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Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. Download the pre-built packages of the latest release for Windows and MacOS; read the help page on how to install Coq with OPAM; or refer to the INSTALL file for the procedure to install from source.

proof-assistant coq theorem-proving dependent-typesStable and nightly binary releases of Lean are available on the homepage. For building Lean from source, see the build instructions.

programming-language theorem-proving type-theory verification dependent-types leanThe F* tutorial provides a first taste of verified programming in F*, explaining things by example. The F* wiki contains additional, usually more in-depth, technical documentation on F*.

programming-language verification dependent-types smt theorem-proving proof-assistant ocaml f-sharp c-language fstarCakeML is a verified implementation of a significant subset of Standard ML. The source and proofs for CakeML are developed in the HOL4 theorem prover. We use the latest development version of HOL4, which we build on PolyML 5.7. Example build instructions can be found in build-instructions.sh.

programming-language formal-verification formal-semantics compiler theorem-proving hol smlThis is the distribution directory for the Kananaskis release of HOL4. See http://hol-theorem-prover.org for online resources. The following is a brief listing of what's available in the distribution.

theorem-proving lambda-calculus higher-order-logicSpecifically, Certigrad is a system for optimizing over stochastic computation graphs, that we debugged systematically in the Lean Theorem Prover, and ultimately proved correct in terms of the underlying mathematics. Stochastic computation graphs extend the computation graphs that underlie systems like TensorFlow and Theano by allowing nodes to represent random variables and by defining the loss function to be the expected value of the sum of the leaf nodes over all the random choices in the graph. Certigrad allows users to construct arbitrary stochastic computation graphs out of the primitives that we provide. The main purpose of the system is to take a program describing a stochastic computation graph and to run a randomized algorithm (stochastic backpropagation) that, in expectation, samples the gradients of the loss function with respect to the parameters.

machine-learning theorem-proving lean verificationPomagma is an inference engine for extensional untyped λ-join-calculus, a simple model of computation in which nondeterminism gives rise to an elegant gradual type system. Pomagma's base theory is being formally verified in the Hstar project.

lambda-calculus theorem-proving inference-engineGAPT is a proof theory framework developed primarily at the Vienna University of Technology. GAPT contains data structures, algorithms, parsers and other components common in proof theory and automated deduction. In contrast to automated and interactive theorem provers whose focus is the construction of proofs, GAPT concentrates on the transformation and further processing of proofs. You can also use Prover9, Vampire, EProver, and lots of other provers instead of the built-in Escargot prover, if you have them installed. There are many more examples in the user manual, and you can look into the API documentation for reference as well.

proofs herbrand-disjunction theorem-proving sat-solver tactics proofCode and documents developed during Chun Tian's MSc of Computer Science study at University of Bologna (Italy).

ml lisp xml theorem-provingWARNING: On rare occasions development versions of ACL2 may be incomplete, fragile, or unable to pass the usual regression tests. You may choose to download an official ACL2 release as described on the ACL2 Home Page or below in this README. The ACL2 theorem proving environment consists of two parts: The ACL2 System and The ACL2 Books. This repository contains both.

acl2 theorem-prover theorem-proving common-lisp rewriting formal-verification formal-methods first-order-logic logicA system under development for (semi-)automated theorem proving, with foundations homotopy type theory, using machine learning, both by reinforcement learing using backward-propagation and using natural language processing to assimilate part of the mathematics literature. The principal developer is Siddhartha Gadgil (Department of Mathematics, Indian Institute of Science, Bangalore).

homotopy theorem-provingDependency: See .pro. Use a lot of C++1y feature so need a good compiler. Build: This is a header only library. Include the header you want.

theorem-proving first-order-logicTo the extent possible under law, the authors have waived all copyright and related or neighboring rights to this text. For copying conditions, consult COPYING.txt, which is the CC0 Public Domain Dedication.

tools verification synthesis static-analysis binary-decision-diagrams model-checking theorem-proving proof-assistant satisfiability-solver satisfiability-modulo-theories smtlib formal-methods
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