Gödel is a declarative, general-purpose

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

that adheres to the

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

programming paradigm Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, suc ...

. It is a strongly typed language, the type system being based on

many-sorted logic Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive " parts of speech ...

with

parametric polymorphism In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorph ...

. It is named after logician Kurt Gödel.

Features

Gödel has a module system, and it supports

arbitrary precision In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are li ...

integers, arbitrary precision rationals, and also floating-point numbers. It can solve constraints over finite domains of integers and also linear rational constraints. It supports processing of

finite set In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, :\ is a finite set with five elements. T ...

s. It also has a flexible computation rule and a pruning operator which generalises the commit of the concurrent logic programming languages. Gödel's

meta-logic Metalogic is the study of the metatheory of logic. Whereas ''logic'' studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems.Harry GenslerIntroduction to Logic Routledge, ...

al facilities provide support for meta-programs that do analysis,

transformation Transformation may refer to: Science and mathematics In biology and medicine * Metamorphosis, the biological process of changing physical form after birth or hatching * Malignant transformation, the process of cells becoming cancerous * Tran ...

, compilation, verification, and debugging, among other tasks.

Sample code

The following Gödel module is a specification of the greatest common divisor (GCD) of two numbers. It is intended to demonstrate the declarative nature of Gödel, not to be particularly efficient. The CommonDivisor predicate says that if i and j are not zero, then d is a common divisor of i and j if it lies between 1 and the smaller of i and j and divides both i and j exactly. The Gcd predicate says that d is a greatest common divisor of i and j if it is a common divisor of i and j, and there is no e that is also a common divisor of i and j and is greater than d. MODULE GCD. IMPORT Integers. PREDICATE Gcd : Integer * Integer * Integer. Gcd(i,j,d) <- CommonDivisor(i,j,d) & ~ SOME (CommonDivisor(i,j,e) & e > d). PREDICATE CommonDivisor : Integer * Integer * Integer. CommonDivisor(i,j,d) <- IF (i = 0 \/ j = 0) THEN d = Max(Abs(i),Abs(j)) ELSE 1 =< d =< Min(Abs(i),Abs(j)) & i Mod d = 0 & j Mod d = 0.

External links

* https://web.archive.org/web/20091207092823/http://www.scs.leeds.ac.uk/hill/GOEDEL/expgoedel.html {{DEFAULTSORT:Godel (programming language) Godel Programming languages created in 1992 Programming languages created by women