Begin chapter on extensionality

Iowa Type Theory Commute

This episode begins a new chapter on extensionality in type theory, where we seek to equate terms in different ways based on their types. The basic example is function extensionality, where we would like to equate functions from A to B if given equal inputs at type A, they produce equal outputs at type B. With this definition, quicksort and mergesort are equal, even though their codes are not syntactically equivalent. The episode begins by reviewing the distinction between definitional and propositional equality.
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