Coding a Lisp Interpreter in Shen: a Case Study

... Is this true? I will argue, to a degree – yes. A type checker for a functional language is in essence, an inference engine; that is to say, it is the machine embodiment of some formal system of proof. What we know, and have known since Godel's incompleteness proof [9] [11], is that the human ability ...

... Is this true? I will argue, to a degree – yes. A type checker for a functional language is in essence, an inference engine; that is to say, it is the machine embodiment of some formal system of proof. What we know, and have known since Godel's incompleteness proof [9] [11], is that the human ability ...

popl13

... • Type system in ML is safe. – When type checker judges that an expression has some type, it is guaranteed that evaluating the expression results in a value of the type. – (ex.) When an expression is a pointer to a string, the value of the expression is guaranteed to be a pointer that points to some ...

... • Type system in ML is safe. – When type checker judges that an expression has some type, it is guaranteed that evaluating the expression results in a value of the type. – (ex.) When an expression is a pointer to a string, the value of the expression is guaranteed to be a pointer that points to some ...

Practical Type Inference Based on Success Typings

... code — often written by some other programmer years ago — can be used. Comments are unreliable, often cryptic and confusing, and more often than not rotten. The programmer is much better off if aided by techniques and tools that can help in such situations. Over the years, many researchers have trie ...

... code — often written by some other programmer years ago — can be used. Comments are unreliable, often cryptic and confusing, and more often than not rotten. The programmer is much better off if aided by techniques and tools that can help in such situations. Over the years, many researchers have trie ...

Type Classes in Haskell - Programming Research Laboratory

... (2) It eases subsequent transformation. A standard and productive technique for compiling functional languages is to apply various transformations at intermediate phases [Peyton Jones 1987]. With annotations, each transformation must carefully preserve annotations on all subterms and add new annotat ...

... (2) It eases subsequent transformation. A standard and productive technique for compiling functional languages is to apply various transformations at intermediate phases [Peyton Jones 1987]. With annotations, each transformation must carefully preserve annotations on all subterms and add new annotat ...

Positive and Negative Results for Higher

... However much less work has been devoted to the proof aspects which are required for verication purposes. Previous works in this direction [Avenhaus and Loria-Saenz, 1994, Prehofer, 1994b, Nipkow and Qian, 1991, Miller, 1992] deal with equational proofs and relevant methods like narrowing and unica ...

... However much less work has been devoted to the proof aspects which are required for verication purposes. Previous works in this direction [Avenhaus and Loria-Saenz, 1994, Prehofer, 1994b, Nipkow and Qian, 1991, Miller, 1992] deal with equational proofs and relevant methods like narrowing and unica ...

A system of constructor classes

... overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes – a natural generalization of type classes in Haskell. We present a wide range of examples which demonstrate the usefulness of such a system. In particular, we show how constructor classes ...

... overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes – a natural generalization of type classes in Haskell. We present a wide range of examples which demonstrate the usefulness of such a system. In particular, we show how constructor classes ...

A Typed Lambda Calculus with Categorical Type Constructors 1

... It also allows duals of recursive types, i.e. lazy types, like inﬁnite lists. It has generalized iterators for recursive types and duals of iterators for lazy types. We will give reduction rules for this simply typed lambda calculus and show that they are strongly normalizing even though it has inﬁn ...

... It also allows duals of recursive types, i.e. lazy types, like inﬁnite lists. It has generalized iterators for recursive types and duals of iterators for lazy types. We will give reduction rules for this simply typed lambda calculus and show that they are strongly normalizing even though it has inﬁn ...

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 ...

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. ...

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 ...

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 ...

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) ...

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 ...

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 ...

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 ...

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 ...

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] ...

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: ...

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. ...

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 ...

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: ...

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. ...

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 ...

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. ...