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    "result": "## Preconditions\n\n1. Every emitted program is a single MLIR module body consisting of a top-level loop-annotation attribute alias definition followed by one or more top-level function definitions, with no enclosing `module { ... }` wrapper.\n2. The attribute alias `#loop_ann` is defined exactly once, at the top of the file, as `#llvm.loop_annotation<mustProgress = true>`, before any function that may reference it.\n3. Every callable is an `llvm.func` with an explicit, non-empty body region written between braces; no callable is declared without a body, and no other callable-defining operation (for example `func.func`) ever appears.\n4. Every `llvm.func` has a single result type `i32` and returns through `llvm.return %r : i32` (or `llvm.return %iv : i32`), so every terminating block of every function yields exactly one `i32` value.\n5. Every function's parameters are explicitly typed in the signature, drawn only from `i1` (branch conditions) and `i32` (data values), and every SSA value referenced in a body is either such a parameter, a block argument declared on that block, or a value defined earlier in the same block.\n6. All intra-function control flow is expressed in `cf` dialect form: only `cf.br` and `cf.cond_br` terminate blocks; no `scf` operation, no unstructured `llvm.br`/`llvm.cond_br`, and no switch-like terminator ever appears.\n7. Every block other than the entry block is introduced by an explicit `^label:` (or `^label(%arg: i32):`) header, and the entry block is implicit (unlabeled) and holds the function's first operations and terminator.\n8. Every block is terminated by exactly one terminator operation, and every block in every function is reachable from the entry block.\n9. Every branch target named in a `cf.br` or `cf.cond_br` is a block defined within the same function, and no branch crosses function boundaries.\n10. Value flow across control-flow merges is carried exclusively by block arguments passed through branch operand lists (`^exit(%a : i32)`), never by cross-block direct SSA references into dominated blocks; block-argument types in the branch operand list match the declared block-argument types.\n11. Any block declaring an argument is entered only by branches supplying exactly that arity and type of operand; blocks declaring no arguments are entered only by operand-free branches.\n12. Non-control operations appearing inside bodies are restricted to `arith.constant`, `arith.addi`, and `arith.cmpi eq`, all at `i32` operand type, with `arith.cmpi` producing the `i1` consumed by the following `cf.cond_br`; no memory, call, or side-effecting operation ever appears.\n13. Each SSA name is assigned at most once within its function, and every function's names are self-contained (no cross-function value references).\n14. Branch weights, when present, appear only on `cf.cond_br` in the form `weights([w_true, w_false])` placed immediately after the condition operand and before the successor list, with exactly two nonnegative integer entries corresponding to the two successors.\n15. At most one weighted `cf.cond_br` occurs per function; all other conditional branches in that function are weight-free, and functions that contain a loop-carrying backedge either contain exactly one weighted branch outside the loop or none at all.\n16. A `llvm.loop_annotation = #loop_ann` discardable attribute, when present, is attached only to an unconditional `cf.br` that closes a backedge to a single dominating header block, i.e. to the loop latch's branch, and never to a conditional branch, an exiting branch, or a branch outside a cycle.\n17. Every cycle emitted is a single-entry, single-latch, single-exit natural loop: one header block taking an `i32` induction block argument, a conditional exit test in the header, a latch block computing the next induction value and branching back to the header, and an exit block that returns the induction value.\n18. The loop induction value enters the header only as a block argument, is initialized by the branches that enter the header from outside, and is updated only by the latch's `arith.addi` before the backedge.\n19. Loop entry from outside the header occurs on all paths before the header is executed, and no branch jumps into the loop body (latch) from outside the header.\n20. Function names are unique within the module, formed from a shape-identifying prefix and the index of the function in emission order.\n21. Every function body, and the module as a whole, is syntactically complete and self-contained: no unresolved attribute alias, no dangling block label, no unterminated block.