc (Vbool b :: stk) loc false)
| PushQ0 x => Some (mkState npc (Vq0 (avm_q0_clamp x) :: stk) loc false)
| Pop => match stk with
| [] => None
| _ :: xs => Some (mkState npc xs loc false)
end
| Dup => match stk with
| [] => None
| x :: xs => Some (mkState npc (x :: x :: xs) loc false)
end
| Swap => match stk with
| a :: b :: xs => Some (mkState npc (b :: a :: xs) loc false)
| _ => None
end
| Load i =>
match nth_error loc i with
| None => None
| Some None => None
| Some (Some v) => Some (mkState npc (v :: stk) loc false)
end
| Store i =>
match stk with
| [] => None
| v :: xs =>
if Nat.leb (length loc) i then None
else
let new_loc := set_nth loc i (Some v) in
Some (mkState npc xs new_loc false)
end
| Jump t =>
if Nat.leb (length prog) t then None
else Some (mkState t stk loc false)
| JumpIf t =>
match stk with
| Vbool true :: xs =>
if Nat.leb (length prog) t then None
else Some (mkState t xs loc false)
| Vbool false :: xs => Some (mkState npc xs loc false)
| _ => None
end
| Primitive p =>
let arity := if p = Not then 1 else 2 in
match stk with
| a :: xs when arity = 1 =>
Some (mkState npc (exec_prim p a a :: xs) loc false)
| b :: a :: xs when arity = 2 =>
Some (mkState npc (exec_prim p a b :: xs) loc false)
| _ => None
end
| Halt => Some (mkState (pc s) stk loc true)
end. end.
(* ── Run (fuel-bounded) ─────────────────────────────────────────── *) Definition q16_mul (a b : Z) : Z := Z.div (a * b) q16_scale.
Fixpoint run (s : State) (prog : list Instr) (fuel : nat) : option State := Definition q16_div (a b : Z) : Z :=
match fuel with if Z.eqb b 0 then q16_scale else Z.div (a * q16_scale) b.
| O => Some s
| S n => Definition exec_prim (p : Prim) (a b : option AvmVal) : option AvmVal :=
if halted s then Some s match p, a, b with
else match step s prog with | AddQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (x + y))
| None => None | SubQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (x - y))
| Some s' => run s' prog n | MulQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (q16_mul x y))
end | DivQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (q16_div x y))
end. | LtQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vbool (Z.ltb x y))
| EqQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vbool (Z.eqb x y))
| And, Some (Vbool x), Some (Vbool y) => Some (Vbool (x && y))
| Or, Some (Vbool x), Some (Vbool y) => Some (Vbool (x || y))
| Not, Some (Vbool x), None => Some (Vbool (negb x))
| _, _, _ => None
end.
Definition step (s : State) (prog : list Instr) : option State :=
if s.(halted) then None else
match List.nth_error prog s.(pc) with
| None => Some (mkState s.(pc) s.(stack) s.(locals) true)
| Some instr =>
let new_pc := S s.(pc) in
let push v := Some (mkState new_pc (v :: s.(stack)) s.(locals) false) in
match instr with
| Push_q16 x => push (Vq16 x)
| Push_bool x => push (Vbool x)
| Pop =>
match s.(stack) with
| _ :: rest => Some (mkState new_pc rest s.(locals) false)
| nil => None
end
| Dup =>
match s.(stack) with
| v :: _ => push v | nil => None
end
| Swap =>
match s.(stack) with
| a :: b :: rest => Some (mkState new_pc (b :: a :: rest) s.(locals) false)
| _ => None
end
| Load i =>
match get_local s i with
| Some v => push v | None => None
end
| Store i =>
match s.(stack) with
| v :: rest =>
Some (mkState new_pc rest
(List.firstn i s.(locals) ++ Some v :: List.skipn (S i) s.(locals)) false)
| nil => None
end
| Jump t => Some (mkState t s.(stack) s.(locals) false)
| Jump_if t =>
match s.(stack) with
| Vbool true :: rest => Some (mkState t rest s.(locals) false)
| Vbool false :: rest => Some (mkState new_pc rest s.(locals) false)
| _ :: _ => None | nil => None
end
| Prim_op p =>
(match p with
| Not =>
match s.(stack) with
| a :: rest =>
match exec_prim p (Some a) None with
| Some v => Some (mkState new_pc (v :: rest) s.(locals) false)
| None => None
end
| nil => None
end
| _ =>
match s.(stack) with
| a :: b :: rest =>
match exec_prim p (Some a) (Some b) with
| Some v => Some (mkState new_pc (v :: rest) s.(locals) false)
| None => None
end
| _ => None
end
end)
| Halt => Some (mkState s.(pc) s.(stack) s.(locals) true)
end
end.
Fixpoint run (s : State) (prog : list Instr) (fuel : nat) {struct fuel} : option State :=
match fuel with
| O => Some s
| S k =>
if s.(halted) then Some s else
match step s prog with
| None => None | Some s' => run s' prog k
end
end.
Lemma step_halted (s : State) (prog : list Instr) (h : s.(halted) = true) :
step s prog = None.
Proof. unfold step; rewrite h; reflexivity. Qed.
End AVM.

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coq/AVMIsa/q16_16.glob Normal file
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@ -0,0 +1,263 @@
DIGEST 674cb8319be2cff2e3564b20efcaccb5
Fq16_16
R72:77 Stdlib.ZArith.ZArith <> <> lib
R79:81 Stdlib.micromega.Lia <> <> lib
prf 91:117 <> le_neg2147483648_2147483647
R133:136 Stdlib.ZArith.BinInt <> ::Z_scope:x_'<='_x not
prf 175:189 <> le_0_2147483647
R195:198 Stdlib.ZArith.BinInt <> ::Z_scope:x_'<='_x not
prf 237:254 <> le_neg2147483648_0
R270:273 Stdlib.ZArith.BinInt <> ::Z_scope:x_'<='_x not
prf 304:327 <> le_2147483647_2147483647
R342:345 Stdlib.ZArith.BinInt <> ::Z_scope:x_'<='_x not
mod 386:391 <> Q16_16
def 430:440 Q16_16 q16_min_raw
R444:444 Corelib.Numbers.BinNums <> Z ind
def 475:485 Q16_16 q16_max_raw
R489:489 Corelib.Numbers.BinNums <> Z ind
def 519:527 Q16_16 q16_scale
R532:532 Corelib.Numbers.BinNums <> Z ind
def 558:565 Q16_16 in_range
R572:572 Corelib.Numbers.BinNums <> Z ind
binder 568:568 <> x:1
R605:608 Corelib.Init.Logic <> ::type_scope:x_'/\'_x not
R600:603 Stdlib.ZArith.BinInt <> ::Z_scope:x_'<='_x not
R589:599 q16_16 Q16_16 q16_min_raw def
R604:604 q16_16 <> x:1 var
R610:613 Stdlib.ZArith.BinInt <> ::Z_scope:x_'<='_x not
R609:609 q16_16 <> x:1 var
R614:624 q16_16 Q16_16 q16_max_raw def
def 641:649 Q16_16 clamp_raw
R656:656 Corelib.Numbers.BinNums <> Z ind
binder 652:652 <> i:2
R661:661 Corelib.Numbers.BinNums <> Z ind
R673:680 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R694:694 q16_16 <> i:2 var
R682:692 q16_16 Q16_16 q16_max_raw def
R725:732 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R736:746 q16_16 Q16_16 q16_min_raw def
R734:734 q16_16 <> i:2 var
R774:774 q16_16 <> i:2 var
R753:763 q16_16 Q16_16 q16_min_raw def
R701:711 q16_16 Q16_16 q16_max_raw def
prf 788:800 Q16_16 clamp_bounded
R807:807 Corelib.Numbers.BinNums <> Z ind
binder 803:803 <> x:3
R812:819 q16_16 Q16_16 in_range def
R822:830 q16_16 Q16_16 clamp_raw def
R832:832 q16_16 <> x:3 var
R856:864 q16_16 Q16_16 clamp_raw def
R867:874 q16_16 Q16_16 in_range def
R887:894 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R896:906 q16_16 Q16_16 q16_max_raw def
R887:894 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R896:906 q16_16 Q16_16 q16_max_raw def
R936:946 q16_16 Q16_16 q16_min_raw def
R949:959 q16_16 Q16_16 q16_max_raw def
R976:1002 q16_16 <> le_neg2147483648_2147483647 thm
R1012:1020 Stdlib.ZArith.BinInt Z le_refl thm
R976:1002 q16_16 <> le_neg2147483648_2147483647 thm
R1012:1020 Stdlib.ZArith.BinInt Z le_refl thm
R1036:1043 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R1047:1057 q16_16 Q16_16 q16_min_raw def
R1036:1043 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R1047:1057 q16_16 Q16_16 q16_min_raw def
R1087:1097 q16_16 Q16_16 q16_min_raw def
R1100:1110 q16_16 Q16_16 q16_max_raw def
R1127:1135 Stdlib.ZArith.BinInt Z le_refl thm
R1145:1171 q16_16 <> le_neg2147483648_2147483647 thm
R1127:1135 Stdlib.ZArith.BinInt Z le_refl thm
R1145:1171 q16_16 <> le_neg2147483648_2147483647 thm
R1196:1203 Stdlib.ZArith.BinInt Z nlt_ge thm
R1196:1203 Stdlib.ZArith.BinInt Z nlt_ge thm
R1196:1203 Stdlib.ZArith.BinInt Z nlt_ge thm
prf 1236:1251 Q16_16 clamp_idempotent
R1258:1258 Corelib.Numbers.BinNums <> Z ind
binder 1254:1254 <> x:4
R1266:1273 q16_16 Q16_16 in_range def
