Functional Programming library
some programs included here are:
start-λογικι-guile.scm a symbolic calculus program for logical expressions (Scheme Guile version)
start-λογικι.scm a symbolic calculus program for logical expressions
start-goodstein-recursive.scm : a symbolic calculus program for goodstein sequences
Scheme+ versions: start-λογικι-guile+.scm start-λογικι-racket+.scm
some examples:
Logical computation of the minimal disjonctive normal form of a logical expression:
(infix-symb-min-dnf '{{(not a) and (not b) and (not c) and (not d)} or {(not a) and (not b) and (not c) and d} or {(not a) and (not b) and c and (not d)} or {(not a) and b and (not c) and d} or {(not a) and b and c and (not d)} or {(not a) and b and c and d} or {a and (not b) and (not c) and (not d)} or {a and (not b) and (not c) and d} or {a and (not b) and c and (not d)} or {c and (not d)}} )
((¬a ∧ b ∧ d) ∨ (¬b ∧ ¬c) ∨ (c ∧ ¬d))
(cnf-infix-symb '{{(not a) and (not b) and (not c) and (not d)} or {(not a) and (not b) and (not c) and d} or {(not a) and (not b) and c and (not d)} or {(not a) and b and (not c) and d} or {(not a) and b and c and (not d)} or {(not a) and b and c and d} or {a and (not b) and (not c) and (not d)} or {a and (not b) and (not c) and d} or {a and (not b) and c and (not d)} or {c and (not d)}})
((¬a ∨ ¬b ∨ c) ∧ (¬a ∨ ¬b ∨ ¬d) ∧ (¬a ∨ ¬c ∨ ¬d) ∧ (b ∨ ¬c ∨ ¬d) ∧ (¬b ∨ c ∨ d))
(infix-symb-bool-min-dnf '(and (<=> (and p q) r) (<=> (not (and p q)) r)))
□
Goodstein sequences:
;; goodstein-init-atomic-rec2 : start-up function
;;
;; - set a few variables
;; - define Goodstein function recursively
;; - compute the start number in hereditary base
;; - call the Goodstein recursive function with the start number as argument
;;
;; the Goodstein recursive function do:
;; - check if we have reached zero
;; - display polynomial at each step
;; - bump the base
;; - decrement polynomial by calling symbolic-polynomial-1 function (also called h)
;; - call (recursively) goodstein-rec2
;; > (goodstein-init-atomic-rec2 266)
;; G(266)(1)=((2 ^ (2 ^ (2 + 1))) + (2 ^ (2 + 1)) + 2)
;; P(266)(1)=((ω ^ (ω ^ (ω + 1))) + (ω ^ (ω + 1)) + ω)
;; G(266)(2)=((3 ^ (3 ^ (3 + 1))) + (3 ^ (3 + 1)) + 2)
;; P(266)(2)=((ω ^ (ω ^ (ω + 1))) + (ω ^ (ω + 1)) + 2)
;; G(266)(3)=((4 ^ (4 ^ (4 + 1))) + (4 ^ (4 + 1)) + 1)
;; P(266)(3)=((ω ^ (ω ^ (ω + 1))) + (ω ^ (ω + 1)) + 1)
;; G(266)(4)=((5 ^ (5 ^ (5 + 1))) + (5 ^ (5 + 1)))
;; P(266)(4)=((ω ^ (ω ^ (ω + 1))) + (ω ^ (ω + 1)))
;; G(266)(5)=((6 ^ (6 ^ (6 + 1))) + (5 * (6 ^ 6)) + (5 * (6 ^ 5)) + (5 * (6 ^ 4)) + (5 * (6 ^ 3)) + (5 * (6 ^ 2)) + (5 * 6) + 5)