\n\n## Sampling conventions\n\n1. The module contains between 2 and 4 functions inclusive, chosen uniformly per program.\n2. Functions are emitted in sequence with a running index starting at 0, and each function's name is suffixed with that index, so names are `<shape>_0`, `<shape>_1`, \u2026 and two functions of different shapes can share an index only if they are at different positions (they cannot; the index is global and increments per function).\n3. Each function independently takes one of exactly seven fixed skeletons: `plain_diamond`, `sequential_diamonds`, `counted_cycle`, `weighted_then_plain`, `plain_then_weighted`, `nested_weighted_arm`, `weighted_then_cycle`; no other shape is ever produced and shapes may repeat within a module.\n4. The name prefix always equals the skeleton's identifier, so the shape of each function is textually recoverable from its symbol name.\n5. The constant preamble is always exactly `#loop_ann = #llvm.loop_annotation<mustProgress = true>` followed by a blank line, and it is emitted whether or not any function actually uses it; no other alias, and no other loop-annotation payload fields, are ever emitted.\n6. Each function is followed by a blank line, giving a uniform two-newline separator between top-level items and a trailing blank line at end of file.\n7. Parameter names are fixed per skeleton (`%c`, `%a`, `%b`, `%first`, `%second`, `%limit`, `%weighted`, `%plain`) rather than generated, and block labels are fixed mnemonic names (`^yes`, `^no`, `^exit`, `^one_yes`, `^middle`, `^header`, `^latch`, `^left`, `^right`, etc.) reused verbatim across functions of the same shape.\n8. `plain_diamond` is a fixed, parameter-only body with no arithmetic: a condition parameter selecting between two `i32` parameters via a two-armed diamond merging at `^exit`.\n9. `sequential_diamonds` emits exactly two diamonds in series sharing a merge-to-merge chain, with an `arith.constant` named `%k` whose literal value is an integer chosen uniformly from 1 through 6, added to the merged value only on the second diamond's true arm.\n10. `counted_cycle` initializes the induction variable from a `%zero` constant that is always literally `0`, and uses a `%step` constant whose value is chosen uniformly from 1 through 4; the exit test is always `arith.cmpi eq` between the induction variable and the `%limit` parameter, with the equal case taking the exit successor.\n11. The loop latch's backedge branch in `counted_cycle` and `weighted_then_cycle` either carries the `{llvm.loop_annotation = #loop_ann}` attribute or carries no attribute at all, chosen independently per loop; no intermediate or alternative annotation form is emitted.\n12. Every weighted branch uses a weight pair summing to exactly 10, of the form `[w, 10 - w]` with `w` chosen uniformly from 1 through 9, so neither weight is ever 0 and the pair is never degenerate or non-normalized.\n13. Exactly one weighted branch is placed per weighted skeleton, and its position varies by skeleton: before a plain diamond (`weighted_then_plain`), after a plain diamond (`plain_then_weighted`), dominating a nested plain diamond on one arm only (`nested_weighted_arm`), or before a counted loop (`weighted_then_cycle`).\n14. In `weighted_then_plain` and `plain_then_weighted` the second diamond's two arms both forward the same merged `%seed` value, so the trailing diamond is data-trivial while remaining structurally a two-armed merge.\n15. In `nested_weighted_arm` the weighted branch's right arm is a bare unconditional branch to the merge while the left arm holds the whole plain diamond, producing an asymmetric nesting rather than two symmetric nested arms.\n16. In `weighted_then_cycle` the loop's step is always the constant `%one` (literally `1`), and the two weighted arms differ only in the loop's initial induction value, `%zero` versus `%one`; no per-program randomization of these constants occurs.\n17. Loops are never nested inside one another, never appear more than once per function, and never follow a loop within the same function; loop-bearing shapes are exactly `counted_cycle` and `weighted_then_cycle`.\n18. No function takes or returns aggregate, pointer, floating-point, or non-32-bit integer types, and no attribute other than the loop annotation is ever attached to any operation or function.\n19. All whitespace is fixed: two-space indentation for operations, column-zero block labels, and a single space before the loop-annotation attribute brace on the latch branch.",
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