R1275:1275 q16_16 <> x:4 var
binder 1262:1262 <> h:5
R1291:1293 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R1280:1288 q16_16 Q16_16 clamp_raw def
R1290:1290 q16_16 <> x:4 var
R1294:1294 q16_16 <> x:4 var
R1346:1354 q16_16 Q16_16 clamp_raw def
R1367:1374 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R1376:1386 q16_16 Q16_16 q16_max_raw def
R1421:1430 Stdlib.ZArith.Zorder <> Zlt_not_le thm
R1367:1374 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R1376:1386 q16_16 Q16_16 q16_max_raw def
R1421:1430 Stdlib.ZArith.Zorder <> Zlt_not_le thm
R1459:1466 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R1470:1480 q16_16 Q16_16 q16_min_raw def
R1513:1522 Stdlib.ZArith.Zorder <> Zlt_not_le thm
R1459:1466 Stdlib.ZArith.ZArith_dec <> Z_lt_dec def
R1470:1480 q16_16 Q16_16 q16_min_raw def
R1513:1522 Stdlib.ZArith.Zorder <> Zlt_not_le thm
def 1579:1582 Q16_16 zero
R1586:1586 Corelib.Numbers.BinNums <> Z ind
def 1607:1609 Q16_16 one
R1613:1613 Corelib.Numbers.BinNums <> Z ind
def 1638:1644 Q16_16 epsilon
R1648:1648 Corelib.Numbers.BinNums <> Z ind
def 1669:1672 Q16_16 half
R1676:1676 Corelib.Numbers.BinNums <> Z ind
def 1701:1704 Q16_16 pct1
R1710:1710 Corelib.Numbers.BinNums <> Z ind
def 1733:1737 Q16_16 pct70
R1742:1742 Corelib.Numbers.BinNums <> Z ind
def 1767:1771 Q16_16 pct30
R1776:1776 Corelib.Numbers.BinNums <> Z ind
def 1801:1805 Q16_16 one50
R1810:1810 Corelib.Numbers.BinNums <> Z ind
def 1836:1838 Q16_16 add
R1847:1847 Corelib.Numbers.BinNums <> Z ind
binder 1841:1841 <> a:6
binder 1843:1843 <> b:7
R1852:1852 Corelib.Numbers.BinNums <> Z ind
R1857:1865 q16_16 Q16_16 clamp_raw def
R1869:1871 Stdlib.ZArith.BinInt <> ::Z_scope:x_'+'_x not
R1868:1868 q16_16 <> a:6 var
R1872:1872 q16_16 <> b:7 var
def 1889:1891 Q16_16 sub
R1900:1900 Corelib.Numbers.BinNums <> Z ind
binder 1894:1894 <> a:8
binder 1896:1896 <> b:9
R1905:1905 Corelib.Numbers.BinNums <> Z ind
R1910:1918 q16_16 Q16_16 clamp_raw def
R1922:1924 Stdlib.ZArith.BinInt <> ::Z_scope:x_'-'_x not
R1921:1921 q16_16 <> a:8 var
R1925:1925 q16_16 <> b:9 var
def 1942:1944 Q16_16 neg
R1951:1951 Corelib.Numbers.BinNums <> Z ind
binder 1947:1947 <> a:10
R1956:1956 Corelib.Numbers.BinNums <> Z ind
R1961:1969 q16_16 Q16_16 clamp_raw def
R1972:1972 Stdlib.ZArith.BinInt <> ::Z_scope:'-'_x not
R1973:1973 q16_16 <> a:10 var
def 1990:1992 Q16_16 mul
R2001:2001 Corelib.Numbers.BinNums <> Z ind
binder 1995:1995 <> a:11
binder 1997:1997 <> b:12
R2006:2006 Corelib.Numbers.BinNums <> Z ind
R2011:2019 q16_16 Q16_16 clamp_raw def
R2022:2026 Stdlib.ZArith.BinInt Z div def
R2030:2032 Stdlib.ZArith.BinInt <> ::Z_scope:x_'*'_x not
R2029:2029 q16_16 <> a:11 var
R2033:2033 q16_16 <> b:12 var
R2036:2044 q16_16 Q16_16 q16_scale def
def 2061:2063 Q16_16 div
R2072:2072 Corelib.Numbers.BinNums <> Z ind
binder 2066:2066 <> a:13
binder 2068:2068 <> b:14
R2077:2077 Corelib.Numbers.BinNums <> Z ind
R2089:2096 Stdlib.ZArith.BinInt Z eq_dec def
R2098:2098 q16_16 <> b:14 var
R2117:2125 q16_16 Q16_16 clamp_raw def
R2128:2132 Stdlib.ZArith.BinInt Z div def
R2136:2138 Stdlib.ZArith.BinInt <> ::Z_scope:x_'*'_x not
R2135:2135 q16_16 <> a:13 var
R2139:2147 q16_16 Q16_16 q16_scale def
R2150:2150 q16_16 <> b:14 var
R2107:2110 q16_16 Q16_16 zero def
prf 2165:2172 Q16_16 add_comm
R2181:2181 Corelib.Numbers.BinNums <> Z ind
binder 2175:2175 <> a:15
binder 2177:2177 <> b:16
R2193:2195 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R2186:2188 q16_16 Q16_16 add def
R2190:2190 q16_16 <> a:15 var
R2192:2192 q16_16 <> b:16 var
R2196:2198 q16_16 Q16_16 add def
R2200:2200 q16_16 <> b:16 var
R2202:2202 q16_16 <> a:15 var
R2221:2223 q16_16 Q16_16 add def
R2234:2243 Stdlib.ZArith.BinInt Z add_comm thm
R2234:2243 Stdlib.ZArith.BinInt Z add_comm thm
R2234:2243 Stdlib.ZArith.BinInt Z add_comm thm
prf 2275:2286 Q16_16 add_in_range
R2295:2295 Corelib.Numbers.BinNums <> Z ind
binder 2289:2289 <> a:17
binder 2291:2291 <> b:18
R2304:2311 q16_16 Q16_16 in_range def
R2313:2313 q16_16 <> a:17 var
binder 2299:2300 <> ha:19
R2322:2329 q16_16 Q16_16 in_range def
R2331:2331 q16_16 <> b:18 var
binder 2317:2318 <> hb:20
R2346:2353 q16_16 Q16_16 in_range def
R2357:2359 Stdlib.ZArith.BinInt <> ::Z_scope:x_'+'_x not
R2356:2356 q16_16 <> a:17 var
R2360:2360 q16_16 <> b:18 var
binder 2339:2342 <> hsum:21
R2373:2375 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R2366:2368 q16_16 Q16_16 add def
R2370:2370 q16_16 <> a:17 var
R2372:2372 q16_16 <> b:18 var
R2377:2379 Stdlib.ZArith.BinInt <> ::Z_scope:x_'+'_x not
R2376:2376 q16_16 <> a:17 var
R2380:2380 q16_16 <> b:18 var
R2403:2405 q16_16 Q16_16 add def
R2416:2431 q16_16 Q16_16 clamp_idempotent thm
R2416:2431 q16_16 Q16_16 clamp_idempotent thm
R2416:2431 q16_16 Q16_16 clamp_idempotent thm
R2416:2431 q16_16 Q16_16 clamp_idempotent thm
prf 2461:2468 Q16_16 sub_self
R2475:2475 Corelib.Numbers.BinNums <> Z ind
binder 2471:2471 <> a:22
R2484:2491 q16_16 Q16_16 in_range def
R2493:2493 q16_16 <> a:22 var
binder 2479:2480 <> ha:23
R2505:2507 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R2498:2500 q16_16 Q16_16 sub def
R2502:2502 q16_16 <> a:22 var
R2504:2504 q16_16 <> a:22 var
R2508:2511 q16_16 Q16_16 zero def
R2534:2536 q16_16 Q16_16 sub def
R2539:2542 q16_16 Q16_16 zero def
R2553:2562 Stdlib.ZArith.BinInt Z sub_diag thm
R2553:2562 Stdlib.ZArith.BinInt Z sub_diag thm
R2553:2562 Stdlib.ZArith.BinInt Z sub_diag thm
R2575:2590 q16_16 Q16_16 clamp_idempotent thm
R2600:2607 q16_16 Q16_16 in_range def
R2617:2627 q16_16 Q16_16 q16_min_raw def
R2630:2640 q16_16 Q16_16 q16_max_raw def
R2575:2590 q16_16 Q16_16 clamp_idempotent thm
R2661:2678 q16_16 <> le_neg2147483648_0 thm
R2688:2702 q16_16 <> le_0_2147483647 thm
R2661:2678 q16_16 <> le_neg2147483648_0 thm
R2688:2702 q16_16 <> le_0_2147483647 thm
prf 2724:2731 Q16_16 mul_comm
R2740:2740 Corelib.Numbers.BinNums <> Z ind
binder 2734:2734 <> a:24
binder 2736:2736 <> b:25
R2752:2754 Corelib.Init.Logic <> ::type_scope:x_'='_x not
R2745:2747 q16_16 Q16_16 mul def
R2749:2749 q16_16 <> a:24 var
R2751:2751 q16_16 <> b:25 var
R2755:2757 q16_16 Q16_16 mul def
R2759:2759 q16_16 <> b:25 var
R2761:2761 q16_16 <> a:24 var
R2780:2782 q16_16 Q16_16 mul def
R2793:2802 Stdlib.ZArith.BinInt Z mul_comm thm
R2793:2802 Stdlib.ZArith.BinInt Z mul_comm thm
R2793:2802 Stdlib.ZArith.BinInt Z mul_comm thm
prf 2834:2846 Q16_16 in_range_zero
R2850:2857 q16_16 Q16_16 in_range def
R2878:2885 q16_16 Q16_16 in_range def
R2888:2898 q16_16 Q16_16 q16_min_raw def
R2901:2911 q16_16 Q16_16 q16_max_raw def
R2928:2945 q16_16 <> le_neg2147483648_0 thm
R2955:2969 q16_16 <> le_0_2147483647 thm
R2928:2945 q16_16 <> le_neg2147483648_0 thm
R2955:2969 q16_16 <> le_0_2147483647 thm
prf 2989:3000 Q16_16 in_range_one
R3004:3011 q16_16 Q16_16 in_range def
R3032:3039 q16_16 Q16_16 in_range def
R3042:3052 q16_16 Q16_16 q16_min_raw def
R3055:3065 q16_16 Q16_16 q16_max_raw def
R3082:3099 q16_16 <> le_neg2147483648_0 thm
R3109:3123 q16_16 <> le_0_2147483647 thm
R3082:3099 q16_16 <> le_neg2147483648_0 thm
R3109:3123 q16_16 <> le_0_2147483647 thm
R3137:3142 q16_16 Q16_16 <> mod

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(* Coq Formalization of Q16_16 Fixed-Point Arithmetic *)
Require Import ZArith Lia.
Lemma le_neg2147483648_2147483647 : (-2147483648 <= 2147483647)%Z.
Proof. lia. Qed.
Lemma le_0_2147483647 : (0 <= 2147483647)%Z.
Proof. lia. Qed.
Lemma le_neg2147483648_0 : (-2147483648 <= 0)%Z.
Proof. lia. Qed.
Lemma le_2147483647_2147483647 : (2147483647 <= 2147483647)%Z.
Proof. lia. Qed.
Module Q16_16.
Open Scope Z_scope.
Definition q16_min_raw : Z := -2147483648.
Definition q16_max_raw : Z := 2147483647.
Definition q16_scale : Z := 65536.
Definition in_range (x : Z) : Prop :=
q16_min_raw <= x /\ x <= q16_max_raw.
Definition clamp_raw (i : Z) : Z :=
if Z_lt_dec q16_max_raw i then q16_max_raw
else if Z_lt_dec i q16_min_raw then q16_min_raw
else i.
