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Introduction, Scheme basics (expressions, values)
Introduction, Scheme basics (expressions, values)

... • Note: there is nothing in the syntax for defining types! This is a convention we manually enforce (for now..). ...
PPT
PPT

... procedure p(a : array [1..10] of integer) procedure p(n: integer, a : array [1..n] of integer) • Attempt at orthogonal design backfires – parameter must be given a type – type cannot contain variables How could this have happened? Emphasis on teaching ...
Notes
Notes

... That shouldn’t be surprising. What might be surprising is that every SML program can be compiled down to a pure lambda calculus program! (Though that’s not exactly what the compiler actually does—it wouldn’t be efficient.) That’s true for many other functional languages, too. Lambda calculus is the ...
PowerPoint-presentatie
PowerPoint-presentatie

... constraints (the specification) from solving those constraints (the implementation). Therefore, the type inferencer can not only simulate well known algorithms such as W and M, but it can also solve constraints by using type graphs. A type graph is an advanced data structure to represent a substitut ...
Type Systems
Type Systems

... very useful in multi-parameter type classes implemented in Hugs and GHC ...
Type
Type

... This can be very convenient but can make debugging more difficult. There can be performance penalties (why?) Examples – Lisp, Scheme, Perl. ...
4-up
4-up

... function that maps proofs of A to proofs of B pair of a proof of A and a proof of B either a proof of A or a proof of B ...
Practice Problem 9.1 Snow Removal
Practice Problem 9.1 Snow Removal

... function. To illustrate this, write a formula in cell OpCosts!K7, using an IF function, to calculate total operating cost per storm for the corresponding equipment type. Write the formula so that it can be copied down the column. ...
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Hindley–Milner type system

In type theory and functional programming, Hindley–Milner (HM) (also known as Damas–Milner or Damas–Hindley–Milner) is a classical type system for the lambda calculus with parametric polymorphism, first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis.Among HM's more notable properties is completeness and its ability to deduce the most general type of a given program without the need of any type annotations or other hints supplied by the programmer. Algorithm W is a fast algorithm, performing type inference in almost linear time with respect to the size of the source, making it practically usable to type large programs. HM is preferably used for functional languages. It was first implemented as part of the type system of the programming language ML. Since then, HM has been extended in various ways, most notably by constrained types as used in Haskell.
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