
A book that presents mathematical logic and proof structure using the Haskell functional programming language, and presents Haskell using mathematical logic and proof structure.
https://staff.fnwi.uva.nl/d.j.n.vaneijck2/HR/ - The Haskell Road to Logic, Maths and Programming - Uses Haskell, as the title suggests
https://mitp-content-server.mit.edu/books/content/sectbyfn/b... - The Structure and Interpretation of Classical Mechanics - Uses Scheme
The REPL is an incredibly user-friendly way to learn to program. Try it. I'm surprised you like math and don't want to use the REPL, since the REPL in many ways resembles a powerful calculator (and can be used as such)
If you really like the math approach, and grow to appreciate the REPL, give "The Haskell Road to Logic, Maths and Programming" by Doets and van Eijck a try.
But no, you can't pick up programming just from reading books without attempting to program. You could pick up a good bit of computer science like that, but not programming. Programming must be experienced.
In fact, the book is even called "The Haskell Road to Logic, Maths and Programming" [0]. It covers mathematical notation, proof construction, and lots of interesting portions of discrete math that should be of interest to programmers. And large portions of the results are demonstrated or used in interesting Haskell programs.
[0] http://www.amazon.com/Haskell-Programming-Second-Edition-Com...
Then you can move to a discrete math book like Discrete Mathematics with Applications or Mathematics for Computer Science (free pdf courses.csail.mit.edu/6.042/fall10/mcs-ftl.pdf) and any Calculus book of your liking.
There are also great resources to learn Math using Haskell. I'm working through The Haskell Road to Logic, Maths and Programming and it's proving to be great http://www.haskell.org/haskellwiki/Books_and_tutorials/Mathe...