What is Agda used for?
Because of strong typing and dependent types, Agda can be used as a proof assistant, allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms.
Is Agda written in Haskell?
Agda is also a proof assistant based on the propositions-as-types paradigm, but unlike Coq, has no separate tactics language, and proofs are written in a functional programming style….Agda (programming language)
| Website | wiki.portal.chalmers.se/agda |
| Influenced by | |
|---|---|
| Coq, Epigram, Haskell | |
| Influenced | |
| Idris |
What is Idris used for?
Idris is a purely-functional programming language with dependent types, optional lazy evaluation, and features such as a totality checker. Idris may be used as a proof assistant, but it is designed to be a general-purpose programming language similar to Haskell.
What is lean programming language?
Lean is a functional programming language that makes it easy to write correct and maintainable code. You can also use Lean as an interactive theorem prover. Lean programming primarily involves defining types and functions.
What is a type in type theory?
A “type” in type theory has a role similar to a “type” in a programming language: it dictates the operations that can be performed on a term and, for variables, the possible values it might be replaced with. Some type theories serve as alternatives to set theory as a foundation of mathematics.
What are dependent functions?
A function whose type of return value varies with its argument (i.e. there is no fixed codomain) is a dependent function and the type of this function is called dependent product type, pi-type or dependent function type.
Can Idris replace Haskell?
Idris 2 is written in Idris 2 and compiles to Scheme so far (Chez by default, there is also support for Racket and Gambit), it’s not tied to scheme but there is no pluggable backend functionality yet. So Scheme is replacing C, and Idris is replacing Haskell. The goal was self-hosting by writing the compiler in Idris.
What is Idris written in?
C
Idris supports multiple back ends (C and JavaScript by default, with the ability to add more via plugins) and has a reference run time system, written in C, with a garbage collector and built-in message passing concurrency.
Who invented type theory?
When the philosopher Bertrand Russell invented type theory at the beginning of the 20th century, he could hardly have imagined that his solution to a simple logic paradoxdefining the set of all sets not in themselveswould one day shape the trajectory of 21st century computer science.