Mathematical terms, definitions, and propositions in as many languages as possible with a translation to and from type-theory.
Most concepts are linked to Wikidata identifiers and labels.
The list of concepts and Wikidata links are from MathGloss.
The syntax in grammars is adapted from this old GF code and follows the ideas of the paper "Translating between language and logic: what is easy and what is difficult" by A Ranta in CADE-2011 Springer page free preprint
The work is also related to GFLeanTransfer, whose English grammar is re-implemented by using the RGL here. To compile this version, clone the GFLeanTransfor repository and create a symlink to its subdirectory resources/simplifiedForThel/ in gflean-extensions.
ToDo (among other things):
- parsing and translating the Chicago definitions in MathGloss
- connection to Lean (initiated by a grammar evolving in ./lean-bnfc)
- adding languages
- improving the current ones (at the moment bootstrapped semi-automatically from Wikidata labels and GF Resource Grammar Library)
Example: two definitions of the abelian group. Notice that natural language swaps the places of the definiendum and definiens, but the type-theoretical translation is the same (modulo the use of function composition).
$ cd data/grammars
$ make
$ gf MathText.pgf
MathText> parse -lang=Eng "an abelian group is a group whose binary operation is commutative ." | linearize -bind -treebank
MathText: ParDefinition (DefWhose (KindQN abelian_group_Q181296_QN) (KindQN mathematical_group_Q83478_QN) (Fun1QN binary_operation_Q164307_QN) commutative_Property)
MathTextCore: def abelian_group_Q181296 := (Σ x : mathematical_group_Q83478 ) Commutative ( binary_operation_Q164307 ( x ) )
MathTextEng: an abelian group is a group whose binary operation is commutative .
MathTextFin: Abelin ryhmä on ryhmä, jonka binäärioperaatio on kommutatiivinen .
MathTextFre: un groupe abélien est un groupe dont l'opération binaire est commutative .
MathTextGer: eine abelsche Gruppe ist eine Gruppe , deren zweistellige Verknüpfung kommutativ ist .
MathTextIta: un gruppo abeliano è un gruppo di cui operazione binaria è commutativa .
MathTextPor: um grupo abeliano é um grupo cuja operação binária é comutativa .
MathTextSwe: en abelsk grupp är en grupp vars binära operator är kommutativ .
MathText> p -lang=Eng "a group is an abelian group if its binary operation is commutative ." | l -bind -treebank
MathText: ParDefinition (DefIsAIf (KindQN abelian_group_Q181296_QN) (KindQN mathematical_group_Q83478_QN) (CondItsFun1 (Fun1QN binary_operation_Q164307_QN) commutative_Property))
MathTextCore: def abelian_group_Q181296 := (Σ x : mathematical_group_Q83478 ) ( Commutative ∘ binary_operation_Q164307 ) ( x )
MathTextEng: a group is an abelian group if its binary operation is commutative .
MathTextFin: ryhmä on Abelin ryhmä jos sen binäärioperaatio on kommutatiivinen .
MathTextFre: un groupe est un groupe abélien si son opération binaire est commutative .
MathTextGer: eine Gruppe ist eine abelsche Gruppe wenn ihre zweistellige Verknüpfung kommutativ ist .
MathTextIta: un gruppo è un gruppo abeliano se la sua operazione binaria è commutativa .
MathTextPor: um grupo é um grupo abeliano se sua operação binária é comutativa .
MathTextSwe: en grupp är en abelsk grupp om dess binära operator är kommutativ .