Description 1ML is a reboot of ML starting from first-class modules, and unifies core and module layer into one small and consistent language. It is described in the following papers: Andreas Rossberg. 1ML — core and modules united. ICFP 2015. Andreas Rossberg. 1ML — core and modules united (Extended). 2015. Expanded version including Technical Appendix. Andreas Rossberg. 1ML — core and modules un
Copyright Microsoft Corporation 2023 and Lean FRO, LLC 2023–2025 This is a free book on using Lean as a programming language. All code samples are tested with Lean release 4.21.0.
Lean is an open-source programming language and proof assistant that enables correct, maintainable, and formally verified code -- 'Grind' efficiently manages complex pattern matching and -- case analysis beyond standard tactics. example (x : Nat) : 0 < match x with | 0 => 1 | n+1 => x + n := by grind -- Automatically solves systems of linear inequalities. example (x y : Int) : 27 ≤ 11*x + 13*y → 1
Introduction F* (pronounced F star) is a general-purpose proof-oriented programming language, supporting both purely functional and effectful programming. It combines the expressive power of dependent types with proof automation based on SMT solving and tactic-based interactive theorem proving. F* programs compile, by default, to OCaml. Various fragments of F* can also be extracted to F#, to C or
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