The Frege Programming Language ( Draft)
The Frege Programming Language (Draft) by Ingo Wechsung last changed May 14, 2014 3.21.285 Abstract This document describes the functional programming language Frege and its implemen- tation for the Java virtual machine. Commonplace features of Frege are type inference, lazy evaluation, modularization and separate compile-ability, algebraic data types and type classes, pattern matching and list comprehension. Distinctive features are, first, that the type system supports higher ranked polymorphic types, and, second, that Frege code is compiled to Java. This allows for maximal interoperability with existing Java software. Any Java class may be used as an abstract data type, Java functions and methods may be called from Frege functions and vice versa. Despite this interoperability feature Frege is a pure functional language as long as impure Java functions are declared accordingly. What is or who was Frege? Friedrich Ludwig Gottlob Frege was a German mathematician, who, in the second half of the 19th century tried to establish the foundation of mathematics in pure logic. Al- though this attempt failed in the very moment when he was about to publish his book Grundgesetze der Arithmetik, he is nevertheless recognized as the father of modern logic among philosophers and mathematicians. In his essay Funktion und Begriff [1] Frege introduces a function that takes another function as argument and remarks: Eine solche Funktion ist offenbar grundverschieden von den bisher betrachteten; denn als ihr Argument kann nur eine Funktion auftreten. Wie nun Funktionen von Gegenst¨andengrundverschieden sind, so sind auch Funktionen, deren Argu- mente Funktionen sind und sein m¨ussen,grundverschieden von Funktionen, deren Argumente Gegenst¨andesind und nichts anderes sein k¨onnen.
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