Regular Ruby method calls use () not curly braces which are for blocks. If you don’t like [] for calling a lambda, you can always use the call method. Example: >> by_two = lambda { |x| x * 2 } #=> #<Proc:0x0000000101304588@(irb):1> >> by_two[5] #=> 10 >> by_two.call(5) #=> 10 Edit In newer version of … Read more
First, it is possible to compile the lambda calculus efficiently to machine code even on existing architectures. After all, scheme is the lambda calculus plus a bit extra, and it can be compiled efficiently. However, scheme & co are the lambda calculus under strict evaluation. It is also possible to compile the lambda calculus under … Read more
Normally, the specific variable names that we chose in the lambda calculus are meaningless – a function of x is the same thing as a function of a or b or c. In other words: (λx.(λy.yx)) is equivalent to (λa.(λb.ba)) – renaming x to a and y to b does not change anything. From this, … Read more
In a word, general recursion. Haskell allows for arbitrary recursion while System F has no form of recursion. The lack of infinite types means fix isn’t expressible as a closed term. There is no primitive notion of names and recursion. In fact, pure System F has no notion of any such thing as definitions! So … Read more
Lambda calculus Lambda calculus has a way of spiraling into a lot of steps, making solving problems tedious, and it can look real hard, but it isn’t actually that bad. In lambda calculus, there are only lambdas, and all you can do with them is substitution. Lambdas are like a function or a method – … Read more
If you are done with the Wikipedia entry, follow its link to the online Structure and Interpretation of Computer Programs, do the assignments, or read the book.
To compare it to C, the current continuation is like the current state of the stack. It has all the functions waiting for the result of the current function to finish so they can resume execution. The variable captured as the current continuation is used like a function, except that it takes the provided value … Read more
The benefit of lambda calculus is that it’s an extremely simple model of computation that is equivalent to a Turing machine. But while a Turing machine is more like assembly language, lambda calculus is more a like a high-level language. And if you learn Church encodings that will help you learn the programming technique called … Read more
The phenomenon comes from the amount of shared beta-reduction steps, which can be dramatically different in Haskell-style lazy evaluation (or usual call-by-value, which is not that far in this respect) and in Vuillemin-Lévy-Lamping-Kathail-Asperti-Guerrini-(et al…) “optimal” evaluation. This is a general feature, that is completely independent from the arithmetic formulas you could use in this particular … Read more
I agree with Dietrich Epp: it’s a combination of several things that make GHC fast. First and foremost, Haskell is very high-level. This enables the compiler to perform aggressive optimisations without breaking your code. Think about SQL. Now, when I write a SELECT statement, it might look like an imperative loop, but it isn’t. It … Read more