The following repository contains two files CatL.hs and GCat.hs which are an generalisation of Size-proportionate Bijective encoding / decodings
for de Bruijn terms over Cat (Catalan Objects). The generalised de Bruijn terms notation is compressed into combinatorial objects, in particular,
binary tree data structures. Each term is tested by yielding large random numbers by encoding / decoding terms all efficiently represented through
Haskell classes.
De Bruijn terms are another class of syntax for formal Lambda calculi whereby variables within some application binds to the inner notation of the Lambda term rather than its outer body. Key logical rules must apply and as long as the arity of the application holds, two formal terms in both Lambda and de Bruijn should hold as equal - even though the notation differs. Therefore, de Bruijn terms are applicative arity-reserving notations for formal Lambda calculi. With this in mind, any terms in Lambda that are too complex to capture in notation can be encoded into de Bruijn terms as an alternative.
Original paper written by Paul Tarau, provided source of inspiration for continuous experimentation.
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