Unification in Elixir
Pattern matching in Elixir, inspired by Erlang and Prolog, includes unification for equality assertion and variable assignment. Unification handles terms, variables, and lists, allowing for symbolic equation solving efficiently.
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Pattern matching is a fundamental feature in Elixir, inspired by Erlang's roots in Prolog. Unification, a two-sided pattern matching technique, asserts equality and assigns variables accordingly. In Elixir, unification operates on terms, which can be variables, atomic values, or lists of terms. Successful unification results in a substitution mapping variables to values. Unlike Elixir's pattern matching, unification allows for partially known values, enabling powerful symbolic equation solving. Unification examples illustrate successful and failed matches, showcasing the flexibility and constraints of the process. Variables play a crucial role in unification, representing placeholders for values that must align across terms. The implementation of unification involves walking through terms, testing equivalence, handling variables, and unifying lists recursively. By leveraging Elixir's pattern matching capabilities and substitution mappings, unification offers a structured approach to solving symbolic equations efficiently.
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4 commentsTo this end, good coverage of decent (destructive) unification algorithms can be found in any simple resource on type inference (https://okmij.org/ftp/ML/generalization/sound_eager.ml) or the Warren Abstract Machine (https://github.com/a-yiorgos/wambook/blob/master/wambook.pdf).
Of course, there are times where you would want to reify substitutions as a data structure to compose and apply, but most of the time you just want to immediately apply them in a pervasive way.
Despite what another comment says, unification is a valid - and rather convenient - way to implement pattern matching (as in the style of ML) in an interpreter: much like how you rewrite type variables with types you are unifying them with, you can rewrite the pattern variables to refer to the parts of the (evaluated) value you are matching against (which you then use to extend the environment with when evaluating the right hand side).
https://github.com/norvig/paip-lisp
There is also an implementation in Python, but I have never tested it, just googled it now: https://github.com/dhconnelly/paip-python/blob/master/prolog...
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