HallaSurvivor / LanguageExpander

Takes a description of (a family of) extensions by definition, and outputs a program that converts between the extensions

Language Expander

Takes in a description of languages and outputs a parser converting high level languages into low level ones. This makes it possible to automate the unraveling of a complicated chain of extension by definitions like those found in Set Theory.

Converter, when run, opens a repl that allows the following commands:

• <lang> <formula> -- prints the formula unambiguously as a tree
• Convert<lang1>To<lang2> <formula_in_lang_1> -- prints the version of the given formula converted to lang2

if lang1 extends lang2, then lang1 gains access to all the symbols defined in lang2

syntax available in all languages is:

• Eq(x,y)
• formula && formula
• formula || formula
• formula -> formula
• formula <-> formula
• Not(formula)
• ForAll var (formula)
• Exists var (formula)

language_file should be a file written in the syntax shown in the following example:

---

BST:
relNew (In, 2)

BSTA: 
extending BST
funDef (Empty,0) ForAll z (Not In(z,o))
funDef (PowerSet,1) ForAll z (In(z,o) <-> ForAll w (In(w,z) -> In(w,v1)))
relDef (Subset,2) ForAll z (In(z,v1) -> In(z,v2))
funDef (Union,1) ForAll z (In(z,o) <-> Exists w (In(z,w) && In(w,v1)))
funDef (Singleton, 1) ForAll z (In(z,o) <-> Eq(z,v1))
funDef (Pairing, 2) ForAll z (In(z,o) <-> Eq(z,v1) || Eq(z,v2))

BSTB:
extending BSTA
funDef (BinUnion, 2) Eq(o,Union(Pairing(v1,v2)))

GroupT:
funNew (E,0)
funNew (Inv,1)
funNew (Mult,2)

GTComm:
extending GroupT
funDef (Comm,2) Eq(o,Mult(Inv(v1),Mult(Inv(v2),Mult(v1,v2))))

---

Keep in mind this was made for personal use, so I was OK leaving things kind of brittle. In particular, errors are handled extremely disgracefully. Here's a list of all the possible pitfalls I could think of:

• each block should be separated by a blank line
• each language can extend at most one language
• each language name should begin with a Capital
• language names should not contain numerals
• all symbols should start with a Capital
• all variables should start with a lowercase letter
• relNew and funNew create new symbols, with no definition
• relDef and funDef define new symbols, coupled with a way to expand them
• don't use relNew/funNew with extends
• don't use relDef/funDef without extends
• constant symbols are 0-arity functions
• for definitions, the input variables should be called v1 ... vn
• for function definitions, the output variable should be called o
• don't use v or o for anything else.

---