Write a list circularity test
a) Implement implication_string that tests if a string is an implication of the form "P=>Q" where P and Q are letters in the 'A'..'Z' range:
let implication_string s = ... ;; val implication_string : string -> bool = <fun>
b) Consider the following fonction:
let transitive_implication s1 s2 = assert (implication_string s1); assert (implication_string s2); s1.[3]=s2.[0];;
This function tests if two ordered implications are transitive, for exemple:
transitive_implication "P=>Q" "Q=>R";; - : bool = true
c) Let pred be a binary predicate like transitive_implication is. Implement the circular_chain function:
let circular_chain pred l = ... ;;
val circular_chain : ('a -> 'a -> bool) -> 'a list -> bool = <fun>
As a use-case, given three well ordered implications, the circular_chain function is used to prove the equivalence "P<=>Q<=>R" by just typing:
circular_chain transitive_implication ["P=>Q";"Q=>R";"R=>P"];; - : bool = true