Theorem clamp_bounded (x : Z) : in_range (clamp_raw x).
Proof.
unfold clamp_raw, in_range.
case (Z_lt_dec q16_max_raw x); intros H1.
- unfold q16_min_raw, q16_max_raw; split; [apply le_neg2147483648_2147483647 | apply Z.le_refl].
- case (Z_lt_dec x q16_min_raw); intros H2.
+ unfold q16_min_raw, q16_max_raw; split; [apply Z.le_refl | apply le_neg2147483648_2147483647].
+ split; apply Z.nlt_ge; assumption.
Qed.
Theorem clamp_idempotent (x : Z) (h : in_range x) : clamp_raw x = x.
Proof.
destruct h as [Hlo Hhi].
unfold clamp_raw.
case (Z_lt_dec q16_max_raw x); intros Hgt; [exfalso; exact (Zlt_not_le _ _ Hgt Hhi) |].
case (Z_lt_dec x q16_min_raw); intros Hlt; [exfalso; exact (Zlt_not_le _ _ Hlt Hlo) |].
reflexivity.
Qed.
Definition zero : Z := 0.
Definition one : Z := 65536.
Definition epsilon : Z := 1.
Definition half : Z := 32768.
Definition pct1 : Z := 655.
Definition pct70 : Z := 45875.
Definition pct30 : Z := 19661.
Definition one50 : Z := 98304.
Definition add (a b : Z) : Z := clamp_raw (a + b).
Definition sub (a b : Z) : Z := clamp_raw (a - b).
Definition neg (a : Z) : Z := clamp_raw (-a).
Definition mul (a b : Z) : Z := clamp_raw (Z.div (a * b) q16_scale).
Definition div (a b : Z) : Z :=
if Z.eq_dec b 0 then zero else clamp_raw (Z.div (a * q16_scale) b).
Theorem add_comm (a b : Z) : add a b = add b a.
Proof. unfold add; rewrite Z.add_comm; reflexivity. Qed.
Theorem add_in_range (a b : Z) (ha : in_range a) (hb : in_range b)
(hsum : in_range (a + b)) : add a b = a + b.
Proof.
unfold add; rewrite clamp_idempotent; trivial.
Qed.
Theorem sub_self (a : Z) (ha : in_range a) : sub a a = zero.
Proof.
unfold sub, zero; rewrite Z.sub_diag.
apply clamp_idempotent; unfold in_range; unfold q16_min_raw, q16_max_raw.
split; [apply le_neg2147483648_0 | apply le_0_2147483647].
Qed.
Theorem mul_comm (a b : Z) : mul a b = mul b a.
Proof. unfold mul; rewrite Z.mul_comm; reflexivity. Qed.
Theorem in_range_zero : in_range 0.
Proof. unfold in_range, q16_min_raw, q16_max_raw. split; [apply le_neg2147483648_0 | apply le_0_2147483647]. Qed.
Theorem in_range_one : in_range 1.
Proof. unfold in_range, q16_min_raw, q16_max_raw. split; [apply le_neg2147483648_0 | apply le_0_2147483647]. Qed.
End Q16_16.

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0
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// AVM ISA v1 — C++ Port (Strict Functional Execution)
#include <cstdint>
#include <vector>
#include <optional>
#include <variant>
#include <stdexcept>
#include <functional>
constexpr int32_t Q16_SCALE = 65536;
inline int32_t q16_mul(int32_t a, int32_t b) {
return static_cast<int32_t>(
(static_cast<int64_t>(a) * static_cast<int64_t>(b)) / Q16_SCALE);
}
inline int32_t q16_div(int32_t a, int32_t b) {
if (b == 0) throw std::runtime_error("div by zero");
return static_cast<int32_t>(
(static_cast<int64_t>(a) * Q16_SCALE) / b);
}
// ── Value ─────────────────────────────────────────
struct AvmVal {
enum Ty { Q0_16, Q16_16, Bool };
Ty ty;
int32_t raw;
AvmVal(Ty t, int32_t r) : ty(t), raw(r) {}
static AvmVal q16(int32_t x) { return {Q16_16, x}; }
static AvmVal q0(int32_t x) {
if (x < -32767) x = -32767;
if (x > 32767) x = 32767;
return {Q0_16, x};
}
static AvmVal boolean(bool x) { return {Bool, x ? 1 : 0}; }
};
// ── Primitives ─────────────────────────────────────
enum class Prim : int32_t {
AddSatQ0, SubSatQ0, AddSatQ16, SubSatQ16, MulSatQ16, DivSatQ16,
LtQ16, EqQ16, And, Or, Not
};
AvmVal exec_prim(Prim op, const AvmVal& a, const std::optional<AvmVal>& b) {
auto bv = [&]() -> const AvmVal& { return b.value(); };
switch (op) {
case Prim::AddSatQ16: return AvmVal::q16(a.raw + bv().raw);
case Prim::SubSatQ16: return AvmVal::q16(a.raw - bv().raw);
case Prim::MulSatQ16: return AvmVal::q16(q16_mul(a.raw, bv().raw));
case Prim::DivSatQ16: return AvmVal::q16(q16_div(a.raw, bv().raw));
case Prim::LtQ16: return AvmVal::boolean(a.raw < bv().raw);
case Prim::EqQ16: return AvmVal::boolean(a.raw == bv().raw);
case Prim::And: return AvmVal::boolean(a.raw && bv().raw);
case Prim::Or: return AvmVal::boolean(a.raw || bv().raw);
case Prim::Not: return AvmVal::boolean(!a.raw);
default: throw std::runtime_error("unknown prim");
}
}
// ── Instruction ────────────────────────────────────
enum class InstrOp : int8_t {
PushQ16, PushBool, Pop, Dup, Swap, Load, Store, Jump, JumpIf, Prim, Halt
};
struct Instr {
InstrOp op;
int32_t arg;
bool arg2{false};
};
inline Instr push_q16(int32_t x) { return {InstrOp::PushQ16, x, false}; }
inline Instr push_bool(bool x) { return {InstrOp::PushBool, static_cast<int32_t>(x), true}; }
inline Instr pop() { return {InstrOp::Pop, 0, false}; }
inline Instr dup() { return {InstrOp::Dup, 0, false}; }
inline Instr swap() { return {InstrOp::Swap, 0, false}; }
inline Instr load(int i) { return {InstrOp::Load, i, false}; }
inline Instr store(int i) { return {InstrOp::Store, i, false}; }
inline Instr jump(int t) { return {InstrOp::Jump, t, false}; }
inline Instr jump_if(int t) { return {InstrOp::JumpIf, t, false}; }
inline Instr prim(Prim p) { return {InstrOp::Prim, static_cast<int32_t>(p), false}; }
inline Instr halt() { return {InstrOp::Halt, 0, false}; }
// ── State ──────────────────────────────────────────
struct State {
int pc{0};
std::vector<AvmVal> stack;
std::vector<std::optional<AvmVal>> locals;
bool halted{false};
State() : pc(0), locals(16, std::nullopt) {}
State(int pc_, std::vector<AvmVal> stack_, std::vector<std::optional<AvmVal>> locals_, bool halted_)
: pc(pc_), stack(std::move(stack_)), locals(std::move(locals_)), halted(halted_) {}
};
// ── Step ───────────────────────────────────────────
State step(const State& s, const std::vector<Instr>& prog) {
if (s.halted) throw std::runtime_error("halted");
if (s.pc < 0 || s.pc >= (int)prog.size())
return State{};
auto instr = prog[s.pc];
State ns{s.pc + 1, s.stack, s.locals, false};
auto& st = ns.stack;
switch (instr.op) {
case InstrOp::PushQ16: st.push_back(AvmVal::q16(instr.arg)); break;
case InstrOp::PushBool: st.push_back(AvmVal::boolean(instr.arg)); break;
case InstrOp::Pop: st.pop_back(); break;
case InstrOp::Dup: st.push_back(st.back()); break;
case InstrOp::Swap: std::swap(st[st.size()-2], st[st.size()-1]); break;
case InstrOp::Load: {
auto v = ns.locals[instr.arg];
if (!v.has_value()) throw std::runtime_error("missing local");
st.push_back(v.value());
break;
}
case InstrOp::Store: {
ns.locals[instr.arg] = st.back(); st.pop_back();
break;
}
case InstrOp::Jump: ns.pc = instr.arg; break;
case InstrOp::JumpIf: {
if (st.back().raw) ns.pc = instr.arg;
st.pop_back();
break;
}
case InstrOp::Prim: {
auto p = static_cast<Prim>(instr.arg);
int arity = (p == Prim::Not) ? 1 : 2;
std::optional<AvmVal> b;
if (arity == 2) { b = st.back(); st.pop_back(); }
auto a = st.back(); st.pop_back();
st.push_back(exec_prim(p, a, b));
break;
}
case InstrOp::Halt: ns.halted = true; break;
}
return ns;
}
State run(const State& init, const std::vector<Instr>& prog, int fuel) {
State s = init;
for (int i = 0; i < fuel && !s.halted; i++)
s = step(s, prog);
return s;
}

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@ -10,12 +10,12 @@ test harness.
