Math 2.0

Computer science Type theory Concept

Parametricity

Builds on System F

Summary

Parametricity is the property that a polymorphic program acts in the same way at every type. The reason is that it cannot inspect the type it is used at. John C. Reynolds made it precise in 1983 with a relational interpretation of the types of System F. He proved that all terms of System F are parametric. Its consequences are statements about all terms of a given type, which Philip Wadler called "theorems for free". It is a main tool for reasoning about abstraction and data hiding in programming languages.

Reading path

To understand this page from the ground up, read these 25 pages in order. The foundations come first.

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Element, definition, no evidence levelElementdefinitionIntuitionistic logic, concept, no evidence levelIntuitionistic logicconceptLambda calculus, concept, no evidence levelLambda calculusconceptProposition, concept, no evidence levelPropositionconceptSet, concept, no evidence levelSetconceptSet, definition, no evidence levelSetdefinitionConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionTruth table, concept, no evidence levelTruth tableconceptModus ponens, concept, no evidence levelModus ponensconceptMathematical proof, concept, no evidence levelMathematical proofconceptPropositional logic, concept, no evidence levelPropositional logicconceptTautology, definition, no evidence levelTautologydefinitionLogical equivalence, definition, no evidence levelLogical equivalencedefinitionDouble negation law, statement, no evidence levelDouble negation lawstatementProof by contradiction, concept, no evidence levelProof by contradictionconceptRussell's paradox, statement, no evidence levelRussell's paradoxstatementType theory, concept, no evidence levelType theoryconceptCurry–Howard correspondence, concept, no evidence levelCurry–Howard correspo…conceptSimply typed lambda calculus, concept, no evidence levelSimply typed lambda c…conceptSystem F, concept, no evidence levelSystem FconceptParametricity, concept, no evidence levelParametricityconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Element definition
  2. Intuitionistic logic concept
  3. Lambda calculus concept
  4. Proposition concept
  5. Set concept
  6. Set definition
  7. Conjunction definition
  8. Disjunction definition
  9. Implication definition
  10. Negation definition
  11. Biconditional definition
  12. Truth table concept
  13. Modus ponens concept
  14. Mathematical proof concept
  15. Propositional logic concept
  16. Tautology definition
  17. Logical equivalence definition
  18. Double negation law statement
  19. Proof by contradiction concept
  20. Russell's paradox statement
  21. Type theory concept
  22. Curry–Howard correspondence concept
  23. Simply typed lambda calculus concept
  24. System F concept
  25. Parametricity concept

Further reading

  1. Web https://en.wikipedia.org/wiki/Parametricity
About this page
Tag67YR9SNGTX
URIm2://67YR9SNGTX
Kindconcept
WritingW0 stub
MSC68N18, 68Q55, 03B40
UsesSystem F
Same as
Changed3 November 2026

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