TS: the Small-Step Semantics chapter#101
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Slang is the simple expression language (Aexp/Bexp with big-step evaluation and the optimize0plus optimization), extracted from HL/Imp's opening and shared as the common foundation for the HL and TS paths. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
The chapter's opening (~810 lines: variable-free Aexp/Bexp, evaluation, optimization, and evaluation-as-a-relation) duplicated the new Slang chapter. Remove it and add a short bridge telling the reader to read Slang first, then resume here with variables and commands. - Delete the # Arithmetic and Boolean Expressions / # Optimizing Booleans / # Evaluation as a Relation sections (Warmup, AevalRDivision, AevalRExtended). - No import of TS.Slang: nothing here uses it in code, and importing would make HL depend on a TS-volume module, against the independent-paths goal. - Reference Slang in prose (plain text; a live cross-book link isn't supported across separate books yet). - Redirect the two Warmup back-references to Slang. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
# Conflicts: # HL/Imp.lean
- Promote dev-note urgencies/authors to directive args (SOONER -> BeforeNextRelease, LATER -> PotentialImprovement; mwhicks1/chenson2018 -> author strings). - GRADE_THEOREM blocks -> :::gradeTheorem (GRADE_MANUAL stays :::grade). - Add :::quizSolution answer blocks to the two quizzes. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Small-step operational semantics (toy Tm language, typed arithmetic build-up, and the Slang-based arithmetic/boolean small-step + stack machine). Builds on the Slang chapter. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
- Cut the boolean toy language (Temp4/Temp5), the Combined arith+bool language, and the normalize-tactic section: redundant now that the chapter builds on Slang (which already has arithmetic and boolean expressions). The Combined language's stuck-terms lesson is picked up in the Types chapter. - Rename the Slang small-step section to 'Small-Step Slang' and move Nondeterministic Evaluation after Boolean Expressions. - Add astep_deterministic / bstep_deterministic exercises, proved as compact <;>-driven tactic chains with a single uniform closer. - Use Unicode operators (¬, ∧, −, ×) in the boolean/arithmetic inference rules. - Resolve in-file TODOs; drop stale dev/port-status notes; prose + formatting. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
- Dev-note urgencies/authors -> directive args (SOONER/LATER/TODO -> BeforeNextRelease/PotentialImprovement/NOW; mwhicks1/MRC -> author strings); the bare 'Additional Exercises' TODO -> :::dev NOW. - GRADE_THEOREM -> :::gradeTheorem (GRADE_MANUAL stays :::grade). - :::quizSolution for all 8 quizzes (5 converted from :::instructors answers, 3 bare quizzes given computed answers). - compiler_is_correct: (level := Advanced) (Rocq EX3A). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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- Replace <> / <= / ! / && with ≠ / ≤ / ¬ / ∧ in the imp_bexp grammar, macro_rules, and boolean delaborator - Update examples and the #check expected-output annotation to match
- Strip trailing whitespace across prose and dev-note lines - Use * rather than × in the arithmetic BNF for consistency
…space cleanup # Conflicts: # TS/Slang.lean
berberman left a GitHub comment about not using induction principles directly, and preferring the fun_induction tactic. I asked Claude to help me update the proof to do that, and then adjusted the text accordingly, leaving a note that we should either update Automation to add this tactic, or introduce it here.
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Adds the Small-Step Semantics chapter to the Type Systems volume, built on the Slang chapter.
Contents
Tm): determinism, values, strong progress, normal forms, multi-step reduction, and big-step/small-step equivalence.AStep/BStep), with newastep_deterministic/bstep_deterministicexercises (compact<;>-driven proofs).ANStep,⟶n) standing in for Concurrent Imp, plus a small-step stack machine (compiler_is_correct).Combined/normalize-tactic sections were cut as redundant now that the chapter builds on Slang (which already provides arithmetic and boolean expressions); the "stuck terms motivate types" lesson lands in the Types chapter instead.:::gradeTheorem, and:::quizSolution.This chapter no longer depends on full Imp, so Concurrent Imp and the Imp-based stack machine are not there. Changed to nondeterministic Slang and a stack machine on Slang, instead.
Not handled here: Using notation fully (e.g., in the definition of the inductive relation), and formatting width (things are up to 100 columns, which present badly in the HTML).