[ { "api_error_status": null, "duration_api_ms": 59137, "duration_ms": 59177, "fast_mode_disabled_reason": "sdk_opt_in_required", "fast_mode_state": "off", "first_content_frame_ms": 1622, "is_error": false, "modelUsage": { "claude-opus-5": { "cacheCreationInputTokens": 5201, "cacheReadInputTokens": 0, "canonicalModel": "claude-opus-5", "contextWindow": 1000000, "costBasis": "list", "costUSD": 0.16337, "inputTokens": 2, "maxOutputTokens": 64000, "outputTokens": 4454, "provider": "firstParty", "thinkingTokens": 1544, "webSearchRequests": 0 } }, "num_turns": 1, "permission_denials": [], "queued_turn_count": 0, "result": "## Preconditions\n\n1. A valid input is a single top-level `module { ... }` whose body contains only `dataflow.thread` definitions and nothing else.\n2. Each thread is a private symbol definition of the form `dataflow.thread private @NAME domain(#dataflow.thread_domain)(...) ctrl (...) { ... }`, i.e. a thread must carry an explicit domain attribute, a data-argument list, and a separate control-argument list.\n3. Every thread's data-argument list declares exactly four arguments in the fixed order `%value: i32`, `%mem: memref<4xi32>`, `%chan: !dataflow.channel`, `%flag: i1`, and its control list declares exactly one argument `%start: none`.\n4. Every thread body is terminated by `dataflow.thread.yield` with no operands.\n5. Every thread body begins by materialising the index constants it may need \u2014 `arith.constant 0 : index`, `arith.constant 1 : index`, `arith.constant 4 : index` \u2014 before any nested scope or region that uses them, so all index operands are dominated by their definitions.\n6. Each thread body contains exactly one `loom.spatial_region` operation; a thread never contains zero regions and never contains two or more.\n7. The `loom.spatial_region` is written in generic (quoted-op) form and must carry both `operandSegmentSizes = array` and `resultSegmentSizes = array` as inherent properties in a `<{...}>` clause.\n8. The four operand segments are positional and ordered as value inputs, stream inputs, memory imports, stream outputs; the operand list of the op must match that ordering and the segment counts must sum to the number of operands supplied.\n9. The entry block `^bb0` of the region takes exactly one argument per region operand, in the same order and with the same type as the corresponding operand (i32 for value inputs, `!dataflow.channel` for stream bindings, `memref<4xi32>` for memory imports), and takes no arguments at all when the operand list is empty.\n10. The region body is terminated by a `loom.spatial_yield` operation, also in generic form, carrying its own `operandSegmentSizes = array`; the number of values it yields equals the first entry of the region's `resultSegmentSizes`, and both are `0` for a region with no results.\n11. The trailing function type of the generic `loom.spatial_region` op must agree exactly with the operand types and result types (e.g. `(i32, memref<4xi32>) -> ()`, `(i32) -> i32`, `() -> ()`).\n12. Every `loom.spatial_region` carries a `graph_name` string attribute and a `source_maps` array attribute, both mandatory.\n13. `source_maps` is non-empty exactly when the region binds a stream input (one affine map per such binding, here `affine_map<() -> ()>`); regions with no stream input carry `source_maps = []`.\n14. All operands of `loom.spatial_region` are SSA values defined in the enclosing thread (its block arguments), never values produced inside the region.\n15. Region operations that perform channel traffic \u2014 `dataflow.channel.send` and `dataflow.channel.receive` on a stream-bound block argument \u2014 occur only when the `loom.spatial_region` sits directly in the thread body and is not enclosed in any structured-control-flow scope; a region nested inside `scf.for` or `scf.if` never binds a channel and never contains channel send/receive.\n16. Permitted enclosing scopes for the region are only `scf.for` and `scf.if`, possibly an `scf.if` nested inside an `scf.for`; both are result-free forms with implicit terminators, the `scf.for` bounds and step being index values defined in the thread body and the `scf.if` condition being an `i1` value defined in the thread body.\n17. `memref.store` inside a region stores an i32 value into a memory-import block argument at a locally defined constant index within the `memref<4xi32>` bounds, and its types match the memref element type.