(* Prove a simple property manually – no automation! ) lemma add_zero: "add 0 m = m" unfolding add_def by (rule fix_eq) ( primitive rule only *)
If you’ve ever wondered, “What is the absolute minimum logic needed to build an ITP?” – isabelle-extreme is your answer.
No – and that’s the point. isabelle-extreme is intentionally useless for application-scale verification. It lacks data types, recursion schemes, and any form of automation. Trying to prove 1+1=2 requires dozens of manual rewrite steps. However, as a and kernel sanity check , it is invaluable. isabelle-extreme
isabelle extreme This opens a theory file with the extension .ext . Here’s a minimal example:
Have you experimented with minimal logics inside Isabelle? Share your experiences below! (* Prove a simple property manually – no automation
Notice: no simp , no induct . Every proof step must explicitly invoke a primitive inference rule.
| 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 | However, as a and kernel sanity check , it is invaluable
Most people in the formal verification community are familiar with – the powerful, mainstream interactive theorem prover used for everything from operating system kernels (seL4) to financial protocols. But lurking in the source tree and early development history is a hidden gem: isabelle-extreme .