**Project Description**
a simple lambda-calculus interpreter implemented in F#

using NUnit as a test framework and FParsec for parsing

Checks the evaluation for known identifiers (expressions assigned to an name)

**the sources are provided for use with VS2012 RTM and .net 4.5 - the FParsec.dll was compiled with VS2012 RC and is provided in the sources, AFAIK the nuget-version will not work at the moment**
## Syntax

Atoms = one single lower letter and any number (including zero) of digits

Identifiers = beginning with a upper letter and ending in any number of letters or digits

Single Atom or Identifier is an Expression

Application (with or without parentheses) is an Exprewssion (for example "ab", "Id b")

Abstraction (\[atomName].Body where Body is an expression) is an Expression

Assignment:

Identifier :=

Expression
Comparision:

Expression ==

Expression
Evaluation:

Expression
Command:

?command
where command:

- quit = exitst the console
- load file = loads the file as text and interprets it line by line

## Sample run for simple number-arithmetic

LAMBDA CALCULUS INTERPRETER

===========================

>>> ?load numbers

\abf.(fab)

== [MkPair]

\ab.a

== [Fst]

\ab.b

== [Snd]

\nfx.(f(nfx))

== [Succ]

\fx.x

== [Snd, N0]

\fx.(fx)

== [N1]

\fx.(f^{2} x)

== [N2]

\fx.(f^{3} x)

== [N3]

\fx.(f^{4} x)

== [N4]

\fx.(f^{5} x)

== [N5]

\fx.(f^{6} x)

== [N6]

\fx.(f^{7} x)

== [N7]

\fx.(f^{8} x)

== [N8]

\fx.(f^{9} x)

== [N9]

\nmfx.(nf(mfx))

== [Add]

\nm.(n\_mfx.(mf(_mfx))\fx.x)

== [Mult]

\pf.(f(p\ab.b)\fx.(f(p\ab.bfx)))

== [Shift]

\f.(f\fx.x\fx.x)

== [Init]

\n.(n\pf.(f(p\ab.b)\fx.(f(p\ab.bfx)))\f.(f\fx.x\fx.x)\ab.a)

== [Pred]

>>> Mult N9 N8

\f_x.(f^{72} _x)

>>> Sqr := \n.Mult n n

\n.(n\_mfx.(nf(_mfx))\fx.x)

== [Sqr]

>>> Sqr N9

\f_x.(f^{81} _x)

>>> SqrMinusOne := \n.Pred (Sqr n)

\n.(n\_mfx.(nf(_mfx))\fx.x\pf.(f(p\ab.b)\fx.(f(p\ab.bfx)))\f.(f\fx.x\fx.x)\ab.a)

== [SqrMinusOne]

>>> SqrMinusOne N9

\fx.(f^{80} x)

>>> F := \n.Pred (Sqr (Add n N2))

\n.(n\_mfx.(nf(f^{2} (_mfx)))\f__x.(nf(f^{2} (nf(f^{2} __x))))\pf.(f(p\ab.b)\fx.

(f(p\ab.bfx)))\f.(f\fx.x\fx.x)\ab.a)

== [F]

>>> F N3

\fx.(f^{24} x)

>>>?quit