|---|----------|-----|----------|-------|-------------------|--------| |---|----------|-----|----------|-------|-------------------|--------|
| 1 | Lean | `lean --server` | `formal/SilverSight/AVMIsa/` | `E2E.lean` | ✅ | **Reference** | | 1 | Lean | `lean --server` | `formal/SilverSight/AVMIsa/` | `E2E.lean` | ✅ | **Reference** |
| 2 | Rust | `rust-analyzer` | `rust/src/avm/mod.rs` | `test_add_q16` | ✅ | ✅ | | 2 | Rust | `rust-analyzer` | `rust/src/avm/mod.rs` | `test_add_q16` | ✅ | ✅ |
| 3 | Python | `pyright` | `python/avm.py` | ❌ | ❌ | 🔄 | | 3 | Python | `pyright` | `python/avm.py` | `test_avm_python.py` | ❌ | ✅ |
| 4 | Coq | `coq-lsp` | `coq/AVMIsa/avm.v` | ❌ | ❌ | 🔄 | | 4 | Coq | `coq-lsp` | `coq/AVMIsa/avm.v` | ❌ | ❌ | 🔄 |
| 5 | R | — | `r/AVMIsa/avm.r` | `test_avm.r` | ✅ | ✅ | | 5 | R | — | `r/AVMIsa/avm.r` | `test_avm.r` | ✅ | ✅ |
| 6 | Julia | — | `julia/AVMIsa/avm.jl` | `test_avm.jl` | ✅ | ✅ | | 6 | Julia | — | `julia/AVMIsa/avm.jl` | `test_avm.jl` | ✅ | ✅ |
| 7 | Scala | `metals` | `scala/avm.scala` | ❌ | ❌ | 🔄 | | 7 | Scala | `metals` | `scala/avm.scala` | ❌ | ❌ | 🔄 |
| 8 | Go | — | `go/avm.go` | ❌ | ❌ | 🔄 | | 8 | Go | — | `go/avm.go` | `go/avm_test.go` | ❌ | 🔄 |
| 9 | C | `clangd` | `c/avm.c` | ❌ | ❌ | 🔄 | | 9 | C | `clangd` | `c/avm.c` | ❌ | ❌ | 🔄 |
| 10 | C++ | `clangd` | `cpp/avm.hpp` | ❌ | ❌ | 🔄 | | 10 | C++ | `clangd` | `cpp/avm.hpp` | ❌ | ❌ | 🔄 |
| 11 | Fortran | `fortls` | `fortran/avm.f90` | ❌ | ❌ | 🔄 | | 11 | Fortran | `fortls` | `fortran/avm.f90` | ❌ | ❌ | 🔄 |

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! AVM ISA v1 — Fortran Port (Strict Functional Execution)
module avm
implicit none
integer, parameter :: Q16_SCALE = 65536
integer, parameter :: MAX_STACK = 1024
integer, parameter :: MAX_LOCALS = 16
integer, parameter :: MAX_PROG = 256
! Value type codes
integer, parameter :: VAL_Q16 = 0, VAL_BOOL = 1
type :: AvmVal
integer :: ty = VAL_Q16
integer :: val = 0
end type
! Primitive codes
integer, parameter :: PRIM_ADD = 0, PRIM_SUB = 1, PRIM_MUL = 2, PRIM_DIV = 3
integer, parameter :: PRIM_LT = 4, PRIM_EQ = 5, PRIM_AND = 6, PRIM_OR = 7, PRIM_NOT = 8
! Instruction opcodes
integer, parameter :: I_PUSH_Q16 = 0, I_PUSH_BOOL = 1, I_POP = 2, I_DUP = 3
integer, parameter :: I_SWAP = 4, I_LOAD = 5, I_STORE = 6, I_JUMP = 7
integer, parameter :: I_JUMP_IF = 8, I_PRIM = 9, I_HALT = 10
type :: Instr
integer :: op = 0
integer :: arg = 0
end type
type :: State
integer :: pc = 0
type(AvmVal) :: stack(MAX_STACK)
integer :: sp = 0 ! stack pointer
type(AvmVal) :: locals(MAX_LOCALS)
logical :: halted = .false.
end type
contains
function q16_mul(a, b) result(r)
integer, intent(in) :: a, b
integer :: r
r = int((int(a, 8) * int(b, 8)) / Q16_SCALE)
end function
function q16_div(a, b) result(r)
integer, intent(in) :: a, b
integer :: r
if (b == 0) then
r = 2147483647
return
end if
r = int((int(a, 8) * Q16_SCALE) / int(b, 8))
end function
function make_q16(x) result(v)
integer, intent(in) :: x
type(AvmVal) :: v
v%ty = VAL_Q16; v%val = x
end function
function make_bool(x) result(v)
logical, intent(in) :: x
type(AvmVal) :: v
v%ty = VAL_BOOL
if (x) then; v%val = 1; else; v%val = 0; end if
end function
function make_instr(op, arg) result(i)
integer, intent(in) :: op, arg
type(Instr) :: i
i%op = op; i%arg = arg
end function
subroutine push(s, v)
type(State), intent(inout) :: s
type(AvmVal), intent(in) :: v
s%sp = s%sp + 1
s%stack(s%sp) = v
end subroutine
function pop(s) result(v)
type(State), intent(inout) :: s
type(AvmVal) :: v
v = s%stack(s%sp)
s%sp = s%sp - 1
end function
function step(state, prog, prog_len) result(ns)
type(State), intent(in) :: state
type(Instr), intent(in) :: prog(MAX_PROG)
integer, intent(in) :: prog_len
type(State) :: ns
type(AvmVal) :: a, b, result
integer :: arity
ns = state
if (ns%halted) return
if (ns%pc < 0 .or. ns%pc >= prog_len) then
ns%halted = .true.; return
end if
select case (prog(ns%pc + 1)%op) ! +1 for 1-indexed
case (I_PUSH_Q16)
call push(ns, make_q16(prog(ns%pc + 1)%arg))
case (I_PUSH_BOOL)
call push(ns, make_bool(prog(ns%pc + 1)%arg /= 0))
case (I_POP)
a = pop(ns)
case (I_DUP)
a = ns%stack(ns%sp)
call push(ns, a)
case (I_SWAP)
a = pop(ns); b = pop(ns)
call push(ns, a); call push(ns, b)
case (I_LOAD)
call push(ns, ns%locals(prog(ns%pc + 1)%arg + 1))
case (I_STORE)
ns%locals(prog(ns%pc + 1)%arg + 1) = pop(ns)
case (I_JUMP)
ns%pc = prog(ns%pc + 1)%arg - 1; return
case (I_JUMP_IF)
a = pop(ns)
if (a%val /= 0) ns%pc = prog(ns%pc + 1)%arg - 1
case (I_PRIM)
arity = 2
if (prog(ns%pc + 1)%arg == PRIM_NOT) arity = 1
if (arity == 2) b = pop(ns)
a = pop(ns)
select case (prog(ns%pc + 1)%arg)
case (PRIM_ADD); result = make_q16(a%val + b%val)
case (PRIM_SUB); result = make_q16(a%val - b%val)
case (PRIM_MUL); result = make_q16(q16_mul(a%val, b%val))
case (PRIM_DIV); result = make_q16(q16_div(a%val, b%val))
case (PRIM_LT); result = make_bool(a%val < b%val)
case (PRIM_EQ); result = make_bool(a%val == b%val)
case (PRIM_AND); result = make_bool(a%val /= 0 .and. b%val /= 0)
case (PRIM_OR); result = make_bool(a%val /= 0 .or. b%val /= 0)
case (PRIM_NOT); result = make_bool(a%val == 0)
end select
call push(ns, result)
case (I_HALT)
ns%halted = .true.
end select
ns%pc = ns%pc + 1
end function
subroutine run(init, prog, prog_len, fuel, out_state)
type(State), intent(in) :: init
type(Instr), intent(in) :: prog(MAX_PROG)
integer, intent(in) :: prog_len, fuel
type(State), intent(out) :: out_state
type(State) :: s
integer :: i
s = init
do i = 1, fuel
if (s%halted) exit
s = step(s, prog, prog_len)
end do
out_state = s
end subroutine
end module

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// AVM ISA v1 — Go Port (Strict Functional Execution)
package avm
import "errors"
const Q16Scale = 65536
func q16Mul(a, b int32) int32 {
return int32((int64(a) * int64(b)) / Q16Scale)
}
func q16Div(a, b int32) (int32, error) {
if b == 0 { return 0, errors.New("div by zero") }
return int32((int64(a) * Q16Scale) / b), nil
}
// ── Value ─────────────────────────────────────────
type ValType int
const (
ValQ0 ValType = iota
ValQ16
ValBool
)
type AvmVal struct { Ty ValType; Raw int32 }
func Q16(x int32) AvmVal { return AvmVal{ValQ16, x} }
func Bool(x bool) AvmVal {
if x { return AvmVal{ValBool, 1} }
return AvmVal{ValBool, 0}
}
// ── Primitives ─────────────────────────────────────
type Prim int
const (
AddQ16 Prim = iota; SubQ16; MulQ16; DivQ16; LtQ16; EqQ16; And; Or; Not
)
func execPrim(p Prim, a, b AvmVal) (AvmVal, error) {
switch p {
case AddQ16: return Q16(a.Raw + b.Raw), nil
case SubQ16: return Q16(a.Raw - b.Raw), nil
case MulQ16: return Q16(q16Mul(a.Raw, b.Raw)), nil
case DivQ16:
r, e := q16Div(a.Raw, b.Raw)
return Q16(r), e
case LtQ16: return Bool(a.Raw < b.Raw), nil
case EqQ16: return Bool(a.Raw == b.Raw), nil
case And: return Bool(a.Raw != 0 && b.Raw != 0), nil
case Or: return Bool(a.Raw != 0 || b.Raw != 0), nil
case Not: return Bool(a.Raw == 0), nil
}
return AvmVal{}, errors.New("unknown prim")
}
// ── Instruction ────────────────────────────────────
type InstrOp int
const (
PushQ16 InstrOp = iota; PushBool; Pop; Dup; Swap; Load; Store; Jump; JumpIf; PrimOp; Halt
)
type Instr struct { Op InstrOp; Arg int32; Arg2 bool }
func Push(x int32) Instr { return Instr{PushQ16, x, false} }
func PushB(x bool) Instr { return Instr{PushBool, boolTo32(x), true} }
func Pop() Instr { return Instr{Pop, 0, false} }
func Dup() Instr { return Instr{Dup, 0, false} }
func Swap() Instr { return Instr{Swap, 0, false} }
func Load(i int) Instr { return Instr{Load, int32(i), false} }
func Store(i int) Instr { return Instr{Store, int32(i), false} }
func Jump(t int) Instr { return Instr{Jump, int32(t), false} }
func JumpIf(t int) Instr { return Instr{JumpIf, int32(t), false} }
func PrimOp(p Prim) Instr{ return Instr{PrimOp, int32(p), false} }
func Halt() Instr { return Instr{Halt, 0, false} }
func boolTo32(x bool) int32 { if x { return 1 }; return 0 }
// ── State ──────────────────────────────────────────
type State struct {
Pc int
Stack []AvmVal
Locals []*AvmVal
Halted bool
}
func NewState(n int) State {
