migrate all tutorials from Markdown to Org mode

Converted with pandoc 3.7 (markdown → org), all 17 files:
- README, references, 15 tutorial units
- Internal file links updated from .md to .org
- Source code blocks (#+begin_src lean) preserved
- Tables, math notation, links intact

For the Emacs workflow.

tutorial-02-semantics/15-soundness-completeness.org

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+* Unit 15 --- Soundness and Completeness of Algorithm W
+:PROPERTIES:
+:CUSTOM_ID: unit-15-soundness-and-completeness-of-algorithm-w
+:END:
+*Tutorial 2: PL Semantics in Lean* · [[../README.org][← Back to README]]
+
+** Goals
+:PROPERTIES:
+:CUSTOM_ID: goals
+:END:
+- Prove that Algorithm W is *sound*: every inferred type is derivable in the declarative system
+- Prove that Algorithm W is *complete*: every derivable type can be inferred (up to generalization)
+- Understand the relationship between inference and declarative rules
+
+** Sources
+:PROPERTIES:
+:CUSTOM_ID: sources
+:END:
+- [[https://www.jeffvaughan.net/docs/hmproof.pdf][Vaughan 2008, §4]]
+- [[https://github.com/sdemos/type-inference][sdemos/type-inference]] =Soundness.lean=, =Completeness.lean=
+
+** The Theorems
+:PROPERTIES:
+:CUSTOM_ID: the-theorems
+:END:
+*Soundness*: If =infer(Γ, e) = (S, τ)=, then =Γ ⊢ e : τ= declaratively.
+
+*Completeness*: If =Γ ⊢ e : τ= declaratively, then there exists =S, τ'= such that
+=infer(Γ, e) = (S, τ')= and =τ= is a substitution instance of =τ'= (i.e., W finds the /most general/ type).
+
+** Exercises
+:PROPERTIES:
+:CUSTOM_ID: exercises
+:END:
+#+begin_src lean
+open HMTyping
+open MonoType
+
+-- 15.1 — Soundness of Algorithm W
+theorem soundness_W (Γ : HMEnv) (e : HMExpr) (S : Subst) (τ : MonoType) (counter : Nat)
+    (h : inferW Γ e counter = some (S, τ, _)) :
+    HMTyping (applySubstEnv S Γ) e {vars := [], body := τ} :=
+  by
+    induction e generalizing Γ S τ counter with
+    | var i =>
+        -- Case: variable lookup. Need to relate instantiated type scheme to declarative Var rule.
+        sorry
+    | lam body ih =>
+        -- Case: lambda. Use the IH and the Abs rule.
+        sorry
+    | app f a ihf iha =>
+        -- Case: application. The unification produces a substitution that makes types match.
+        -- Need substitution composition lemmas.
+        sorry
+    | lett e₁ e₂ ih₁ ih₂ =>
+        -- Case: let. Generalization produces a type scheme; the body gets the polymorphic type.
+        sorry
+
+-- 15.2 — Completeness of Algorithm W
+theorem completeness_W (Γ : HMEnv) (e : HMExpr) (σ : TypeScheme)
+    (h : HMTyping Γ e σ) :
+    ∃ (S : Subst) (τ : MonoType) (counter : Nat),
+      inferW Γ e 0 = some (S, τ, counter) ∧
+      ∃ (S' : Subst), applySubst S' τ = σ.body :=
+  by
+    induction h with
+    | var Γ i hlook =>
+        sorry
+    | abs Γ e τ₁ τ₂ hbody ih =>
+        sorry
+    | app Γ e₁ e₂ σ τ₁ τ₂ σ' h₁ h₂ h_eq ih₁ ih₂ =>
+        sorry
+    | lett Γ e₁ e₂ σ σ' τ h₁ h₂ ih₁ ih₂ =>
+        sorry
+    | gen Γ e σ αs hbody hfresh ih =>
+        sorry
+    | inst Γ e σ τ subst hbody hinst ih =>
+        sorry
+
+-- 15.3 — Principal Types Corollary
+-- Every well-typed expression has a *principal type* — one that all others are instances of.
+theorem principal_types (Γ : HMEnv) (e : HMExpr) (σ : TypeScheme)
+    (h : HMTyping Γ e σ) :
+    ∃ (τ_principal : MonoType),
+      -- W finds the principal type
+      (∃ S c, inferW Γ e 0 = some (S, τ_principal, c)) ∧
+      -- σ's body is an instance of the principal type
+      (∃ S', applySubst S' τ_principal = σ.body) :=
+  by
+    exact completeness_W Γ e σ h
+#+end_src
+
+--------------
+
+← [[file:14-algorithm-w.org][Previous: Unit 14]] · [[file:.][← Tutorial 2 Index]] · [[../README.org][← Back to README]]