;; P(266)(5)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (5 * ω) + 5)
;; G(266)(6)=((7 ^ (7 ^ (7 + 1))) + (5 * (7 ^ 7)) + (5 * (7 ^ 5)) + (5 * (7 ^ 4)) + (5 * (7 ^ 3)) + (5 * (7 ^ 2)) + (5 * 7) + 4)
;; P(266)(6)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (5 * ω) + 4)
;; G(266)(7)=((8 ^ (8 ^ (8 + 1))) + (5 * (8 ^ 8)) + (5 * (8 ^ 5)) + (5 * (8 ^ 4)) + (5 * (8 ^ 3)) + (5 * (8 ^ 2)) + (5 * 8) + 3)
;; P(266)(7)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (5 * ω) + 3)
;; G(266)(8)=((9 ^ (9 ^ (9 + 1))) + (5 * (9 ^ 9)) + (5 * (9 ^ 5)) + (5 * (9 ^ 4)) + (5 * (9 ^ 3)) + (5 * (9 ^ 2)) + (5 * 9) + 2)
;; P(266)(8)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (5 * ω) + 2)
;; G(266)(9)=((10 ^ (10 ^ (10 + 1))) + (5 * (10 ^ 10)) + (5 * (10 ^ 5)) + (5 * (10 ^ 4)) + (5 * (10 ^ 3)) + (5 * (10 ^ 2)) + (5 * 10) + 1)
;; P(266)(9)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (5 * ω) + 1)
;; G(266)(10)=((11 ^ (11 ^ (11 + 1))) + (5 * (11 ^ 11)) + (5 * (11 ^ 5)) + (5 * (11 ^ 4)) + (5 * (11 ^ 3)) + (5 * (11 ^ 2)) + (5 * 11))
;; P(266)(10)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (5 * ω))
;; G(266)(11)=((12 ^ (12 ^ (12 + 1))) + (5 * (12 ^ 12)) + (5 * (12 ^ 5)) + (5 * (12 ^ 4)) + (5 * (12 ^ 3)) + (5 * (12 ^ 2)) + (4 * 12) + 11)
;; P(266)(11)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 11)
;; G(266)(12)=((13 ^ (13 ^ (13 + 1))) + (5 * (13 ^ 13)) + (5 * (13 ^ 5)) + (5 * (13 ^ 4)) + (5 * (13 ^ 3)) + (5 * (13 ^ 2)) + (4 * 13) + 10)
;; P(266)(12)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 10)
;; G(266)(13)=((14 ^ (14 ^ (14 + 1))) + (5 * (14 ^ 14)) + (5 * (14 ^ 5)) + (5 * (14 ^ 4)) + (5 * (14 ^ 3)) + (5 * (14 ^ 2)) + (4 * 14) + 9)
;; P(266)(13)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 9)
;; G(266)(14)=((15 ^ (15 ^ (15 + 1))) + (5 * (15 ^ 15)) + (5 * (15 ^ 5)) + (5 * (15 ^ 4)) + (5 * (15 ^ 3)) + (5 * (15 ^ 2)) + (4 * 15) + 8)
;; P(266)(14)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 8)
;; G(266)(15)=((16 ^ (16 ^ (16 + 1))) + (5 * (16 ^ 16)) + (5 * (16 ^ 5)) + (5 * (16 ^ 4)) + (5 * (16 ^ 3)) + (5 * (16 ^ 2)) + (4 * 16) + 7)
;; P(266)(15)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 7)
;; G(266)(16)=((17 ^ (17 ^ (17 + 1))) + (5 * (17 ^ 17)) + (5 * (17 ^ 5)) + (5 * (17 ^ 4)) + (5 * (17 ^ 3)) + (5 * (17 ^ 2)) + (4 * 17) + 6)
;; P(266)(16)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 6)
;; G(266)(17)=((18 ^ (18 ^ (18 + 1))) + (5 * (18 ^ 18)) + (5 * (18 ^ 5)) + (5 * (18 ^ 4)) + (5 * (18 ^ 3)) + (5 * (18 ^ 2)) + (4 * 18) + 5)
;; P(266)(17)=((ω ^ (ω ^ (ω + 1))) + (5 * (ω ^ ω)) + (5 * (ω ^ 5)) + (5 * (ω ^ 4)) + (5 * (ω ^ 3)) + (5 * (ω ^ 2)) + (4 * ω) + 5)
;;