λ.Lambda Calculus Engine

Lambda interpreter built in Scala. Supports AST View, CbN, CbV and Free Variables calculations.

Lambda Expression Symbols available:

• "λ": The lambda symbol represents the beginning of an abstraction.
• " ": The space allows for separating the argument from the function in an application.
• ".": The dot allows for separating the argument from the body of an abstraction.
• "(": The left parenthesis allows for representing the beginning of an application.
• ")":" The right parenthesis allows for representing the end of an application.
• string: Any other string, different from the ones above, will be interpreted as a variable.

Commands and syntax:

1. The Lambda expression must follow the syntax structure defined as:

   • <λexp> ::=
     • <var> #Variable
     • <LAMBDA> <var> <DOT> <λexp> #Abstraction
     • <LPAR> <λexp> <SPACE> <λexp> <RPAR> #Application

2. set <reduction strategy>

   • set call-by-name (default strategy)
   • set call-by-value
   • set free-variables

3. exit

IO Examples:

Expression	Call-by-Name Result	Call-by-Value Result
(λx.λy.y (λx.(x x) λx.(x x)))	λy.y	Infinite recursion
(λx.λx.(y x) z)	λx.(y x)	λx.(y x)
(λx.λy.x y)	λy*.y	λy*.y
(λy.λb.b ((λf.λb.f b) b))	λb*.b*	λb*.b*
(λf.(f λx.λy.x) ((λx.λy.λf.((f x) y) a) b))	a	a

To do:

• Add boolean and arithmetic expressions support

Compilation:

The project uses Scala 3.3.3 and sbt.

For running the program open the sbt interpreter using:

sbt

• Compile with:

compile

• And execute with:

run

• For exiting the program:

exit

Demo run:

Note: If you run the project on Windows, use the symbol "/" instead of the symbol "λ" as PowerShell does not support it.