return State{0, []AvmVal{}, make([]*AvmVal, n), false}
}
// ── Step ───────────────────────────────────────────
func Step(s State, prog []Instr) (State, error) {
if s.Halted { return s, errors.New("halted") }
if s.Pc < 0 || s.Pc >= len(prog) {
s.Halted = true; return s, nil
}
instr := prog[s.Pc]
ns := State{s.Pc + 1, append([]AvmVal{}, s.Stack...),
append([]*AvmVal{}, s.Locals...), false}
st := &ns.Stack
switch instr.Op {
case PushQ16: *st = append(*st, Q16(instr.Arg))
case PushBool: *st = append(*st, Bool(instr.Arg != 0))
case Pop: *st = (*st)[:len(*st)-1]
case Dup: *st = append(*st, (*st)[len(*st)-1])
case Swap:
(*st)[len(*st)-2], (*st)[len(*st)-1] = (*st)[len(*st)-1], (*st)[len(*st)-2]
case Load:
if ns.Locals[instr.Arg] == nil { return s, errors.New("missing local") }
*st = append(*st, *ns.Locals[instr.Arg])
case Store:
ns.Locals[instr.Arg] = &(*st)[len(*st)-1]
*st = (*st)[:len(*st)-1]
case Jump: ns.Pc = int(instr.Arg)
case JumpIf:
v := (*st)[len(*st)-1]; *st = (*st)[:len(*st)-1]
if v.Raw != 0 { ns.Pc = int(instr.Arg) }
case PrimOp: {
p := Prim(instr.Arg)
arity := 2; if p == Not { arity = 1 }
var b AvmVal
if arity == 2 { b = (*st)[len(*st)-1]; *st = (*st)[:len(*st)-1] }
a := (*st)[len(*st)-1]; *st = (*st)[:len(*st)-1]
r, e := execPrim(p, a, b)
if e != nil { return s, e }
*st = append(*st, r)
}
case Halt: ns.Halted = true
}
return ns, nil
}
func Run(init State, prog []Instr, fuel int) (State, error) {
s := init
for i := 0; i < fuel && !s.Halted; i++ {
var e error
s, e = Step(s, prog)
if e != nil { return s, e }
}
return s, nil
}

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package avm
import "testing"
func q16(x int32) Val { return Val{Ty: Q16_16, Q: avmClamp(int64(x))} }
func runTest(prog []Instr, fuel int) (*State, error) {
return Run(NewState(0), prog, fuel)
}
func TestBasicAdd(t *testing.T) {
prog := []Instr{
{Op: PushQ16, Arg: 5 * Q16Scale},
{Op: PushQ16, Arg: 3 * Q16Scale},
{Op: Primitive, Arg: int32(AddSatQ16)},
{Op: Halt},
}
s, err := runTest(prog, 100)
if err != nil { t.Fatal(err) }
if s.Stack[0].Q != 8*Q16Scale { t.Fatalf("got %d", s.Stack[0].Q) }
}
func TestFloorDiv(t *testing.T) {
// (3 * Q16) / (5 * Q16) = floor(0.6) = 0.6 in Q16
prog := []Instr{
{Op: PushQ16, Arg: 3 * Q16Scale},
{Op: PushQ16, Arg: 5 * Q16Scale},
{Op: Primitive, Arg: int32(DivSatQ16)},
{Op: Halt},
}
s, err := runTest(prog, 100)
if err != nil { t.Fatal(err) }
expected := (3 * Q16Scale) / 5
if s.Stack[0].Q != expected { t.Fatalf("got %d, expected %d", s.Stack[0].Q, expected) }
}
func TestSaturation(t *testing.T) {
prog := []Instr{
{Op: PushQ16, Arg: AVMClampMax - 1},
{Op: PushQ16, Arg: 2},
{Op: Primitive, Arg: int32(AddSatQ16)},
{Op: Halt},
}
s, err := runTest(prog, 100)
if err != nil { t.Fatal(err) }
if s.Stack[0].Q != AVMClampMax { t.Fatalf("got %d", s.Stack[0].Q) }
}
func TestV6LtQ16(t *testing.T) {
cases := []struct{ a, b int32; exp bool }{
{-5 * Q16Scale, -3 * Q16Scale, true},
{-3 * Q16Scale, -5 * Q16Scale, false},
{5 * Q16Scale, 3 * Q16Scale, false},
{3 * Q16Scale, 5 * Q16Scale, true},
{-1 * Q16Scale, 2 * Q16Scale, true},
}
for _, c := range cases {
prog := []Instr{
{Op: PushQ16, Arg: c.a},
{Op: PushQ16, Arg: c.b},
{Op: Primitive, Arg: int32(LtQ16)},
{Op: Halt},
}
s, err := runTest(prog, 100)
if err != nil { t.Fatal(err) }
if s.Stack[0].Bval != c.exp { t.Fatalf("ltQ16(%d,%d): got %v", c.a, c.b, s.Stack[0]) }
}
}
func TestDivByZero(t *testing.T) {
prog := []Instr{
{Op: PushQ16, Arg: Q16Scale},
{Op: PushQ16, Arg: 0},
{Op: Primitive, Arg: int32(DivSatQ16)},
}
_, err := runTest(prog, 100)
if err == nil { t.Fatal("expected error") }
}
func TestStackOverflow(t *testing.T) {
prog := make([]Instr, AVMMaxStack+1)
for i := range prog { prog[i] = Instr{Op: PushQ16, Arg: 0} }
_, err := runTest(prog, 10000)
if err == nil { t.Fatal("expected overflow") }
}
func TestControlFlow(t *testing.T) {
prog := []Instr{
{Op: PushBool, Arg2: true},
{Op: JumpIf, Arg: 4},
{Op: PushQ16, Arg: 0},
{Op: Halt},
{Op: PushQ16, Arg: Q16Scale},
{Op: Halt},
}
s, err := runTest(prog, 100)
if err != nil { t.Fatal(err) }
if s.Stack[0].Q != Q16Scale { t.Fatalf("got %d", s.Stack[0].Q) }
}
func TestLocals(t *testing.T) {
s := NewState(1)
prog := []Instr{
{Op: PushQ16, Arg: 42 * Q16Scale},
{Op: Store, Arg: 0},
{Op: Load, Arg: 0},
{Op: Halt},
}
result, err := Run(s, prog, 100)
if err != nil { t.Fatal(err) }
if result.Stack[0].Q != 42*Q16Scale { t.Fatalf("got %d", result.Stack[0].Q) }
}

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% AVM ISA v1 — Octave Port (Strict Functional Execution)
% All functions are pure (no global mutation).
Q16_SCALE = 65536;
function r = q16_mul(a, b)
r = int32((int64(a) * int64(b)) / Q16_SCALE);
end
function r = q16_div(a, b)
if b == 0, error("div by zero"); end
r = int32((int64(a) * Q16_SCALE) / int64(b));
end
% ── Constructors ──────────────────────────────────
function v = make_q16(x)
v.ty = 'q16'; v.val = int32(x);
end
function v = make_bool(x)
v.ty = 'bool'; v.val = int32(x);
end
function i = make_instr(op, arg)
i.op = int8(op); i.arg = int32(arg);
end
% ── Instructions ──────────────────────────────────
function i = push_q16(x); i = make_instr(0, x); end
function i = push_bool(x); i = make_instr(1, x); end
function i = pop(); i = make_instr(2, 0); end
function i = dup(); i = make_instr(3, 0); end
function i = swap(); i = make_instr(4, 0); end
function i = load(x); i = make_instr(5, x); end
function i = store(x); i = make_instr(6, x); end
function i = jump(x); i = make_instr(7, x); end
function i = jump_if(x); i = make_instr(8, x); end
function i = prim(x); i = make_instr(9, x); end
function i = halt(); i = make_instr(10, 0); end
% Primitives
PRIM_ADD=0; PRIM_SUB=1; PRIM_MUL=2; PRIM_DIV=3;
PRIM_LT=4; PRIM_EQ=5; PRIM_AND=6; PRIM_OR=7; PRIM_NOT=8;
% ── State ─────────────────────────────────────────
function s = new_state(n)
s.pc = 1;
s.stack = cell(1024, 1); s.sp = 0;
s.locals = cell(n, 1);
s.halted = false;
end
function s = state_push(s, v)
s.sp = s.sp + 1;
s.stack{s.sp} = v;
end
function [v, s] = state_pop(s)
v = s.stack{s.sp};
s.sp = s.sp - 1;
end
% ── Step ──────────────────────────────────────────
function ns = step(state, prog)
ns = state;
if ns.halted, return; end
if ns.pc < 1 || ns.pc > length(prog)
ns.halted = true; return;
end
instr = prog{ns.pc};
switch instr.op
case 0 % push_q16
ns = state_push(ns, make_q16(instr.arg));
case 1 % push_bool
ns = state_push(ns, make_bool(instr.arg));
case 2 % pop
[~, ns] = state_pop(ns);
case 3 % dup
ns = state_push(ns, ns.stack{ns.sp});
case 4 % swap
[a, ns] = state_pop(ns); [b, ns] = state_pop(ns);
ns = state_push(ns, a); ns = state_push(ns, b);
case 5 % load
ns = state_push(ns, ns.locals{instr.arg + 1});
case 6 % store
[v, ns] = state_pop(ns);
ns.locals{instr.arg + 1} = v;
case 7 % jump
ns.pc = instr.arg; return;
case 8 % jump_if
[v, ns] = state_pop(ns);
if v.val != 0, ns.pc = instr.arg; end
case 9 % prim
arity = 2;
if instr.arg == PRIM_NOT, arity = 1; end
if arity >= 2, [b, ns] = state_pop(ns); end
[a, ns] = state_pop(ns);
switch instr.arg
case PRIM_ADD
r = make_q16(a.val + b.val);
case PRIM_SUB
r = make_q16(a.val - b.val);
case PRIM_MUL
r = make_q16(q16_mul(a.val, b.val));
case PRIM_DIV
r = make_q16(q16_div(a.val, b.val));
case PRIM_LT
r = make_bool(a.val < b.val);
case PRIM_EQ
r = make_bool(a.val == b.val);
case PRIM_AND
r = make_bool(a.val && b.val);
case PRIM_OR
r = make_bool(a.val || b.val);
case PRIM_NOT
r = make_bool(a.val == 0);
end
ns = state_push(ns, r);
case 10 % halt
ns.halted = true;
end
ns.pc = ns.pc + 1;
end
function s = run(init, prog, fuel)
s = init;
for i = 1:fuel
if s.halted, break; end
s = step(s, prog);
end
end

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""" """
AVM ISA v1 — Python Port (Strict Functional Execution) AVM ISA v1 — Python Port
Mirrors formal/SilverSight/AVMIsa/Step.lean Strict functional: step(state, program) -> state, run(state, program, fuel) -> state
""" """
from __future__ import annotations
from dataclasses import dataclass, field from dataclasses import dataclass, field
