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. ...

... 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. ...

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 ...

... 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 ...

Type

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

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

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 ...

... 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 ...

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 ...

... 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 ...

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 ...

... 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 ...

Introduction, Scheme basics (expressions, values)

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

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

Type Checking

... ie the system can derive the types of all objects. This is different to the philosophy of languages like Pascal where all typing is explicit. The aim in this part of the course is to examine in more detail how the type of any object (function, or expression) can be derived. ...

... ie the system can derive the types of all objects. This is different to the philosophy of languages like Pascal where all typing is explicit. The aim in this part of the course is to examine in more detail how the type of any object (function, or expression) can be derived. ...

A static analysis for Bulk Synchronous Parallel ML to avoid

... of a BSP program composed of S super-steps is thus s Time(s). In general this execution time is a function of p and of the size of data n, or of more complex parameters like data skew and histogram sizes. There is currently no implementation of a full Bulk Synchronous Parallel ML language but rathe ...

... of a BSP program composed of S super-steps is thus s Time(s). In general this execution time is a function of p and of the size of data n, or of more complex parameters like data skew and histogram sizes. There is currently no implementation of a full Bulk Synchronous Parallel ML language but rathe ...

19th Century Logic and 21st Century Computing

... paper on lambda calculus was published in 1932, two years before Gentzen’s paper on natural deduction. As we will see, the two works are in remarkably close correspondence, though they were developed for different reasons entirely. ...

... paper on lambda calculus was published in 1932, two years before Gentzen’s paper on natural deduction. As we will see, the two works are in remarkably close correspondence, though they were developed for different reasons entirely. ...

The next Haskell will be strict

... Well typed programs don’t go wrong Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: ...

... Well typed programs don’t go wrong Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: ...

Getting Started With . . . Haskell for Knowledge Representation

... Examples: [Int] is the type of lists of integers; [Char] is the type of lists of characters, or strings. • By pair- or tuple-formation: if a and b are types, then (a,b) is the type of pairs with an object of type a as their first component, and an object of type b as their second component. If a, b ...

... Examples: [Int] is the type of lists of integers; [Char] is the type of lists of characters, or strings. • By pair- or tuple-formation: if a and b are types, then (a,b) is the type of pairs with an object of type a as their first component, and an object of type b as their second component. If a, b ...

Chapter 7: Functional Programming Languages

... In fact, it has all types of the form A -> A Hence it is impossible to do type inference for all expressions - if we expect a unique type. ...

... In fact, it has all types of the form A -> A Hence it is impossible to do type inference for all expressions - if we expect a unique type. ...

A retrospective on Haskell

... Well typed programs don’t go wrong Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: ...

... Well typed programs don’t go wrong Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: ...

Theorems for free! - Computing Science

... extent by Sheeran [She89]. So there is reason to believe that further research will further extend the applicability of this method. Many functional languages, including Standard ML [Mil84, Mil87], Miranda1 [Tur85], and Haskell [HW88], are based on the Hindley/Milner type system [Hin69, Mil78, DM82] ...

... extent by Sheeran [She89]. So there is reason to believe that further research will further extend the applicability of this method. Many functional languages, including Standard ML [Mil84, Mil87], Miranda1 [Tur85], and Haskell [HW88], are based on the Hindley/Milner type system [Hin69, Mil78, DM82] ...

Notes - Cornell Computer Science

... 3. We are studying the functional programming paradigm, algorithm design, and precise problem specification using data structures for which functional languages work well. Typical examples of such data are lists, trees, arbitrarily large natural numbers (Big nums), real numbers, and of course functi ...

... 3. We are studying the functional programming paradigm, algorithm design, and precise problem specification using data structures for which functional languages work well. Typical examples of such data are lists, trees, arbitrarily large natural numbers (Big nums), real numbers, and of course functi ...

Constructive logic and type theory (lecture notes 2009)

... calculus as a programming language. It has the unusual property that all programs terminate. To prove this formally is very complicated, see for instance (Hindley and Seldin 1986) for a proof concerning a simplified calculus. The fact that all programs terminate implies that a programming language i ...

... calculus as a programming language. It has the unusual property that all programs terminate. To prove this formally is very complicated, see for instance (Hindley and Seldin 1986) for a proof concerning a simplified calculus. The fact that all programs terminate implies that a programming language i ...

Testing an Optimising Compiler by Generating Random Lambda

... The formal language that we choose to develop our ideas is essentially the simply-typed λ-calculus [13] extended with constants and basic types. The calculus allows programs to define and manipulate variables and functions. Specifically, programs are constructed from four different kinds of terms: v ...

... The formal language that we choose to develop our ideas is essentially the simply-typed λ-calculus [13] extended with constants and basic types. The calculus allows programs to define and manipulate variables and functions. Specifically, programs are constructed from four different kinds of terms: v ...

Sexy types in action - Indiana University Computer Science

... in lists and other data structures (Läufer 1996). Furthermore, given a type system that supports subtyping—as with type class constraints in Haskell (Wadler and Blott 1989; Hall et al. 1996), or extensible records in some Haskell extensions (Gaster and Jones 1996; Jones and Peyton Jones 1999)—we can ...

... in lists and other data structures (Läufer 1996). Furthermore, given a type system that supports subtyping—as with type class constraints in Haskell (Wadler and Blott 1989; Hall et al. 1996), or extensible records in some Haskell extensions (Gaster and Jones 1996; Jones and Peyton Jones 1999)—we can ...

type system is a tractable syntactic method for proving the absence

... – Checking is done at compile or runtime – E.g., Java (static) and Scheme (dynamic) ...

... – Checking is done at compile or runtime – E.g., Java (static) and Scheme (dynamic) ...

ppt

... values of type X, and pattern-matching can be used on a value of type X to extract a String or an Int as appropriate. An enumerated type is a disjoint union of copies of the unit type (which has just one value). Algebraic datatypes unify enumerations and disjoint unions (and recursive types) into a ...

... values of type X, and pattern-matching can be used on a value of type X to extract a String or an Int as appropriate. An enumerated type is a disjoint union of copies of the unit type (which has just one value). Algebraic datatypes unify enumerations and disjoint unions (and recursive types) into a ...

ppt

... – All type errors are detected at compile-time – Triangle is statically typed – Most modern languages have a large emphasis on static typechecking ...

... – All type errors are detected at compile-time – Triangle is statically typed – Most modern languages have a large emphasis on static typechecking ...

Type Class

... – symbol always represents the same value – Equational reasoning (equals can be substituted by equals) • easy mathematical manipulation, parallel execution, etc. ...

... – symbol always represents the same value – Equational reasoning (equals can be substituted by equals) • easy mathematical manipulation, parallel execution, etc. ...

Functional Programming - II

... • A functional program consists of an expression, not a sequence of statements. • Higher-order functions are first-class citizen in the language. – It can be nameless • List processing is convenient and expressive • In ML, every expression must be well-typed. • Algebraic data types empowers the lang ...

... • A functional program consists of an expression, not a sequence of statements. • Higher-order functions are first-class citizen in the language. – It can be nameless • List processing is convenient and expressive • In ML, every expression must be well-typed. • Algebraic data types empowers the lang ...