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    "result": "## Preconditions\n\n1. Every emitted program is a single MLIR module body consisting of one or more module-scope `dataflow.thread` definitions followed by exactly one `func.func` named `@host`, in that order.\n2. Every `dataflow.thread` definition is declared with `private` visibility and a symbol name, and every symbol name is distinct within the module.\n3. Every `dataflow.thread` definition carries exactly one `domain(#dataflow.thread_domain<...>)` clause, which is either a closed dense domain (`dense`) or a dynamic-work domain (`dynamic_work, work_item_arg = N`); no other domain kind appears.\n4. A `dynamic_work` domain always names a `work_item_arg` ordinal `N`, and that ordinal is a valid zero-based index into the definition's own declared argument list, so a dynamic-work definition always has at least one declared argument.\n5. A `dynamic_work` definition never carries a coordinate (`iv`) clause \u2014 its coordinate rank is zero.\n6. A `dense` definition never carries a `work_item_arg` ordinal, and it carries an `iv (...)` clause exactly when its coordinate rank is nonzero; every coordinate argument in that clause has type `index`.\n7. Every `dataflow.thread` definition's entry signature has the fixed three-part shape: a parenthesized data-argument list, then a control clause `ctrl (%thread_ctrl: none)`, then (dense only, rank > 0) the coordinate clause \u2014 in that fixed order.\n8. Every `dataflow.thread` definition has a non-empty region terminated by a `dataflow.thread.yield`, which either takes no operands or takes exactly the control value `%thread_ctrl` of type `none`; the region contains no other operations.\n9. Each `dataflow.thread` definition is accompanied by exactly one `dataflow.thread.launch` in the host function, and the launches appear in the same order as the definitions they target.\n10. Every `dataflow.thread.launch` references its definition by the definition's symbol via `@`-symbol reference, and that symbol is always defined in the same module.\n11. The operand list of every launch has exactly the same arity as the referenced definition's data-argument list, and the i-th operand's type equals the i-th declared argument type of the definition.\n12. The explicit type signature written on every launch, `(types...) -> !dataflow.thread_token`, lists exactly the referenced definition's data-argument types in order and always produces the single result type `!dataflow.thread_token`.\n13. Every launch carries a `grid(...)` clause exactly when the referenced definition is a dense definition of nonzero coordinate rank, and the number of grid upper bounds equals that coordinate rank; launches targeting rank-zero or dynamic-work definitions carry no grid clause.\n14. Every grid upper bound operand has type `index`.\n15. Every launch binds its token result to an SSA name, and each such token name is unique within the host function.\n16. Every `dataflow.thread.wait` operand is the token produced by a preceding launch in the same block, and is written with the result type `!dataflow.thread_token`.\n17. Every SSA value used as a launch operand or grid bound is defined earlier in the host function \u2014 either as the function's own block argument or by an `arith.constant` in the entry block \u2014 so all uses are dominated by their definitions.\n18. The host function is terminated by `return` and returns no results.\n19. No `scf.forall` appears anywhere in an emitted program; the carrier shape is purely definition-plus-launch, with no mapping attribute, no `shared_outs`, no forall results and no combining region.\n20. No launch produces or consumes results other than its thread token, and no value flows back out of a thread definition to the host.\n\n## Sampling conventions\n\n1. The grammar emits between 1 and 3 thread definitions per module, never zero and never more than three.\n2. Definition symbols follow the fixed scheme `t_<i>` where `<i>` is the definition's zero-based position, and launch tokens follow the parallel scheme `%token_<i>` for the same index.\n3. Each definition's data arity is sampled from 0 to 3 inclusive; arities above three are never emitted.\n4. Argument types are drawn from a fixed cyclic palette of five types \u2014 `i32`, `f32`, `i64`, `index`, `memref<?xf32>` \u2014 by taking a contiguous run starting at a per-definition offset of 0 to 4, so the argument type list of any definition is always a contiguous rotation-free slice of that palette rather than an arbitrary combination; with arity at most 3 and offset at most 4, only palette positions 0 through 6 are ever reached.\n5. Data arguments are named `%arg_0`, `%arg_1`, ... in ascending order with no gaps.\n6. Coordinate rank for dense definitions is sampled from 0 to 2 inclusive, so no dense domain of rank 3 or higher is ever emitted; coordinate arguments are named `%coord_0`, `%coord_1`, ... in order.\n7. Dynamic-work versus dense is chosen by an even binary selection, but the dynamic branch is only taken when arity is greater than zero; zero-arity definitions are therefore always dense, and choosing the dynamic branch also forces the definition's recorded coordinate rank to zero.\n8. The `work_item_arg` ordinal of a dynamic-work definition is drawn uniformly over the whole valid range `0 .. arity-1`, so it may select any declared argument, not only the first or last.\n9. The control argument is always spelled exactly `%thread_ctrl: none`; no other control name or type is emitted.\n10. Both yield forms \u2014 the bare `dataflow.thread.yield` and the operand form `dataflow.thread.yield %thread_ctrl : none` \u2014 are emitted, chosen independently per definition.\n11. Each definition block is followed by a blank line; definitions and the host function are separated by that fixed whitespace skeleton.\n12. The host function has the fixed signature `func.func @host(%m_ref: memref<?xf32>)`, so the only memref value in scope is the function's block argument rather than a locally allocated buffer.\n13. The host entry block always begins with the same four-constant preamble, regardless of what the launches actually need: `%c_i32 = arith.constant 1 : i32`, `%c_f32 = arith.constant 1.000000e+00 : f32`, `%c_i64 = arith.constant 1 : i64`, and `%c_idx = arith.constant 4 : index`.\n14. Launch operands are selected by a name palette that mirrors the type palette one-for-one (`%c_i32`, `%c_f32`, `%c_i64`, `%c_idx`, `%m_ref`) using the same offset and position, so operand identity is fully determined by the argument's type slot and the same constant is reused for every occurrence of a given type.\n15. Every grid upper bound is the single constant `%c_idx` (value 4), so all launch domains are square and no varying or non-constant extents are exercised.\n16. A `dataflow.thread.wait` is optionally emitted immediately after each launch, chosen independently per launch, so a program may mix awaited and un-awaited launches; waits are never grouped, reordered, or placed anywhere other than directly after their own launch.\n17. Launch bodies are emitted in a fixed textual order \u2014 operands, then optional grid clause, then the `: (types) -> !dataflow.thread_token` signature \u2014 and always with the explicit type signature spelled out rather than elided.\n18. All launches are placed in a single straight-line block between the constant preamble and `return`, with no control flow, nesting, or interleaved computation.\n19. Indentation is fixed at two spaces for all operations inside the host function and inside thread regions.",
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