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•  package provingground

  This is work towards automated theorem proving based on learning, using homotopy type theory (HoTT) as foundations and natural language processing.

  This is work towards automated theorem proving based on learning, using homotopy type theory (HoTT) as foundations and natural language processing.

  The implementation of homotopy type theory is split into:

  • the object HoTT with terms, types, functions and dependent functions, pairs etc
  • the package induction with general inductive types and recursion/induction on these.

  The learning package has the code for learning.

  Scala code, including the spire library, is integrated with homotopy type theory in the scalahott package

  We have implemented a functor based approach to translation in the translation package, used for nlp as well as serialization and parsing.

  The library package is contains basic structures implemented in HoTT.

  Definition Classes

  root

•  package translation

  Translation primarily using a functorial framework - see Translator$, for natural language processing as well as serialization, formatted output, parsing, interface with formal languages etc.

  Translation primarily using a functorial framework - see Translator$, for natural language processing as well as serialization, formatted output, parsing, interface with formal languages etc.

  Besides the Translator framework and helper typeclasses is Functors, several structures for concrete languages including our implementation of HoTT are in this package.

  Definition Classes

  provingground

•  object MathExpr

  Expression in a language to represent terms in HoTT and trees representing them in prose, including partially collapsed trees.

  Expression in a language to represent terms in HoTT and trees representing them in prose, including partially collapsed trees. At the level of structure, we do not make distinctions between words and phrases; the distinction is specific to trees, where a word is a leaf.

  We model expressions that will mostly become Terms in HoTT, mostly following Naproche. At the upper level are sentential phrases. We typically start with a tree that encodes a sentential phrase.

  We have various case classes for syntax, but a single trait

  Definition Classes

  translation

• AP
• AreAdj
• ConjSP
• ConjunctNP
• ConjunctSP
• Core
• DP
• Determiner
• DisjSP
• DisjunctNP
• DisjunctSP
• ExistentialSP
• Exists
• ForAllSP
• Formula
• IfThen
• Iff
• IsAdj
• IsAdjPrep
• IsNoun
• IsPrep
• IsSuchThat
• It
• JJ
• JJPP
• NN
• NP
• NPVP
• NegSP
• NegVP
• PP
• Prep
• Preposition
• SP
• SuchThat
• ThatIsSP
• They
• VB
• VP
• VPIf
• Variable
• VerbAdj
• VerbObj
• VerbPP
• Which

provingground.translation.MathExpr

AP

Companion class AP