refactor(Circuit): bundle gate count in circuits - #949
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…r#947) ## Summary - Define `Cslib.BitString` and `Cslib.BooleanFunction` in Foundations. - Update Boolean circuits to import and use the shared definitions, so other Boolean complexity developments can use these types without a circuit dependency. This is the first part of the split of leanprover#943. The stack continues in leanprover#948 and leanprover#949. ## Validation - `lake build --wfail --iofail` - `lake exe mk_all --check` - `lake test` - `lake lint` - `lake exe lint-style` Codex assisted with splitting leanprover#943 into three focused PRs and running these local checks.
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## Summary - Generalize `Circuit.Computes` to specify all designated outputs as a function returning an output tuple. - Add zero-gate `Circuit.wiring` for selecting, permuting, and duplicating inputs, with size, depth, evaluation, and computation lemmas. - Rename synthesis extraction to `Synthesis.exists_circuit_outputs` and adapt scalar counting, Shannon, Lupanov, and tests to the tuple-valued API. This is the second part of the split of leanprover#943. It builds on leanprover#947 and retains the explicit gate-count index; leanprover#949 changes that representation. ## Validation - `lake build --wfail --iofail` - `lake exe mk_all --check` - `lake test` - `lake lint` - `lake exe lint-style` Codex assisted with splitting leanprover#943 into three focused PRs, adapting this output change to the explicit gate-count representation, and running these local checks.
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Summary
Circuit.sizefield, leaving input and output counts as circuit type parameters.Program × Wirepairs for the counting bounds while stating computability and irredundancy membership through circuits.Circuitfiniteness and cardinality API is removed with its old type index.This is the final part of the split of #943 and builds on #948. The resulting circuit source and tests match the final code of #943 on the updated main branch.
Validation
lake build --wfail --iofaillake exe mk_all --checklake testlake lintlake exe lint-styleCodex assisted with splitting #943 into three focused PRs, restacking the gate-count changes, and running these local checks.