I just thought I would mention (in case you are still interested in
putting the code into FriCAS) that I have fixed the bugs that I know
about in file computation.spad.pamphlet at:
https://github.com/martinbaker/multivector/

In this pamphlet are implementations of various mathematical
structures related to computation. such as:
* lambda.spad
* ski.spad
* ILogic.spad

The aim here is to model and study λ-calculus, Combinators and
Intuitionistic logic as abstact mathematical structures which were
discovered before modern computers and are worthy of study in their
own right.

These domains all represent systems of logic and are constructed from
tree structures and act on tree structures. These 'tree logics' seem
to 'generate' other algebras, for instance, in the tutorials below, we
see that this λ structure:

\x.\y.y x

can be converted to this SKI structure:

S(K(SI))(S(KK)I)

This allows us to 'abstract' the definition, in that it takes a
definition in terms of arbitrary variables and it converts to a
definition without arbitrary variables. So these structures are
equivalent and they both reverse two operands. That is they generate
an n-ary to n-ary function, in this case:

(x,y) -> (y,x)

This seems to be a 'monad' and it would be interesting to see if these
domains could be implemented as instances of a monad (a monad in
category theory terms, not the current FriCAS monad category).

I would also like to extend this to investigate abstract structures
such as 'tree automata'.

For more details see:
Code availible in file computation.spad.pamphlet at:
https://github.com/martinbaker/multivector/
Overview:
http://www.euclideanspace.com/maths/standards/program/mycode/computation/
Tutorial for lambda calculus:
http://www.euclideanspace.com/maths/standards/program/mycode/computation/lambda/
Tutorial for SKI calculus:
http://www.euclideanspace.com/maths/standards/program/mycode/computation/ski/
Tutorial for Intuitionistic Logic
http://www.euclideanspace.com/maths/standards/program/mycode/computation/intuitionistic/
Tutorial for utilities to coerce between computation domains
http://www.euclideanspace.com/maths/standards/program/mycode/computation/utility/

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