A simple REPL for lambda calculus
Project description
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*:
(* church-lambda EBNF *) (* --- meta --- *) (* line or line, line, line... *) program = {line}; (* define or function *) line = (define | function); (* ex: @ID: λx.x *) define = "@" alias ":" function; (* --- lambdas --- *) (* lambda or an application *) function = lambda | application; (* ex: λx.x) lambda = "λ" variable "." expr; (* ex: '(λx.x λy.y) application = '(' expr expr ')'; (* lambda or application or variable or alias *) expr = (lambda | application | variable | alias ); (* --- primitives --- *) (* one lowercase letter *) variable = /[a-z]/; (* one underscore or capital followed by zero or more [underscores, captials, or digits] *) 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.
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