lispy | LISP interpreter in Python | Interpreter library

In Clojure, the only one of those extra data structures that is required for some language constructs, besides lists, are vectors, and those are in well-known places such as around sequences of arguments to a function, or in symbol/expression pairs of a let. All of them can be used for data literals, but data literals are less often something you want to involve when writing a Clojure macro, as compared to function calls and macro invocations, which are always in lists.

I am not aware of anything in Clojure that makes writing macros more difficult than in Common Lisp, and there are a few features there distinct to Clojure that can make it a little bit easier, such as the behavior where Clojure backquoted expressions by default will namespace-qualify symbols, which is often what you want to prevent 'capturing' a name accidentally.

It makes sense that you cannot find variable inputsliceexample, because the variable you defined is named inputlistsliceexample. So your string-replace has worked fine. I'm not sure about your problem with open-input-string, but from the link you posted it looks to me like read takes in a file or a port or something like that, while your open-input-string returns a string.

I would define an identity function and use it as a default parameter:

Yes. It is very non lispy that we have a modifier ... that changes the meaning of element in front. eg. something ... is basically similar to . something except it works with structures like this:

Because the IF operator of Emacs Lisp allows one then form and multiple else forms. The else forms are indented differently from the then form for readability.

simple version for your inspiration:

I sort of figured it out. I'm still not completely sure how tk works, but from this other answer I got the information to fix it.

Tcl/Tk: Frames misbehave when resizing.

It took a sligth translation, but removing the :expand option for the right panel managed to solve the issue. The new code now looks like this:

You could implement it yourself. Here is an attempt:

I will quickly summarize the chapter about Unification Theory by Baader and Snyder from the Handbook of Automated Reasoning:

Terms are built from constants (starting with a lower case letter) and variables (starting with an upper case letter):

• a constant without arguments is a term: e.g. car
• a constant with terms as arguments, a so called function application, is a term. e.g. date(1,10,2000)
• a variable is a term, e.g. Date (variables never have arguments)

A substitution is a map assigning terms to variables. In the literature, this is often written as {f(Y)/X, g(X)/Y} or with arrows {X→f(Y), Y→g(X)}. Applying a substitution to a term replaces each variable by the corresponding term in the list. E.g. the substitution above applied to tuple(X,Y) results in the term tuple(f(Y),g(X)).

Given two terms s and t, a unifier is a substitution that makes s and t equal. E.g. if we apply the substitution {a/X, a/Y} to the term date(X,1,2000), we get date(a,1,2000) and if we apply it to date(Y,1,2000) we also get date(a,1,2000). In other words, the (syntactic) equality date(X,1,2000) = date(Y,1,2000) can be solved by applying the unifier {a/X,a/Y}. Another, simpler unifier would be X/Y. The simplest such unifier is called the most general unifier. For our purposes it's enough to know that we can restrict ourselves to the search of such a most general unifier and that, if it exists, it is unique (up to the names of some variables).

Mortelli and Montanari (see section 2.2. of the article and the references there) gave a set of rules to compute such a most general unifier, if it exists. The input is a set of term pairs (e.g. { f(X,b) = f(a,Y), X = Y } ) and the output is a most general unifier, if it exists or failure if it does not exist. In the example, the substitution {a/X, b/Y} would make the first pair equal (f(a,b) = f(a,b)), but then the second pair would be different (a = b is not true).

The algorithm nondeterministically picks one equality from the set and applies one of the following rules to it:

• Trivial: an equation s = s (or X=X) is already equal and can be safely removed.
• Decomposition: an equality f(u,v) = f(s,t) is replaced by the equalities u=s and v=t.
• Symbol Clash: an equality a=b or f(X) = g(X) terminates the process with failure.
• Orient: an equality of the form t=X where t is not another variable is flipped to X=t such that the variable is on the left side.
• Occurs check: if the equation is of the form X=t, t is not X itself and if X occurs somewhere within t, we fail. [1]
• Variable elimination: of we have an equation X=t where X does not occur in t, we can apply the substitution t/X to all other problems.

When there is no rule left to apply, we end up with a set of equations {X=s, Y=t, ...} that represents the substitution to apply.

Here are some more examples:

• {f(a,X) = f(Y,b)} is unifiable: decompose to get {a=Y, X=b} and flip to get {Y=a, X=b}
• {f(a,X,X) = f(a,a,b)} is not unifiable: decompose to get {a=a,X=a, X=b}, eliminate a=a by triviality, then eliminate the variable X to get {a=b} and fail with symbol clash
• {f(X,X) = f(Y,g(Y))} is not unifiable: decompose to get {X=Y, X=g(Y)}, eliminate the variable X to get {Y=g(Y)}, fail with occurs check

Even though the algorithm is non-deterministic (because we need to pick a equality to work on), the order does not matter. Because you can commit to any order, it is never necessary to undo your work and try a different equation instead. This technique is usually called backtracking and is necessary for the proof search in Prolog, but not for unification itself.

Now you're only left to pick a suitable data-structure for terms and substitutions and implement the algorithms for applying a substitution to a term as well as the rule based unification algorithm.

[1] If we try to solve X = f(X), we would see that X needs to be of the form f(Y) to apply decomposition. That leads to solving the problem f(Y) = f(f(Y)) and subsequently Y = f(Y). Since the left hand side always has one application of f less than the right hand side, they can not be equal as long we see a term as a finite structure.