from enum import IntEnum, auto from typing import List, Union, Tuple
from typing import Union, Optional
import sys
from q16_canonical import Q16_SCALE, float_to_q16, q16_to_float
# ── Constants ──────────────────────────────────────────────────────── # ── Constants ────────────────────────────────────────────────────────
Q16_SCALE = 65536
AVM_CLAMP_MIN = -2147483647 AVM_CLAMP_MIN = -2147483647
AVM_CLAMP_MAX = 2147483647 AVM_CLAMP_MAX = 2147483647
AVM_Q0_MIN = -32767 AVM_Q0_MIN = -32767
AVM_Q0_MAX = 32767 AVM_Q0_MAX = 32767
AVM_MAX_STACK = 1024 AVM_MAX_STACK = 1024
def avm_clamp(x: int) -> int: def avm_clamp(x):
return max(AVM_CLAMP_MIN, min(AVM_CLAMP_MAX, x)) return max(AVM_CLAMP_MIN, min(AVM_CLAMP_MAX, int(x)))
def avm_q0_clamp(x: int) -> int: def avm_q0_clamp(x):
return max(AVM_Q0_MIN, min(AVM_Q0_MAX, x)) return max(AVM_Q0_MIN, min(AVM_Q0_MAX, int(x)))
def floor_div(a: int, b: int) -> int: def floor_div(a, b):
"""Floor division matching Lean Int.ediv.""" if b == 0: raise ValueError("div by zero")
if b == 0: q, r = divmod(a, b)
raise ValueError("division by zero") return q - 1 if r and (a ^ b) < 0 else q
return -((-a) // b) if (a < 0) != (b < 0) and a % b != 0 else a // b
def lt_q16_v6(a: int, b: int) -> bool: def lt_q16_v6(a, b):
sa = a < 0 sa, sb = a < 0, b < 0
sb = b < 0
return sa if sa != sb else a < b return sa if sa != sb else a < b
def q16_mul(a, b):
return floor_div(a * b, Q16_SCALE)
def q16_div(a, b):
if b == 0: raise ValueError("div by zero")
return floor_div(a * Q16_SCALE, b)
# ── Types ──────────────────────────────────────────────────────────── # ── Types ────────────────────────────────────────────────────────────
class AvmTy(IntEnum): class Prim:
Q0_16 = 0 ADD_SAT_Q0, SUB_SAT_Q0, ADD_SAT_Q16, SUB_SAT_Q16, \
Q16_16 = 1 MUL_SAT_Q16, DIV_SAT_Q16, LT_Q16, EQ_Q16, AND, OR, NOT = range(11)
BOOL = 2
# ── Values ─────────────────────────────────────────────────────────── prim_arity = {Prim.NOT: 1}.get # all others are 2
@dataclass
class AnyVal:
ty: AvmTy
val: Union[int, bool]
class AvmVal:
def __init__(self, ty, val):
self.ty = ty
self.val = val
@staticmethod @staticmethod
def q16(x: int) -> 'AnyVal': def q0(x): return AvmVal('q0', avm_q0_clamp(x))
return AnyVal(AvmTy.Q16_16, avm_clamp(x))
@staticmethod @staticmethod
def q0(x: int) -> 'AnyVal': def q16(x): return AvmVal('q16', avm_clamp(x))
return AnyVal(AvmTy.Q0_16, avm_q0_clamp(x))
@staticmethod @staticmethod
def b(x: bool) -> 'AnyVal': def bool(x): return AvmVal('bool', bool(x))
return AnyVal(AvmTy.BOOL, x)
# ── Instructions ─────────────────────────────────────────────────────
class Prim(IntEnum):
ADD_SAT_Q0 = 0
SUB_SAT_Q0 = 1
ADD_SAT_Q16 = 2
SUB_SAT_Q16 = 3
MUL_SAT_Q16 = 4
DIV_SAT_Q16 = 5
LT_Q16 = 6
EQ_Q16 = 7
AND = 8
OR = 9
NOT = 10
@property
def arity(self) -> int:
return 1 if self == Prim.NOT else 2
class Instr: class Instr:
PUSH_Q16, PUSH_BOOL, PUSH_Q0, POP, DUP, SWAP, LOAD, STORE, JUMP, JUMP_IF, PRIM, HALT = range(12) PUSH, PUSH_BOOL, PUSH_Q0, POP, DUP, SWAP, LOAD, STORE, \
JUMP, JUMP_IF, PRIM, HALT = range(12)
# ── Primitive execution ────────────────────────────────────────────── Q0_OPS = {Prim.ADD_SAT_Q0, Prim.SUB_SAT_Q0}
def eval_prim(p: Prim, a: AnyVal, b: Optional[AnyVal] = None) -> AnyVal: Q16_BIN_OPS = {Prim.ADD_SAT_Q16, Prim.SUB_SAT_Q16, Prim.MUL_SAT_Q16, Prim.DIV_SAT_Q16, Prim.LT_Q16, Prim.EQ_Q16}
if p == Prim.ADD_SAT_Q0: BOOL_BIN_OPS = {Prim.AND, Prim.OR}
assert a.ty == b.ty == AvmTy.Q0_16
return AnyVal.q0(a.val + b.val)
elif p == Prim.SUB_SAT_Q0:
assert a.ty == b.ty == AvmTy.Q0_16
return AnyVal.q0(a.val - b.val)
elif p == Prim.ADD_SAT_Q16:
assert a.ty == b.ty == AvmTy.Q16_16
return AnyVal.q16(a.val + b.val)
elif p == Prim.SUB_SAT_Q16:
assert a.ty == b.ty == AvmTy.Q16_16
return AnyVal.q16(a.val - b.val)
elif p == Prim.MUL_SAT_Q16:
assert a.ty == b.ty == AvmTy.Q16_16
return AnyVal.q16(floor_div(a.val * b.val, Q16_SCALE))
elif p == Prim.DIV_SAT_Q16:
assert a.ty == b.ty == AvmTy.Q16_16
if b.val == 0:
raise ValueError("division by zero")
return AnyVal.q16(floor_div(a.val * Q16_SCALE, b.val))
elif p == Prim.LT_Q16:
assert a.ty == b.ty == AvmTy.Q16_16
return AnyVal.b(lt_q16_v6(a.val, b.val))
elif p == Prim.EQ_Q16:
assert a.ty == b.ty == AvmTy.Q16_16
return AnyVal.b(a.val == b.val)
elif p == Prim.AND:
assert a.ty == b.ty == AvmTy.BOOL
return AnyVal.b(a.val and b.val)
elif p == Prim.OR:
assert a.ty == b.ty == AvmTy.BOOL
return AnyVal.b(a.val or b.val)
elif p == Prim.NOT:
assert a.ty == AvmTy.BOOL
return AnyVal.b(not a.val)
# ── Errors ─────────────────────────────────────────────────────────── def check_type(val_ty, expected, label):
class StepError(Exception): if val_ty != expected:
def __init__(self, kind: str): raise TypeError(f"type mismatch: expected {expected}, got {val_ty}")
self.kind = kind
def make_instr(op, arg=None, arg2=None):
return {'op': op, 'arg': arg, 'arg2': arg2}
def push_q16(x): return make_instr(Instr.PUSH, avm_clamp(x))
def push_bool(x): return make_instr(Instr.PUSH_BOOL, 0, x)
def push_q0(x): return make_instr(Instr.PUSH_Q0, avm_q0_clamp(x))
def pop(): return make_instr(Instr.POP)
def dup(): return make_instr(Instr.DUP)
def swap(): return make_instr(Instr.SWAP)
def load(i): return make_instr(Instr.LOAD, i)
def store(i): return make_instr(Instr.STORE, i)
def jump(t): return make_instr(Instr.JUMP, t)
def jump_if(t): return make_instr(Instr.JUMP_IF, t)
def prim(p): return make_instr(Instr.PRIM, p)
def halt(): return make_instr(Instr.HALT)
# ── State ────────────────────────────────────────────────────────────
@dataclass @dataclass
class State: class State:
pc: int = 0 pc: int = 0
stack: list = field(default_factory=list) stack: list = field(default_factory=list)
locals: list = field(default_factory=list) locals: list = field(default_factory=lambda: [None] * 16)
halted: bool = False halted: bool = False
@staticmethod # ── Primitive execution ──────────────────────────────────────────────
def new(n_locals: int = 0): def exec_prim(op, a, b=None):
return State(pc=0, stack=[], locals=[None] * n_locals, halted=False) if op == Prim.ADD_SAT_Q0:
check_type(a.ty, 'q0', 'a'); check_type(b.ty, 'q0', 'b')
return AvmVal.q0(a.val + b.val)
if op == Prim.SUB_SAT_Q0:
check_type(a.ty, 'q0', 'a'); check_type(b.ty, 'q0', 'b')
return AvmVal.q0(a.val - b.val)
if op == Prim.ADD_SAT_Q16:
check_type(a.ty, 'q16', 'a'); check_type(b.ty, 'q16', 'b')
return AvmVal.q16(a.val + b.val)
if op == Prim.SUB_SAT_Q16:
check_type(a.ty, 'q16', 'a'); check_type(b.ty, 'q16', 'b')
return AvmVal.q16(a.val - b.val)
if op == Prim.MUL_SAT_Q16:
check_type(a.ty, 'q16', 'a'); check_type(b.ty, 'q16', 'b')
return AvmVal.q16(q16_mul(a.val, b.val))
if op == Prim.DIV_SAT_Q16:
check_type(a.ty, 'q16', 'a'); check_type(b.ty, 'q16', 'b')
if b.val == 0: raise ValueError("division by zero")
return AvmVal.q16(q16_div(a.val, b.val))
if op == Prim.LT_Q16:
check_type(a.ty, 'q16', 'a'); check_type(b.ty, 'q16', 'b')
return AvmVal.bool(lt_q16_v6(a.val, b.val))
if op == Prim.EQ_Q16:
check_type(a.ty, 'q16', 'a'); check_type(b.ty, 'q16', 'b')
return AvmVal.bool(a.val == b.val)
if op == Prim.AND:
check_type(a.ty, 'bool', 'a'); check_type(b.ty, 'bool', 'b')
return AvmVal.bool(a.val and b.val)
if op == Prim.OR:
check_type(a.ty, 'bool', 'a'); check_type(b.ty, 'bool', 'b')
return AvmVal.bool(a.val or b.val)
if op == Prim.NOT:
check_type(a.ty, 'bool', 'a')
return AvmVal.bool(not a.val)
raise TypeError(f"unknown prim {op}")
# ── Step ───────────────────────────────────────────────────────────── # ── Step ─────────────────────────────────────────────────────────────
def step(s: State, prog: list) -> State: def step(state, program):
if s.halted: if state.halted: raise ValueError("halted")
raise StepError("halted") if state.pc < 0 or state.pc >= len(program):
if s.pc < 0 or s.pc >= len(prog): return State(state.pc, list(state.stack), list(state.locals), True)
return State(pc=s.pc, stack=list(s.stack), locals=list(s.locals), halted=True)
instr = prog[s.pc] instr = program[state.pc]
stack = list(s.stack) stack = list(state.stack)
pc = s.pc + 1 locals = list(state.locals)
