Applications and libraries/Theorem provers
Tools for formal reasoning, written in Haskell.
- Agda is a system for incrementally developing proofs and programs. Agda is also a functional language with Dependent types. This language is very similar to cayenne and agda is intended to be a (almost) full implementation of it in the future.
- Djinn generates Haskell code from a type declaration, using a decision procedure from intuitionistic propositional calculus.
- Paradox processes first-order logic problems and tries to find finite-domain models for them.
- Dumatel is a prover based on many-sorted term rewriting (TRW) and equational reasoning
- Camila is a system for software development using formal methods. Other materials on formal methods can be found also on the analysis and design page.
- Epigram is a prototype dependently typed functional programming language, equipped with an interactive editing and typechecking environment. High-level Epigram source code elaborates into a dependent type theory based on Zhaohui Luo's UTT. Programming with evidence lies at the heart of Epigram's design.
- Cayenne is a functional language with a powerful dependent type system. The basic types are functions, products, and sums. Functions and products use dependent types to gain additional power. As with Epigram, a dependently typed language may be used to encode strong proofs in the type system.
- Yarrow is a proof-assistant for Pure Type Systems (PTSs) with several extensions. In Yarrow you can experiment with various pure type systems, representing different logics and programming languages.
- Proof General Kit
- The Proof General Kit designs and implements a component-based framework for interactive theorem proving. The central middleware of the toolkit is implemented in Haskell. The project is the sucessor of the highly successful Emacs-based Proof General interface.
- Expander2 is a flexible multi-purpose workbench for rewriting, verification, constraint solving, flow graph analysis and related procedures that build up proofs or computation sequences. Moreover, tailor-made interpreters display terms as 2D structures ranging from trees and rooted graphs to tables, fractals and other turtle-system-generated pictures.