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proofs's Introduction

Some proofs written in Dafny and HOL4

Simple ones

  • dafny/deque.dfy (an implementation of deque in dafny)
  • dafny/free_list.dfy (an implementation of a free list in dafny)
  • hol/myPairScript.sml (an implementation of product type in HOL)
  • hol/mySumScript.sml (an implementation of sum type using my product type)
  • hol/surjEpicScript.sml (a proof that surjective function is epic)

Interesting ones

  • dafny/funopw.dfy (an implemenation of a higher order function funpow that accept a partial function as argument in dafny, which is more clumsy than what I expected)
  • hol/partialFunctionScript.sml (an implementation of a partial function type in HOL)
  • hol/fibScript.sml (an proof and implementation of calculating fibonacci using matrix and exponentiation by squaring (using the fact that matrix multiplicatoin is associative)
  • hol/posetScript.sml (some proofs about proset (poset without antisym) and completet lattices)

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