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Intuitionistic type theory: Art, Type theory & Extensional versus intensional

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of the type theory: Martin-Löf…

Language: English [EN]
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Intuitionistic type theory topic overview

The analysis highlights Art, Type theory and Extensional versus intensional as prominent areas in the source structure around Intuitionistic type theory.

Related topics
76
Source areas
7
Connected nodes
83
Extracted relationships
68
Concept neighborhoods
27
Bridge connections
83

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Type theory · 29 topics
Extensional versus intensional · 14 topics
Overview · 12 topics
Implementations of type theory · 10 topics
Design · 4 topics
Martin-Löf type theories · 4 topics
Categorical models of type theory · 3 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Design

Type theory

Categorical models of type theory

Extensional versus intensional

Implementations of type theory

Martin-Löf type theories

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Intuitionistic type theory connects Entity context

The extracted context around Intuitionistic type theory shows recurring relationship patterns in the source. For example, Intuitionistic type theory → Addison-Wesley, Bengt, Functional Programming, Giovanni Sambin, Granström, ISBN, Jan, Johan, Kent, Martin-Löf's Type Theory, Nordström, Oxford University Press, Per Martin-Löf's Notes, Petersson, Programming, Simon, Smith, Springer, Thompson, Treatise Another extracted example is Intuitionistic type theory → At, English-language, For, It, Lastly, Martin-Löf, SSSS0, Synonyms, Terms, The, There, This. Use these groups to spot repeated connection types before inspecting the individual relationships.

Intuitionistic type theory

Top relations

related to Further reading · 21
Intuitionistic type theory → Addison-Wesley, Bengt, Functional Programming, Giovanni Sambin, Granström, ISBN, Jan, Johan, Kent, Martin-Löf's Type Theory, Nordström, Oxford University Press, Per Martin-Löf's Notes, Petersson, Programming, Simon, Smith, Springer, Thompson, Treatise
related to Judgements · 12
Intuitionistic type theory → At, English-language, For, It, Lastly, Martin-Löf, SSSS0, Synonyms, Terms, The, There, This
related to Design · 11
Intuitionistic type theory → BHK, Constructivism, Curry, For, Howard, Intuitionistic, Martin-Löf, Martin-Löf's, Prior, So, This
related to References · 10
Intuitionistic type theory → Bibliopolis, Giovanni, Intuitionistic, ISBN, Martin-Löf, Napoli, OCLC, PDF, Per, Sambin
related to Type theory · 5
Intuitionistic type theory → Frege's, In, Intuitionistic, So, Unlike
related to = type constructor · 4
Intuitionistic type theory → Given, In, The, Thus

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

type theory displaystyle types term martin-löf intuitionistic also proof terms objects mathbb dependent inductive mathbin first example extensional canonical written

Intuitionistic type theory relationships Subject–Predicate–Object triples

TTTA extracted 68 structured relationships around Intuitionistic type theory. Examples in this analysis include ATS → instance of → Dependent types also feature in the design of programming languages and Intuitionistic type theory → related to = type constructor → Given. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
ATSinstance ofDependent types also feature in the design of programming languages0.80text
Cayenneinstance ofDependent types also feature in the design of programming languages0.80text
Epigraminstance ofDependent types also feature in the design of programming languages0.80text
Agdainstance ofDependent types also feature in the design of programming languages0.80text
and Idrisinstance ofDependent types also feature in the design of programming languages0.80text
Intuitionistic type theoryrelated to = type constructorGiven0.60section
Intuitionistic type theoryrelated to = type constructorThe0.60section
Intuitionistic type theoryrelated to = type constructorThus0.60section
Intuitionistic type theoryrelated to = type constructorIn0.60section
Intuitionistic type theoryrelated to DesignMartin-Löf0.60section
Intuitionistic type theoryrelated to DesignConstructivism0.60section
Intuitionistic type theoryrelated to DesignSo0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Intuitionistic type theory bring nearby vocabulary together. In this analysis, examples include Theory, Extensional and Martin-löf. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Intuitionistic type theory
    • Theory
    • Extensional
    • Martin-löf
    • Type
    • Per
    • Using
    • Proof
    • Mathbin
    • Second
    • Terms
    • Value
    • Example
  • intuitionistic type theory
    • Type
    • Displaystyle
    • Theory
    • Extensional
    • Martin-löf
    • Term
    • Types
    • Mathbin
    • Mathbb
    • Per
    • Terms
    • Using
  • type theory
    • Type
    • Displaystyle
    • Extensional
    • Martin-löf
    • Term
    • Types
    • Mathbin
    • Mathbb
    • Terms
    • Proof
    • Second
    • Canonical
  • dependent types
    • Inductive
    • Theories
    • First
    • Types
    • Objects
    • Object
    • Second
    • Type
    • Logic
    • Pair
    • Universe
    • Example
  • empty type
    • Displaystyle
    • Term
    • Mathbin
    • Mathbb
    • Types
    • Terms
    • Proof
    • Second
    • Canonical
    • Value
    • Example
    • Contains
  • unit type
    • Displaystyle
    • Term
    • Mathbin
    • Mathbb
    • Types
    • Terms
    • Proof
    • Second
    • Canonical
    • Value
    • Example
    • Contains
  • proof theory
    • Type
    • Equality
    • Extensional
    • Value
    • Martin-löf
    • Types
    • Ordered
    • Second
    • Written
    • Mathbb
    • One
    • Using
  • homotopy type theory
    • Type
    • Displaystyle
    • Extensional
    • Martin-löf
    • Term
    • Types
    • Mathbin
    • Mathbb
    • Terms
    • Proof
    • Second
    • Canonical

Connections between topic areas Semantic bridges

For Intuitionistic type theory, one of the stronger structural bridges in this analysis connects Intuitionistic type theory with Type theory. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Intuitionistic type theory — Type theory · splits 54 ⟂ 30
Intuitionistic type theory — Extensional versus intensional · splits 69 ⟂ 15
Intuitionistic type theory — Overview · splits 71 ⟂ 13
Intuitionistic type theory — Implementations of type theory · splits 73 ⟂ 11
Intuitionistic type theory — Design · splits 79 ⟂ 5
Intuitionistic type theory — Martin-Löf type theories · splits 79 ⟂ 5
Intuitionistic type theory — Categorical models of type theory · splits 80 ⟂ 4

Map overview Semantic statistics

Intuitionistic type theory

Nodes84
Edges83
Triples68
Avg. degree1.98
Density0.02381
Components1

Source & methodology

TTTA analyzes the structure around Intuitionistic type theory to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Art, Type theory & Extensional versus intensional, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Intuitionistic type theory · EN edition · Analysis: TopicsToTalkAbout

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