Abstract This paper describes a theorem prover for Dependent Type Systems. We start with an introduction to Dependent Type Systems and highlight the properties that make them specifically suited for computational semantics. We proceed with a brief description of the ALLIGATOR system, including its architecture and some implementation issues. Alligator works with a specific generalization of Dependent Type Systems: Pure Type Systems extended with Sigma Types. The paper concludes with examples of proofs constructed by ALLIGA-TOR. These have been selected to illustrate how certain problems in anaphora/presupposition resolution can be addressed with the current system.
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