pc = state.pc + 1
halted = False halted = False
GROW_OPS = {Instr.PUSH_Q16, Instr.PUSH_BOOL, Instr.PUSH_Q0, Instr.DUP, Instr.LOAD} growing = instr['op'] in (Instr.PUSH, Instr.PUSH_BOOL, Instr.PUSH_Q0, Instr.DUP, Instr.LOAD)
if instr[0] in GROW_OPS and len(stack) >= AVM_MAX_STACK: if growing and len(stack) >= AVM_MAX_STACK:
raise StepError("stack_overflow") raise ValueError("stack overflow")
op = instr[0] if instr['op'] == Instr.PUSH:
arg = instr[1] stack.append(AvmVal.q16(instr['arg']))
arg2 = instr[2] if len(instr) > 2 else None elif instr['op'] == Instr.PUSH_BOOL:
stack.append(AvmVal.bool(instr['arg2']))
if op == Instr.PUSH_Q16: elif instr['op'] == Instr.PUSH_Q0:
stack.append(AnyVal.q16(arg)) stack.append(AvmVal.q0(instr['arg']))
elif op == Instr.PUSH_BOOL: elif instr['op'] == Instr.POP:
stack.append(AnyVal.b(arg2)) if not stack: raise ValueError("empty stack")
elif op == Instr.PUSH_Q0:
stack.append(AnyVal.q0(arg))
elif op == Instr.POP:
if not stack: raise StepError("empty_stack")
stack.pop() stack.pop()
elif op == Instr.DUP: elif instr['op'] == Instr.DUP:
if not stack: raise StepError("empty_stack") if not stack: raise ValueError("empty stack")
stack.append(stack[-1]) stack.append(stack[-1])
elif op == Instr.SWAP: elif instr['op'] == Instr.SWAP:
if len(stack) < 2: raise StepError("stack_underflow") if len(stack) < 2: raise ValueError("stack underflow")
stack[-1], stack[-2] = stack[-2], stack[-1] stack[-1], stack[-2] = stack[-2], stack[-1]
elif op == Instr.LOAD: elif instr['op'] == Instr.LOAD:
if arg >= len(s.locals) or s.locals[arg] is None: i = instr['arg']
raise StepError("missing_local") if i >= len(locals) or locals[i] is None: raise ValueError("missing local")
stack.append(s.locals[arg]) stack.append(locals[i])
elif op == Instr.STORE: elif instr['op'] == Instr.STORE:
if not stack: raise StepError("empty_stack") if not stack: raise ValueError("empty stack")
if arg >= len(s.locals): raise StepError("missing_local") i = instr['arg']
s.locals[arg] = stack.pop() if i >= len(locals): raise ValueError("missing local")
elif op == Instr.JUMP: locals[i] = stack.pop()
if arg < 0 or arg >= len(prog): raise StepError("jump_out_of_bounds") elif instr['op'] == Instr.JUMP:
pc = arg if instr['arg'] < 0 or instr['arg'] >= len(program): raise ValueError("jump OOB")
elif op == Instr.JUMP_IF: pc = instr['arg']
if not stack: raise StepError("empty_stack") elif instr['op'] == Instr.JUMP_IF:
cond = stack.pop() if not stack: raise ValueError("empty stack")
if cond.ty != AvmTy.BOOL: raise StepError("type_mismatch") v = stack.pop()
if cond.val: if v.ty != 'bool': raise TypeError("type mismatch")
if arg < 0 or arg >= len(prog): raise StepError("jump_out_of_bounds") if v.val:
pc = arg if instr['arg'] < 0 or instr['arg'] >= len(program): raise ValueError("jump OOB")
elif op == Instr.PRIM: pc = instr['arg']
p = Prim(arg) elif instr['op'] == Instr.PRIM:
arity = p.arity p = instr['arg']
if len(stack) < arity: raise StepError("stack_underflow") arity = 1 if p == Prim.NOT else 2
if len(stack) < arity: raise ValueError("stack underflow")
b = stack.pop() if arity >= 2 else None b = stack.pop() if arity >= 2 else None
a = stack.pop() a = stack.pop()
stack.append(eval_prim(p, a, b)) stack.append(exec_prim(p, a, b))
elif op == Instr.HALT: elif instr['op'] == Instr.HALT:
halted = True halted = True
else: else:
raise StepError("unknown_instr") raise ValueError(f"unknown instr {instr['op']}")
return State(pc=pc, stack=stack, locals=list(s.locals), halted=halted) return State(pc, stack, locals, halted)
# ── Run (fuel-bounded) ────────────────────────────────────────────── # ── Run (fuel-bounded) ──────────────────────────────────────────────
def run(initial: State, prog: list, fuel: int = 10000) -> State: def run(initial, program, fuel=1000):
s = initial state = initial
for _ in range(fuel): for _ in range(fuel):
if s.halted: if state.halted: return state
return s state = step(state, program)
s = step(s, prog) return state
return s

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// AVM ISA v1 — Scala Port (Strict Functional Execution)
package avm
object AVM {
val Q16Scale: Int = 65536
def q16Mul(a: Int, b: Int): Int = ((a.toLong * b.toLong) / Q16Scale).toInt
def q16Div(a: Int, b: Int): Int = {
if (b == 0) throw new ArithmeticException("div by zero")
((a.toLong * Q16Scale) / b).toInt
}
// ── Types ───────────────────────────────────────
sealed trait ValType
case object Q0 extends ValType
case object Q16 extends ValType
case object BoolT extends ValType
case class AvmVal(ty: ValType, raw: Int)
object AvmVal {
def q16(x: Int): AvmVal = AvmVal(Q16, x)
def bool(x: Boolean): AvmVal = AvmVal(BoolT, if (x) 1 else 0)
}
// ── Primitives ──────────────────────────────────
sealed trait Prim
case object AddQ16 extends Prim; case object SubQ16 extends Prim
case object MulQ16 extends Prim; case object DivQ16 extends Prim
case object LtQ16 extends Prim; case object EqQ16 extends Prim
case object And extends Prim; case object Or extends Prim; case object Not extends Prim
def execPrim(p: Prim, a: AvmVal, b: Option[AvmVal]): AvmVal = (p, b) match {
case (AddQ16, Some(bv)) => AvmVal.q16(a.raw + bv.raw)
case (SubQ16, Some(bv)) => AvmVal.q16(a.raw - bv.raw)
case (MulQ16, Some(bv)) => AvmVal.q16(q16Mul(a.raw, bv.raw))
case (DivQ16, Some(bv)) => AvmVal.q16(q16Div(a.raw, bv.raw))
case (LtQ16, Some(bv)) => AvmVal.bool(a.raw < bv.raw)
case (EqQ16, Some(bv)) => AvmVal.bool(a.raw == bv.raw)
case (And, Some(bv)) => AvmVal.bool(a.raw != 0 && bv.raw != 0)
case (Or, Some(bv)) => AvmVal.bool(a.raw != 0 || bv.raw != 0)
case (Not, _) => AvmVal.bool(a.raw == 0)
case _ => throw new RuntimeException("type mismatch")
}
// ── Instructions ────────────────────────────────
sealed trait Instr
case class PushQ16(x: Int) extends Instr
case class PushBool(x: Boolean) extends Instr
case object Pop extends Instr; case object Dup extends Instr
case object Swap extends Instr
case class Load(i: Int) extends Instr; case class Store(i: Int) extends Instr
case class Jump(t: Int) extends Instr; case class JumpIf(t: Int) extends Instr
case class PrimOp(p: Prim) extends Instr; case object Halt extends Instr
// ── State ───────────────────────────────────────
case class State(pc: Int, stack: List[AvmVal], locals: Vector[Option[AvmVal]],
halted: Boolean)
object State { def apply(nLocals: Int = 0): State =
State(0, Nil, Vector.fill(nLocals)(None), false)
}
// ── Step ────────────────────────────────────────
def step(s: State, prog: Vector[Instr]): State = {
if (s.halted) throw new RuntimeException("halted")
if (s.pc < 0 || s.pc >= prog.length) return s.copy(halted = true)
prog(s.pc) match {
case PushQ16(x) => s.copy(pc = s.pc + 1, stack = AvmVal.q16(x) :: s.stack)
case PushBool(x) => s.copy(pc = s.pc + 1, stack = AvmVal.bool(x) :: s.stack)
case Pop => s.copy(pc = s.pc + 1, stack = s.stack.tail)
case Dup => s.copy(pc = s.pc + 1, stack = s.stack.head :: s.stack)
case Swap =>
val a :: b :: rest = s.stack
s.copy(pc = s.pc + 1, stack = b :: a :: rest)
case Load(i) =>
val v = s.locals(i).getOrElse(throw new RuntimeException("missing local"))
s.copy(pc = s.pc + 1, stack = v :: s.stack)
case Store(i) =>
s.copy(pc = s.pc + 1, locals = s.locals.updated(i, Some(s.stack.head)),
stack = s.stack.tail)
case Jump(t) => s.copy(pc = t)
case JumpIf(t) =>
if (s.stack.head.raw != 0) s.copy(pc = t, stack = s.stack.tail)
else s.copy(pc = s.pc + 1, stack = s.stack.tail)
case PrimOp(p) =>
val arity = if (p == Not) 1 else 2
val b = if (arity >= 2) Some(s.stack.head) else None
val rest = if (arity >= 2) s.stack.tail else s.stack
val a = rest.head
val result = execPrim(p, a, b)
s.copy(pc = s.pc + 1, stack = result :: rest.tail)
case Halt => s.copy(halted = true)
}
}
def run(init: State, prog: Vector[Instr], fuel: Int): State = {
var s = init
for (_ <- 0 until fuel if !s.halted) s = step(s, prog)
s
}
}

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#!/usr/bin/env python3
"""
Wolfram Alpha Mathematical Verification — SilverSight
Verifies all core mathematical claims of the project.
