

Programming Languages, lambda calculus, calculus of constructions  - gtani
http://northhorizon.net/2010/interview-with-kalani-thielen-trends-in-programming-languages/

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maxdemarzi
"Languages like F#, Scala and Haskell each fall somewhere in between these two
extremes. None of them are precise enough to accept only halting programs
(although Haskell is inching more and more toward a dependently-typed language
every year). Yet all of them are more precise than (say) Scheme, where
fallible human convention alone determines whether or not the “+” function
returns an integer or a chicken."

There's some material for xkcd.com

Reading the rest of the article, one thing I don't get is why the focus on the
idea that "programs and proofs are equivalent". You can do math in isolation,
but your programs have to run on something which runs on something which runs
on something all the way down to the hardware level where at any step along
the way you lose control of the "precision" of the code being run or some
anomaly environmental/hardware factor affects the overall outcome and the
proof is out the window.

