From 3586ed9e429c37c0e3532a631f9644e7b7f3fe3a Mon Sep 17 00:00:00 2001
From: Masaya Tojo <masaya@tojo.tokyo>
Date: Sat, 16 Jan 2021 22:41:22 +0900
Subject: wip80

---
 vikalpa/the-little-prover.scm | 163 ------------------------------------------
 1 file changed, 163 deletions(-)
 delete mode 100644 vikalpa/the-little-prover.scm

(limited to 'vikalpa/the-little-prover.scm')

diff --git a/vikalpa/the-little-prover.scm b/vikalpa/the-little-prover.scm
deleted file mode 100644
index fe7735e..0000000
--- a/vikalpa/the-little-prover.scm
+++ /dev/null
@@ -1,163 +0,0 @@
-;;; Vikalpa --- Proof Assistant
-;;; Copyright © 2020 Masaya Tojo <masaya@tojo.tokyo>
-;;;
-;;; This file is part of Vikalpa.
-;;;
-;;; Vikalpa is free software; you can redistribute it and/or modify it
-;;; under the terms of the GNU General Public License as published by
-;;; the Free Software Foundation; either version 3 of the License, or
-;;; (at your option) any later version.
-;;;
-;;; Vikalpa is distributed in the hope that it will be useful, but
-;;; WITHOUT ANY WARRANTY; without even the implied warranty of
-;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-;;; General Public License for more details.
-;;;
-;;; You should have received a copy of the GNU General Public License
-;;; along with Vikalpa.  If not, see <http://www.gnu.org/licenses/>.
-
-(define-module (vikalpa the-little-prover)
-  #:export (atom? nat? the-little-prover)
-  #:use-module (vikalpa))
-
-(define (atom? x)
-  (not (pair? x)))
-
-(define (nat? x)
-  (and (integer? x)
-       (<= 0 x)))
-
-(define-system the-little-prover ()
-  (define-core-function atom? (x) atom?)
-  (define-core-function nat? (x) nat?)
-  (define-core-function < (x y)
-    (lambda (x y)
-      (if (number? x)
-          (if (number? y)
-              (< x y)
-              (< x 0))
-          (if (number? y)
-              (< 0 y)
-              #f))))
-  (set-measure-predicate nat?)
-  (set-measure-less-than <)
-  (define-core-function + (x y)
-    (lambda (x y)
-      (if (number? x)
-          (if (number? y)
-              (+ x y)
-              x)
-          (if (number? y)
-              y
-              0))))
-  (define-core-function cons (x y) cons)
-  (define-core-function car (x)
-    (lambda (x)
-      (if (atom? x) '() (car x))))
-  (define-core-function cdr (x)
-    (lambda (x)
-      (if (atom? x) '() (cdr x))))
-  (define-trivial-total-function size (x)
-    (if (atom? x)
-        0
-        (+ 1
-           (+ (size (car x))
-              (size (cdr x))))))
-
-  ;; Axioms of Equal
-  (define-axiom equal-same (x)
-    (equal? (equal? x x) #t))
-  (define-axiom equal-swap (x y)
-    (equal? (equal? x y) (equal? y x)))
-  (define-axiom equal-if (x y)
-    (if (equal? x y) (equal? x y) #t))
-
-  ;; Axioms of Cons
-  (define-axiom atom/cons (x y)
-    (equal? (atom? (cons x y)) #f))
-  (define-axiom car/cons (x y)
-    (equal? (car (cons x y)) x))
-  (define-axiom cdr/cons (x y)
-    (equal? (cdr (cons x y)) y))
-  (define-axiom cons/car+cdr (x)
-    (if (atom? x)
-        #t
-        (equal? (cons (car x) (cdr x)) x)))
-
-  ;; Axioms of If
-  (define-axiom if-true (x y)
-    (equal? (if #t x y) x))
-  (define-axiom if-false (x y)
-    (equal? (if #f x y) y))
-  (define-axiom if-same (x y)
-    (equal? (if x y y) y))
-  (define-axiom if-nest-A (x y z)
-    (if x (equal? (if x y z) y) #t))
-  (define-axiom if-nest-E (x y z)
-    (if x #t (equal? (if x y z) z)))
-
-  ;; Axioms of Size
-  (define-axiom nat/size (x)
-    (equal? (nat? (size x)) #t))
-  (define-axiom size/car (x)
-    (if (atom? x)
-        #t
-        (equal? (< (size (car x)) (size x)) #t)))
-  (define-axiom size/cdr (x)
-    (if (atom? x)
-        #t
-        (equal? (< (size (cdr x)) (size x)) #t)))
-
-  ;; Axioms of `+` and `<`
-  (define-axiom identity-+ (x)
-    (if (nat? x)
-        (equal? (+ 0 x) x)
-        #t))
-  (define-axiom commute-+ (x y)
-    (equal? (+ x y) (+ y x)))
-  (define-axiom associate-+ (x y z)
-    (equal? (+ (+ x y) z) (+ x (+ y z))))
-  (define-axiom positive-+ (x y)
-    (if (< '0 x)
-        (if (< '0 y)
-            (equal? (< '0 (+ x y)) #t)
-            #t)
-        #t))
-  (define-axiom nat/+ (x y)
-    (if (nat? x)
-        (if (nat? y)
-            (equal? (nat? (+ x y)) #t)
-            #t)
-        #t))
-  (define-axiom common-addends-< (x y z)
-    (equal? (< (+ x z) (+ y z))
-            (< x y)))
-  
-  ;; Prelude
-  (define-function list-induction (x)
-    (if (atom? x)
-        x
-        (cons (car x)
-              (list-induction (cdr x)))))
-
-  (define-function star-induction (x)
-    (if (atom? x)
-        x
-        (cons (star-induction (car x))
-              (star-induction (cdr x)))))
-
-  (define-proof list-induction
-    (size x)
-    (((2 3) size/cdr)
-     ((2) if-same)
-     ((1) nat/size)
-     (() if-true)))
-
-  (define-proof star-induction
-    (size x)
-    (((2 3 1) size/car)
-     ((2 3 2) size/cdr)
-     ((2 3) if-true)
-     ((2) if-same)
-     ((1) nat/size)
-     (() if-true))))
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