\n18. `dataflow.channel.send` sends a value of the channel's element type on a stream-output binding, and `dataflow.channel.receive` produces a value of the channel's element type from a stream-input binding.\n19. Values produced by a region (when `resultSegmentSizes` declares one) need not be consumed; an unused region result is well formed.\n20. Thread arguments need not all be used; `%start`, `%flag`, `%chan`, and `%mem` may be left unreferenced in a given thread.\n\n## Sampling conventions\n\n1. The module contains between one and three thread definitions inclusive, never zero and never more than three.\n2. Threads are named by a zero-based counter, `@thread_0`, `@thread_1`, `@thread_2`, in emission order.\n3. The `graph_name` attribute of a thread's region reuses that same counter, `\"graph_0\"`, `\"graph_1\"`, `\"graph_2\"`, so graph names are unique per module and tied to the thread index rather than being independently chosen.\n4. Each thread independently draws one of exactly four nesting shapes: no wrapper; a single `scf.for`; a single `scf.if`; or an `scf.if` nested inside an `scf.for` \u2014 nesting depth never exceeds two and no other control-flow op (e.g. `scf.while`, `scf.parallel`, `scf.execute_region`, branches) is ever emitted.\n5. The `scf.for` is always the fixed loop `scf.for %i = %c0 to %c4 step %c1` (trip count 4, unit step), and the `scf.if` always tests the thread's `%flag` argument and has no `else` region.\n6. All three index constants `%c0 = 0`, `%c1 = 1`, `%c4 = 4` are emitted in every thread even when the chosen nesting shape uses none of them.\n7. Each thread independently draws one of exactly five region forms: a store form (value input plus memory import, no results), an empty form (no operands, no results), a stream-output form (value input plus outgoing channel), a value form (one value input, one i32 result), and a stream-input form (incoming channel plus memory import).\n8. When nesting is present, the two channel-using forms are replaced deterministically rather than resampled: the stream-output form degrades to the empty form, and the stream-input form degrades to the store form, so nested threads only ever show the store, empty, or value forms.\n9. Region body contents are fixed per form: the store form does one `memref.store` of the payload at index 0; the empty form has an empty entry block; the stream-output form does one `dataflow.channel.send`; the value form computes `arith.addi %payload, %payload`; the stream-input form does one `dataflow.channel.receive` followed by a `memref.store` at index 0.\n10. Region interfaces are limited to at most two operands and at most one result; the second result segment is always `0`, and no region ever combines a stream input with a stream output or uses more than one binding of a given kind.\n11. Only the segment patterns `1,0,1,0`, `0,0,0,0`, `1,0,0,1`, `1,0,0,0` and `0,1,1,0` are emitted; other admissible operand mixes are never produced.\n12. The single result-producing form names its result `%sum_N` using the thread index and leaves it unused; no consumer of a region result is ever emitted.\n13. `loom.spatial_region` and `loom.spatial_yield` are always printed in generic quoted form with explicit `<{...}>` property dictionaries, while `arith`, `memref`, `scf`, and `dataflow` operations are always printed in their custom assembly form.\n14. Types are monomorphic throughout: payload type is always `i32`, memory type always `memref<4xi32>`, channel type always `!dataflow.channel`, index constants always `index`, and the condition always `i1`.\n15. SSA names are fixed per position: thread arguments `%value`, `%mem`, `%chan`, `%flag`, `%start`; loop induction variable `%i`; region block arguments `%payload`, `%memory`, `%output`, `%channel`, `%target`; region-local values `%zero`, `%doubled`, `%message`.\n16. The only affine map ever emitted in `source_maps` is the nullary `affine_map<() -> ()>`, and only in the stream-input form.\n17. Indentation is a fixed skeleton \u2014 two spaces for the thread, four for body operations and wrappers, six for the region op and its attributes \u2014 and the region's own indentation does not change with nesting depth.\n18. 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