A Variant of Higher-Order Anti-Unification
This is a Java implementation of the higher-order anti-unification
algorithm described in:
-
Alexander Baumgartner,
Temur Kutsia,
Jordi Levy,
Mateu Villaret.
A Variant of Higher-Order Anti-Unification.
In: F. van Raamsdonk, editor, Proceedings of the 24th International Conference on Rewriting Techniques and Applications, RTA 2013. June 24-26, 2013, Eindhoven, The Netherlands. Vol. 21 of the Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl, 2013, 113-127.
-
Alexander Baumgartner,
Temur Kutsia,
Jordi Levy,
Mateu Villaret.
Higher-Order Pattern Anti-Unification in Linear Time.
Journal of Automated Reasoning. 58(2):293–310, 2017.
Part of the Library of Unification and Anti-Unification Algorithms.
The algorithm solves the following problem:
| GIVEN: |
Higher-order terms t and s. |
| FIND: |
A higher-order pattern least general generalization of t and s. |
The anti-unification algorithm relies on
a subalgorithm that constructively decides about the existence of a variable renaming such that two lambda terms become alpha-equivalent. This subalgorithm can also be
accessed separately.
The algorithm works both for untyped and simply-typed λ-terms. For
untyped terms, the input should not contain β-redexes. For simply typed
terms, the input should be in the η-long β-normal form.
Input Syntax:
-
The symbols A-Z, a-z, 1-9 are allowed for variable names and
function names. Names can be of any length.
- If the first letter of the name is within [u,z] or [U,Z], then it
is a variable.
- The backslash "\" is used for the lambda symbol.
- The colon ":" is used to declare the type.
- The dash "-" is used as type constructor.
- Mixed mode of typed and untyped calculus is allowed.
This software is released under the
GNU Lesser General Public License ("LGPL").
For presentation purpose, the Java source code has been translated into JavaScript by the
GWT compiler.
Some examples (click on them to prepared the input form):
- \x.f(x,x) =^= \x.f(a,x)
- \x.f(b,x) =^= \x.f(a,x)
- \x,y.f(f(g(x),y),f(g(y),x)) =^= \x,y.f(h(y,g(x)),h(x,g(y)))
- \x,y.f(x,y) =^= \x,y.f(y,x)
- \y:i2.\z:i3. f:i2-i3-i1(y,z) =^= \y:i2.\z:i3. x:i3-i2-i1(z,y)
- \x,y,z.g(f(x,z),f(y,z),f(y,x)) =^= \x,y,z.g(h(y,x),h(x,y),h(z,y))
- \x,y.f(\z.g(z,y),g(x,y)) =^= \x,y.f(\z.h(y,z),h(y,x))
- \x.f(\y.g(x,y),\y.g(y,x)) =^= \x.f(\y.h(x,y,x),\y.h(y,x,y))
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