A TeX format file stores initialized internal structures for a TeX format, usually under a .fmt filename. Loading it reconstructs prepared definitions and related state more quickly than rereading the initialization input. Creating it uses the initialization facility and the \dump command.[ref]
This is an example of serialization. Suppose an initialization input defines \def\banner{First} and its state is saved. Changing the original input to define Second does not by itself replace the already saved state. The format must be regenerated, or the loaded definition explicitly changed, for subsequent processing to use that new initialization.
A loaded TeX format file initializes future document processing. The document can then add further TeX macros, change parameters and request mathematical typesetting. The relevant implementation must be able to read the saved representation; a .fmt suffix alone does not establish compatibility between different implementations.

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