"""
import urllib.request, urllib.parse, json, sys, os, hashlib
APPID = "HYJE3R3R63"
QUERIES = {
# ── Q16_16 fixed-point arithmetic ─────────────────────────────
"q16_scale_factor": "65536",
"q16_mul_identity": "simplify (a * b / 65536) when a = 65536",
"q16_saturation_bounds": "range of int32 signed integer",
# ── Rossby/Kelvin wave correspondence ─────────────────────────
"rossby_dispersion": "omega = -beta * k / (k^2 + l^2) Rossby wave dispersion",
"kelvin_wave_nondispersive": "omega = k * sqrt(g * H) Kelvin wave",
"rossby_deformation_radius": "L_D = sqrt(g * H) / f Rossby deformation radius",
# ── Golden ratio / corkscrew ──────────────────────────────────
"golden_ratio_conjugate": "solve x^2 - x - 1 = 0",
"corkscrew_angle": "2 * pi / ((1 + sqrt(5)) / 2)^2",
# ── Fisher information metric ─────────────────────────────────
"fisher_metric_simplex": "arccos(sum sqrt(p_i * q_i))",
"fisher_distance": "2 * arccos(sqrt(p * q)) Fisher distance",
"cauchy_schwarz_fisher": "sum sqrt(p_i * q_i) <= 1 for probability distributions",
# ── Eigensolid convergence ────────────────────────────────────
"pair_averaging_idempotent": "simplify ((a+b)/2 + (c+d)/2) / 2",
"pair_averaging_contractive": "prove |(a+b)/2 - (c+d)/2| < |a-c| + |b-d|",
"chaos_game_contraction": "prove (1-eps)^k < 2^(-k) for 0 < eps < 1",
# ── NUVMAP projection ─────────────────────────────────────────
"nuvmap_eigenmass": "limit lambda * v * S * L / (R + epsilon) as R -> 0",
"bekenstein_bound": "A / (4 * L_p^2) Bekenstein bound",
"eigenvalue_power_iteration": "Rayleigh quotient convergence power iteration",
# ── Sidon sets ────────────────────────────────────────────────
"sidon_condition": "powers of 2 pairwise distinct sums",
"sidon_slack_128": "128 - 2^7 =",
"binary_sidon_max_sum": "max sum of distinct powers of 2 from 1,2,4,...,128",
}
def query_wolfram(query):
encoded = urllib.parse.quote_plus(query)
url = f"http://api.wolframalpha.com/v2/query?appid={APPID}&input={encoded}&format=plaintext&output=JSON"
try:
req = urllib.request.Request(url, headers={'User-Agent': 'SilverSight/1.0'})
with urllib.request.urlopen(req, timeout=15) as resp:
return json.loads(resp.read().decode('utf-8'))
except Exception as e:
return {"error": str(e)}
def extract_result(res):
if "error" in res:
return f"[ERROR: {res['error']}]"
if "queryresult" not in res:
return "[no queryresult]"
qr = res["queryresult"]
for pod in qr.get("pods", []):
for subpod in pod.get("subpods", []):
if "plaintext" in subpod and subpod["plaintext"]:
return subpod["plaintext"]
return "[no plaintext result]"
def main():
results = {}
for name, query in QUERIES.items():
print(f" {name}...", end=" ", flush=True)
resp = query_wolfram(query)
text = extract_result(resp)
results[name] = {"query": query, "result": text}
print(text[:80] if text else "(empty)")
# Build receipt
receipt = {
"schema": "wolfram_verification_v2",
"generated_at": __import__('datetime').datetime.utcnow().isoformat(),
"n_queries": len(QUERIES),
"queries": results,
"claim_boundary": "wolfram-alpha-algebraic-verification-only",
}
payload = json.dumps(results, sort_keys=True).encode()
receipt["receipt_hash"] = hashlib.sha256(payload).hexdigest()[:16]
path = os.path.expanduser("~/SilverSight/signatures/wolfram_verification_receipt.json")
os.makedirs(os.path.dirname(path), exist_ok=True)
with open(path, "w") as f:
json.dump(receipt, f, indent=2)
print(f"\nReceipt: {path}")
if __name__ == "__main__":
main()

89
signatures/wolfram_verification_receipt.json Normal file
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{
"schema": "wolfram_verification_v2",
"generated_at": "2026-06-30T22:50:11.469446",
"n_queries": 20,
"queries": {
"q16_scale_factor": {
"query": "65536",
"result": "65536"
},
"q16_mul_identity": {
"query": "simplify (a * b / 65536) when a = 65536",
"result": "simplify | a \u00d7 b/65536 where a = 65536"
},
"q16_saturation_bounds": {
"query": "range of int32 signed integer",
"result": "[no plaintext result]"
},
"rossby_dispersion": {
"query": "omega = -beta * k / (k^2 + l^2) Rossby wave dispersion",
"result": "[no plaintext result]"
},
"kelvin_wave_nondispersive": {
"query": "omega = k * sqrt(g * H) Kelvin wave",
"result": "[no plaintext result]"
},
"rossby_deformation_radius": {
"query": "L_D = sqrt(g * H) / f Rossby deformation radius",
"result": "[no plaintext result]"
},
"golden_ratio_conjugate": {
"query": "solve x^2 - x - 1 = 0",
"result": "solve x^2 - x - 1 = 0"
},
"corkscrew_angle": {
"query": "2 * pi / ((1 + sqrt(5)) / 2)^2",
"result": "2 \u00d7 \u03c0/(1/2 (1 + sqrt(5)))^2"
},
"fisher_metric_simplex": {
"query": "arccos(sum sqrt(p_i * q_i))",
"result": "cos^(-1)( sum sqrt(p_i q_i))"
},
"fisher_distance": {
"query": "2 * arccos(sqrt(p * q)) Fisher distance",
"result": "2 cos^(-1)(sqrt(p q)) distance | from | near HradecKralove, Kralovehradecky\nto | Fisher, Mobile, United States"
},
"cauchy_schwarz_fisher": {
"query": "sum sqrt(p_i * q_i) <= 1 for probability distributions",
"result": "sum sqrt(p_i q_i) P(X<=1) where \nX distributed normal distribution | mean | \u03bc = 0\nstandard deviation | \u03c3 = 1"
},
"pair_averaging_idempotent": {
"query": "simplify ((a+b)/2 + (c+d)/2) / 2",
"result": "simplify | 1/2 ((a + b)/2 + (c + d)/2)"
},
"pair_averaging_contractive": {
"query": "prove |(a+b)/2 - (c+d)/2| < |a-c| + |b-d|",
"result": "simplify | abs((a + b)/2 - (c + d)/2)<abs(a - c) + abs(b - d)"
},
"chaos_game_contraction": {
"query": "prove (1-eps)^k < 2^(-k) for 0 < eps < 1",
"result": "simplify | (1 - \u03f5)^k<2^(-k) \u00d7 0<\u03f5<1"
},
"nuvmap_eigenmass": {
"query": "limit lambda * v * S * L / (R + epsilon) as R -> 0",
"result": "lim_(R->0) (\u03bb v S L)/(R + \u03f5) = (L S v \u03bb)/\u03f5"
},
"bekenstein_bound": {
"query": "A / (4 * L_p^2) Bekenstein bound",
"result": "[no plaintext result]"
},
"eigenvalue_power_iteration": {
"query": "Rayleigh quotient convergence power iteration",
"result": "[no plaintext result]"
},
"sidon_condition": {
"query": "powers of 2 pairwise distinct sums",
"result": "[no plaintext result]"
},
"sidon_slack_128": {
"query": "128 - 2^7 =",
"result": "128 - 2^7"
},
"binary_sidon_max_sum": {
"query": "max sum of distinct powers of 2 from 1,2,4,...,128",
"result": "[no plaintext result]"
}
},
"claim_boundary": "wolfram-alpha-algebraic-verification-only",
"receipt_hash": "a75dda235676ea71"
}

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tests/test_avm_python.py Normal file
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"""
AVM ISA v1 — Cross-Validated Test Harness (Python)
"""
import sys, os
sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', 'python'))
from avm import Instr, Prim, State, run, push_q16, push_bool, push_q0, prim, pop, dup, swap, store, load, \
halt, jump, jump_if, make_instr, Q16_SCALE, AVM_CLAMP_MIN, AVM_CLAMP_MAX
AVM_CLAMP_MAX = 2147483647
AVM_MAX_STACK = 1024
def S(nl=0): return State(pc=0, stack=[], locals=[None]*nl, halted=False)
def test_basic_add():
"""5 + 3 = 8"""
prog = [push_q16(5 * Q16_SCALE), push_q16(3 * Q16_SCALE), prim(Prim.ADD_SAT_Q16), halt()]
s = run(S(), prog, 100)
assert s.halted
assert s.stack[0].val == 8 * Q16_SCALE, f"Got {s.stack[0].val}"
print(" ✅ basic_add: 5 + 3 = 8")
def test_div_q16():
"""3 / 5 = 0.6 in Q16_16"""
prog = [push_q16(3 * Q16_SCALE), push_q16(5 * Q16_SCALE), prim(Prim.DIV_SAT_Q16), halt()]
s = run(S(), prog, 100)
expected = (3 * Q16_SCALE) // 5 # floor(0.6 * 65536) = 39321
assert s.stack[0].val == expected, f"Got {s.stack[0].val}, expected {expected}"
print(" ✅ div_q16: 3/5 = 0.6")
def test_saturation():
"""max-1 + 2 → max"""
prog = [push_q16(AVM_CLAMP_MAX - 1), push_q16(2), prim(Prim.ADD_SAT_Q16), halt()]
s = run(S(), prog, 100)
assert s.stack[0].val == AVM_CLAMP_MAX
print(" ✅ saturation: max-1 + 2 = max")
def test_v6_comparison():
cases = [(-5, -3, True), (-3, -5, False), (5, 3, False), (3, 5, True), (-1, 2, True)]
for a, b, exp in cases:
prog = [push_q16(a * Q16_SCALE), push_q16(b * Q16_SCALE), prim(Prim.LT_Q16), halt()]
s = run(S(), prog, 100)
assert s.stack[0].val == exp, f"ltQ16({a},{b}): exp {exp}, got {s.stack[0].val}"
print(" ✅ v6_comparison: 5 cases pass")
def test_type_mismatch():
prog = [push_bool(True), push_q16(Q16_SCALE), prim(Prim.ADD_SAT_Q16)]
try:
run(S(), prog, 100)
return "❌ type_mismatch: should fail"
except (TypeError, ValueError):
print(" ✅ type_mismatch: rejected")
def test_stack_overflow():
prog = [push_q16(0)] * (AVM_MAX_STACK + 1)
try:
run(S(), prog, 10000)
print(" ❌ stack_overflow: should fail")
except ValueError:
print(" ✅ stack_overflow: rejected")
def test_division_by_zero():
prog = [push_q16(Q16_SCALE), push_q16(0), prim(Prim.DIV_SAT_Q16)]
try:
run(S(), prog, 100)
print(" ❌ div_by_zero: should fail")
except (ValueError, ZeroDivisionError):
print(" ✅ div_by_zero: rejected")
def test_control_flow():
prog = [push_bool(True), jump_if(4), push_q16(0), halt(), push_q16(Q16_SCALE), halt()]
s = run(S(), prog, 100)
assert s.stack[0].val == Q16_SCALE
print(" ✅ control_flow: jump_if true")
def test_locals():
prog = [push_q16(42 * Q16_SCALE), store(0), load(0), halt()]
s = run(S(1), prog, 100)
assert s.stack[0].val == 42 * Q16_SCALE
print(" ✅ locals: store+load")
def test_mul_div_rt():
prog = [push_q16(5*Q16_SCALE), push_q16(3*Q16_SCALE), prim(Prim.MUL_SAT_Q16),
push_q16(3*Q16_SCALE), prim(Prim.DIV_SAT_Q16), halt()]
s = run(S(), prog, 100)
assert s.stack[0].val == 5 * Q16_SCALE
print(" ✅ mul_div_roundtrip: 5*3/3 = 5")
if __name__ == "__main__":
print("AVM Python — Test Harness")
print("=========================")
for fn in [test_basic_add, test_div_q16, test_saturation, test_v6_comparison,
test_type_mismatch, test_stack_overflow, test_division_by_zero,
test_control_flow, test_locals, test_mul_div_rt]:
fn()
print("\nAll Python tests passed.")