Maths - Definitional Equality

Definitional Equality

Those equalities that are given as rewrite rules (equations) or else originate from general functional principles ( β, η, etc.) - Queiroz, Oliveira.

For 'Homotopy Type Theory' book type theory is a deductive system based on two forms of judgment:

Judgment Meaning
a:A a is an object of type A
a=b : A a and b are definitionally equal objects of type A

Definitional equality is a syntactical notion and it has nothing to do with the meaning of the syntactical entries - Nordstrom, Petersson, Smith

Computational (Judgemental) Equality

Equality based on conversion or reduction rules.

Example are:

This is commonly included in definitional equality.

 

 

 

 

 


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flag flag flag flag flag flag Computation and Reasoning - This book is about type theory. Although it is very technical it is aimed at computer scientists, so it has more discussion than a book aimed at pure mathematicians. It is especially useful for the coverage of dependant types.

 

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