Concept
Type theory
Overview
study of type systems in mathematical logic and computer science
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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An abstractive hierarchy is called ‘finite’ if it stops at a finite grade of complexity. It is called ‘infinite’ if it includes members belonging respectively to all degrees of complexity. It is to be noted that the base of an abstractive hierarchy may contain any number of members, finite or infinite.
Alfred North Whitehead, Science and the modern world
States what Type theory is; the author is tied to Type theory in the knowledge graph.
The notion of continuity depends upon that of _order_, since continuity is merely a particular type of order. Mathematics has, in modern times, brought order into greater and greater prominence. In former days, it was supposed (and philosophers are still apt to suppose) that quantity was the fundamental notion of mathematics. But nowadays, quantity is banished altogether, except from one little corner of Geometry…
Bertrand Russell, Mysticism and Logic and Other Essays
States what Type theory is; the author is tied to Type theory in the knowledge graph.
In modern expositions of the axioms of geometry certain conditions are laid down which the relation of congruence between segments is to satisfy. It is supposed that we have a complete theory of points, straight lines, planes, and the order of points on planes--in fact, a complete theory of non-metrical geometry. We then enquire about congruence and lay down the set of conditions--or axioms as they are called--which…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Type theory is; the author is tied to Type theory in the knowledge graph.
Philosophers who discussed Type theory
Related ideas
- Formal language
- First-order logic
- Proof assistant
- Free variables and bound variables
- Judgment (mathematical logic)
- Zermelo–Fraenkel set theory
- Negation
- Truth value
- Dana Scott
- Intuitionistic logic
- Foundations of mathematics
- Law of excluded middle
- Logical conjunction
- Lambda calculus
- Function (mathematics)
- Per Martin-Löf
- Mathematical object
- Mathematical logic
- Reflexive relation
- Constructivism (philosophy of mathematics)
- Natural language
- Natural number
- Ordered pair
- Reductio ad absurdum
Opposing perspectives
Place in the tradition
Part of Outline of philosophy.
Narrower topics:
- Compiler
- Per Martin-Löf
- Function application
- ML (programming language)
- Lean (proof assistant)
- Set-theoretic definition of natural numbers
- Cartesian closed category
- Intersection
- Identity type
- Logic for Computable Functions
- Nuprl
- Church encoding
- John Lane Bell
- Journal of Functional Programming
- LEGO (proof assistant)
- Matita
- Cubical type theory
- Homotopy type theory
- Normal form (abstract rewriting)
- Static program analysis
- Induction-recursion
- Joachim Lambek
- Semantic analysis (compilers)