<language> (LCF) Part of the Edinburgh proof assistant. [What is it? Address?] (1995-01-06)

Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in early 1970s, based on the theoretical foundation of logic of computable functions previously proposed by Dana Scott. Work on the LCF system introduced the general-purpose programming language ML to allow users to write theorem-proving tactics, supporting algebraic data types, parametric polymorphism, abstract data types, and exceptions.

In computer science, Programming Computable Functions (PCF) is a typed functional language introduced by Gordon Plotkin in 1977, based on previous unpublished material by Dana Scott. Programming Computable Functions is used by .

In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers or the computable reals or recursive reals.

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory.

<logic, mathematics> Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B. In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic). {History (http://britanica.com/bcom/eb/article/3/0,5716,118173+14+109826,00.html)}. (2001-03-18)

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not include the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic.

<spelling> Incorrect term for "intuitionistic logic". (1999-11-24)

<logic> The discipline that treats formal logic by means of a formalised artificial language or symbolic calculus, whose purpose is to avoid the ambiguities and logical inadequacies of natural language. (1995-12-24)