Isabelle-extreme [top] -

theory Scratch imports Main begin (* Define addition via fixed point *) definition add :: "nat ⇒ nat ⇒ nat" where "add ≡ fix (λadd n m. if n = 0 then m else add (n-1) (m+1))"

Notice: no simp , no induct . Every proof step must explicitly invoke a primitive inference rule. isabelle-extreme

(* Prove a simple property manually – no automation! ) lemma add_zero: "add 0 m = m" unfolding add_def by (rule fix_eq) ( primitive rule only *) theory Scratch imports Main begin (* Define addition

| Feature | isabelle-extreme | Isabelle/HOL | |---------|--------------------|---------------| | Logic | Minimal equational logic + fixed point | Higher-order logic | | Types | Simple types (no type classes) | Rich types with type classes | | Recursion | Via fixed point combinator ( fix ) | Primitive recursion, well-founded recursion | | Automation | None (manual rewriting only) | simp , auto , blast , sledgehammer | | Code generation | No | Yes (to ML, Scala, Haskell) | | Library | Empty | Thousands of theorems | (* Prove a simple property manually – no automation

isabelle-extreme is the "assembly language" of the Isabelle ecosystem – raw, unforgiving, and beautiful in its simplicity. While you will never ship a verified compiler written in it, exploring it offers a rare glimpse into the foundational bedrock on which massive proof developments rest.