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Writing Your First Proofs in Lean Writing Your First Proofs in Lean
7 min read Keywords:  lean, theorem proving, formal verification, tactics, induction, lean 4

The same three theorems from the Python prover, now in Lean 4.

Programming a Mini-Lean in Julia's Type System Programming a Mini-Lean in Julia’s Type System
18 min read Keywords:  theorem proving, julia, lean, curry-howard, Type Systems, formal verification

Guillermo Angeris builds a working theorem prover in 61 lines of Julia. A tiny trusted kernel, six axioms, and the compiler does the rest. This article walks through the full construction.

Can I prove Concrete programs in Lean? Can I prove Concrete programs in Lean?
9 min read Keywords:  concrete, lean, formal verification, systems programming, proofs

I want to prove Concrete programs in Lean. The compiler already produces native Lean data as its IR, and the language is small enough that formalization might actually be tractable.

The Rust Effects Debate and Concrete's Case for a Smaller Language The Rust Effects Debate and Concrete’s Case for a Smaller Language
9 min read Keywords:  Programming Languages, Formal Verification, rust, Type Systems, lean

Wuyts is right about effects and ownership. The Hacker News skeptics are right about complexity. Concrete accepts both and says no to refinement types.

Why Concrete Exists Why Concrete Exists
7 min read Keywords:  Programming Languages, Formal Verification, Type Systems, lean, concrete

Concrete is a systems language designed so the compiler can reason about what code does: authority, allocation, resource lifetimes, and proof surface.