akhileshs

user=> (def ! #(reduce * (take % (iterate inc 1))))
#'user/!
user=> (! 5)
120

akhileshs

>>> def prove(f):
...   s = Solver()
...   s.add(Not(f))
...   if s.check() == unsat:
...     print "proved"
...   else:
...     print "failed to prove"
>>> p, q = Bools('p q')
>>> demorgan = And(p, q) == Not(Or(Not(p), Not(q)))
>>> prove(demorgan)

akhileshs

user=> (defn prime? [x]
  #_=>   (empty? (filter #(= 0 (rem x %)) (range 2 (inc (int (Math/sqrt x)))))))

akhileshs

{-
      FirstScript.hs
      Akhilesh . S
-}


-- The Value size is an integer (Int), defined to be
-- the sum of twelve and thirteen.

fac :: Int -> Int

akhileshs

A collection of a bunch of interesting PL links and papers.**

• Propositions as Types
• Linear Types can change the world!
• Ur/Web: A Simple Model for Programming the Web
• Practical Affine Types
• Dependent Types for JavaScript
• Lazy Abstraction with Interpolants
• Adding Nesting Structure to Words
• Refinement Types for Haskell

akhileshs

(ns fluokitty.core
  (:use [uncomplicate.fluokitten core jvm]))

(map inc [1 2 3])

(fmap inc [1 2 3])

(fmap + [1 2 3] [1 2 3 4])

(fmap + [1 2 3] (list 1 2 3))

akhileshs

scala> trait T[+A] {
     |   def flatMap[B](f: A => T[B]): T[B] // bind operation
     |   def map[B](f: A => B): T[B]
     | }
defined trait T

akhileshs

scala> trait Exp { def eval() : Int }
defined trait Exp

scala> trait Lit extends Exp {
     |   val x : Int 
     |   def eval() = x
     | }
defined trait Lit

scala> trait Add extends Exp {

akhileshs

scala> case class B[F, T](c: B[F, T] => (F => T)) extends (B[F, T] => (F => T)) {
     |   def apply(b: B[F, T]) = c(b);
     | }
defined class B

scala> def Y[F, T] = (f: (F => T) => F => T) => 
     |   B[F, T](x => f(x(x)(_)))(B(x => f(x(x)(_))))
Y: [F, T]=> ((F => T) => (F => T)) => (F => T)

akhileshs

Direct links to free Springer maths books (pdf versions)

duplicates = multiple editions

A Classical Introduction to Modern Number Theory,Kenneth IrelandMichael Rosen

A Classical Introduction to Modern Number Theory,Kenneth IrelandMichael Rosen

A Course in Arithmetic,Jean-Pierre Serre