square root - How do I the calculate the sqrt of a natural or rational number in coq? -


i'm learning coq , i'm trying make own point , line data types. i'd make function returns length of line, can't seem find sqrt function return calculation. tried used coq.reals.r_sqrt, apparently that's used abstract math, won't run calculation.

so tried importing coq.numbers.natural.abstract.nsqrt , coq.numbers.natint.nzsqrt. neither put sqrt function environment.

this have far...

require import coq.qarith.qarith_base. require import coq.numbers.natint.nzsqrt. require import coq.numbers.natural.abstract.nsqrt. require import coq.zarith.binint.  inductive point : type :=   point : q -> q -> point.  inductive line : type :=   line : point -> point -> line.  definition line_fst (l:line) :=   match l   | line x y => x   end.  definition line_snd (l:line) :=   match l   | line x y => y   end.  definition point_fst (p:point) :=   match p   | point x y => x   end.  definition point_snd (p:point) :=   match p   | point x y => y   end.  (* reference sqrt not found in current environment. *) definition line_length (l:line) :=   sqrt(     (minus (point_snd(line_fst l)) (point_fst(line_fst l)))^2      +     (minus (point_snd(line_snd l)) (point_fst(line_snd l)))^2   ).  example line_example : (   line_length (line (point 0 0) (point 0 2)) = 2 ).

if want square root compute, there 2 things can do.

  • use corn library. real number functions compute. however, real numbers functions can ask approximations precision, might not looking for. also, think corn not terribly maintained nowadays.

  • use natural number square root standard library mentioned, , use calculate square roots want precision yourself. function importingbinnat:

    coq < require import binnat. [loading ml file z_syntax_plugin.cmxs ... done]  coq < eval compute in n.sqrt 1000.         = 31%n       : n

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