CHURCH-REPL

A simple REPL for lambda calculus

Use:

when calling churchrepl and new REPL will be opened.

churchrepl [-f --file file [file ...]] [-v --verbose]

Flags:

(optional) Read definitions and expressions from a file before loading the normal REPL.

-f|--file file [file ...]

(optional) print debugging and verbose output.

-v|--verbose

Church repl file structure:

The EBNF grammar is as follows*:

(* Lambda Program *)
program     = {line};
line        = (define | function);
define      = "@" alias ":" function;
function    = lambda | application;
lambda      = ("λ" | "\") variable "." expr;
application = '(' expr  expr ')';
expr        = (lambda | application | variable | alias ) ;
variable    = /[a-z]/;
alias       = /[_A-Z][_A-Z0-9]*/;

A simple example program:

@ID: λx.x
@APPLY: λf.λx.(f x)
@TRUE: λx.λy.x
@FALSE: λx.λy.y
@ZERO: λf.λx.x
@SUCC: λn.λf.λx.(f ((n f) x))
@ONE: (SUCC ZERO)
@TWO: (SUCC ONE)
@THREE: (SUCC TWO)
@FOUR: (SUCC THREE)
(SUCC ZERO)
(SUCC ONE)
(SUCC TWO)
(SUCC THREE)
(SUCC FOUR)

Note: The λ (lambda, unicode u03bb) is equivalent to a backslash as far as this program is concerned. When using the repl it may be easier to use a backslash.