The cl-lambdacalc Reference Manual

Table of Contents

The cl-lambdacalc Reference Manual

This is the cl-lambdacalc Reference Manual, version 0.0.1, generated automatically by Declt version 3.0 "Montgomery Scott" on Sun May 15 03:54:37 2022 GMT+0.

1 Introduction

cl-lambdacalc

This is a simple library that allows you to define lisp functions using lambda calculus syntax. Function strings should use the uppercase letter 'A' as the lambda character. Nested functions may appear in the body of a function (example: Aa.Ab.(Axyz.xyz)ab(Axy.y)), and you may shorten arguments into one group (example: Afx.x is equivalent to Af.Ax.x).

The project includes a number of tests in the cl-lambdacalc-test package. These may be run with the included script.

Installation

You can install the library with Quicklisp.

(ql:quickload "cl-lambdacalc")

Example

> (define-lc-func foo "Ax.Ay.xy")
#<FUNCTION (LAMBDA (X)) {52DF54DB}>

> (funcall (foo (lc-func "Ax.x")) 42)
42

> (funcall (lc-and #'lc-true) #'lc-true)
#<FUNCTION (LAMBDA (X)) {52D34A8B}>

> (lc-true-p (funcall (lc-and #'lc-true) #'lc-true))
T

> (lc-true-p (funcall (lc-and #'lc-true) (lc-not #'lc-true)))
NIL

> (define-lc-func four "Afx.f(f(f(fx)))")
#<FUNCTION (LAMBDA (F)) {52DF583B}>

> (church-numeral-to-number (lc-succ #'four))
5

> (church-numeral-to-number (funcall (lc-expt #'four) #'four))
256

Exported Symbols

• lc-func func-string Returns func-string as a lisp function.
• define-lc-func name func-string (Macro) Binds the func-string function to the function slot of the symbol name.
• lc-true x Axy.x
• lc-false x Axy.y
• lc-if x Axyz.xyz
• lc-and x Axy.(Axyz.xyz)xy(Axy.y)
• lc-or x Axy.(Axyz.xyz)x(Axy.x)y
• lc-not x Ax.(Axyz.xyz)x(Axy.y)(Axy.x)
• lc-true-p func Returns true if func is lc-true, otherwise nil.
• lc-false-p func Returns true if func is lc-false, otherwise nil.
• lc-succ n Anfx.f(nfx)
• lc-add m Amnfx.mf(nfx)
• lc-mult x Axyz.x(yz)
• lc-expt x Axy.yx
• church-numeral-to-number func Returns the number equivalent of the church numeral func.
• number-to-church-numeral num Returns the church numeral function equivalent of the number num.

2 Systems

The main system appears first, followed by any subsystem dependency.

2.1 cl-lambdacalc

Author

S M McLeod

License

MIT

Description

Define Lisp functions using lambda calculus syntax

Version

0.0.1

Dependency

cl-ppcre

Source

cl-lambdacalc.asd (file)

Components

• package.lisp (file)
• cl-lambdacalc.lisp (file)

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

3.1 Lisp

3.1.1 cl-lambdacalc.asd

Location

cl-lambdacalc.asd

Systems

cl-lambdacalc (system)

3.1.2 cl-lambdacalc/package.lisp

Parent

cl-lambdacalc (system)

Location

package.lisp

Packages

cl-lambdacalc

3.1.3 cl-lambdacalc/cl-lambdacalc.lisp

Dependency

package.lisp (file)

Parent

cl-lambdacalc (system)

Location

cl-lambdacalc.lisp

Exported Definitions

• church-numeral-to-number (function)
• define-lc-func (macro)
• lc-false-p (function)
• lc-func (function)
• lc-true-p (function)
• number-to-church-numeral (function)

Internal Definitions

• close-paren-position (function)
• lc-boolean-test (function)
• next-body-token (function)
• parse-func-string (function)
• try-or-nil (macro)
• unstructured-body-list (function)

4 Packages

Packages are listed by definition order.

4.1 cl-lambdacalc

Source

package.lisp (file)

Use List

• cl-ppcre
• common-lisp

Exported Definitions

• church-numeral-to-number (function)
• define-lc-func (macro)
• lc-add (function)
• lc-and (function)
• lc-expt (function)
• lc-false (function)
• lc-false-p (function)
• lc-func (function)
• lc-if (function)
• lc-mult (function)
• lc-not (function)
• lc-or (function)
• lc-succ (function)
• lc-true (function)
• lc-true-p (function)
• number-to-church-numeral (function)

Internal Definitions

• close-paren-position (function)
• lc-boolean-test (function)
• next-body-token (function)
• parse-func-string (function)
• try-or-nil (macro)
• unstructured-body-list (function)

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

5.1 Exported definitions

5.1.1 Macros

Macro: define-lc-func NAME FUNC-STRING

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

5.1.2 Functions

Function: church-numeral-to-number FUNC

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: lc-add M

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-and X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-expt X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-false X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-false-p FUNC

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: lc-func FUNC-STRING

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: lc-if X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-mult X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-not X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-or X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-succ N

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-true X

Package

cl-lambdacalc

Source

/builds/quickref/quickref/bin/declt

Function: lc-true-p FUNC

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: number-to-church-numeral NUM

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

5.2 Internal definitions

5.2.1 Macros

Macro: try-or-nil BODY

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

5.2.2 Functions

Function: close-paren-position S

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: lc-boolean-test FUNC BOOL

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: next-body-token BODY

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: parse-func-string FUNC-STRING

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Function: unstructured-body-list BODY

Package

cl-lambdacalc

Source

cl-lambdacalc.lisp (file)

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types