Thinking·OS

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Turing machine models Algorithm. Activate to inspect this relation.Finite automaton is analogous to Turing machine. Activate to inspect this relation.Computability depends on Turing machine. Activate to inspect this relation.Lambda calculus is analogous to Turing machine. Activate to inspect this relation.Type theory is derived from Lambda calculus. Activate to inspect this relation.Homotopy type theory is a Type theory. Activate to inspect this relation.Formal verification applies to Type theory. Activate to inspect this relation.Proof assistant applies to Formal verification. Activate to inspect this relation.Type system is derived from Lambda calculus. Activate to inspect this relation.Operational Semantics applies to Lambda calculus. Activate to inspect this relation.Denotational Semantics applies to Lambda calculus. Activate to inspect this relation.Closure is derived from Lambda calculus. Activate to inspect this relation.Time Complexity measures Turing machine. Activate to inspect this relation.Turing machine is a Finite automaton. Activate to inspect this relation.Turing machine models Computability. Activate to inspect this relation.Algorithm models Turing machine. Activate to inspect this relation.Proof assistantFormal verificationType theoryLambda calculusHomotopy type theoryTuring machineType systemOperational SemanticsDenotational SemanticsClosureAlgorithmFinite automatonComputabilityTime Complexity
Relationship types
Legend
  • Focused concept
  • Connected concept
  • Arrow points from cause / source to effect / target
  • A line with no arrow is a two-way relationship
  • Node colour marks the concept’s primary discipline
14 concepts16 relationships9 disciplines5 relation families

Proof assistant

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At a glance

Software (Lean, Coq) that mechanically checks and helps build rigorous formal proofs, increasingly paired with AI.

Disciplines
Computer Science · Mathematics
Role in the graph
Leaf concept
Relationships
1 · 1 relation families

Insights from this view

Structural observations about the concepts shown here — descriptions of this graph, not claims about the world.

  • This view connects 9 disciplines: Algorithms, Computational Complexity, Computer Science, Discrete Mathematics, Logic, Mathematics, Programming Languages, Software Engineering, Theory of Computation.
  • Proof assistant is a bridge concept — viewed here through Computer Science, Mathematics.
  • The connections here span 5 relation families.
  • Information explains 2 concepts in this view (Algorithms, Computational Complexity, Computer Science, Discrete Mathematics, Logic, Mathematics, Software Engineering, Theory of Computation).

Relationships as a list

The focused concept’s relationships. Pick another concept in the graph above to update this list.

Explore through a different lens

A lens is a deterministic projection of the graph. Pick a discipline, thinking pattern or journey to reframe the whole view.

By discipline

ChemistryBiologyPhysicsMathematicsComputer ScienceGeologyMineralogyEconomics

By thinking pattern

Bayesian updatingCause and effectCompoundingConservationConstraintsDefense in depthDiffusion & spreadEmergenceEnergy transformationEntropy & irreversibilityEquilibriumFeedback loopIncentivesInformationLevels & hierarchyModularityNetworksOptimizationOscillationProbabilityRecursion & self-similarityScaleSignal vs noiseSource–pathway–receptorStocks and flowsSymmetry & invarianceThresholds & tipping pointsTrade-offsTriangulationVariation & selectionWaves

By journey

From a Leaf to the ClimateWhy Music Moves UsHow Machines LearnReasoning about a Leaf and the Climate

Concept collections

Concept collections are curated lenses onto the fabric — themed sets of ideas that recur across disciplines. They are not journeys; they are a way to read the graph.

About this view

What this is

Start from one concept and expand outward. The view never shows everything at once — click a node to refocus, filter by relationship type, or switch to an accessible list.

One fabric

3750 concepts and 5051 typed relations form one connected component — no isolated silo.

How to read it

Focus a concept, or apply a lens (discipline, mental model, journey) to see only the threads that matter.