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Read a generator as a measure (SPMF.expect, SPMF.prob) rather than as a support. Three results, in StrataGenerators/Expectations.lean: 1. genStmt_expect_numLoops_le: the expected number of loops in a draw of genStmt at `size` is at most loopBound size, where loopBound (n+1) = 2/17 + (5*(n+1)/17) * loopBound n. Both constants come off genStmt's frequency list; the mean body length (size+1)/2 enters through expect_choose_mul (Gauss' formula in ENNReal). 2. genLExprBase_prob_rootFactoryOp_ge and _rootFactoryApp_ge: at a declared-type-constructor position, 2/14 of the draws are a factory operator at the root, and 4/14 * mass of the Indir branch are a factory operator applied to arguments. 3. genStmt_prob_rootLoop_ge and _pos: the loop branch's weight share 2/17, times that branch's mass, bounds the probability that a draw is a single loop statement from below, and that probability is positive. Every result is an inequality. A leaf generator can fail, so a sub-draw carries mass < 1 and each composition step loses mass; an exact expectation would need IsPMF for each leaf generator, which is the acceptance-rate question. SPMF.admissible_expect_le also only admits `expect ... <= B`, so the upper bound is the direction fixpoint reasoning supports.
ngernest
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ngernest
added this pull request to stack #31
September 24, 2026 01:01
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(Note: this PR is stacked on top of #29, please review #29 first -- thanks!)
This PR proves some probabilistic properties about our generators:
genStmt_expect_numLoops_le)By submitting this pull request, I confirm that you can use, modify, copy, and redistribute this contribution, under the terms of your choice.