Abstract
Martin-Lof’s Constructive Type Theory (CTT) is a formal language developed in order to reason constructively about mathematics. It is thus a formal language conceived primarily as a tool to reason with rather than a formal language conceived primarily as a mathematical system to reason about. Constructive Type Theory is therefore much closer in spirit to Frege’s ideography and to the language of Russell and Whitehead’s Principia Mathematica than to the majority of logical systems (“logics”) studied by contemporary logicians. Since CTT is designed as a language to reason with, much attention is paid to the explanation of basic concepts. This is perhaps the main reason why the style of presentation of CTT differs somewhat from the style of presentation typically found in, for instance, ordinary logic textbooks. For those new to the system it might be useful to approach an introduction, such as the one given below, more as a language course than as a course in mathematics.
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