Hugs (Haskell)
... A function should not do any input/output A function should not change any state (any external data) ...
... A function should not do any input/output A function should not change any state (any external data) ...
The gist of side effects in pure functional languages
... Purity is not at odds with computations that require side effects like input-output, destructive updates, concurrency, exceptions, or language inter-operation. How is this possible? It is well-known that expressions in pure functional languages are referentially transparent so variables are immutabl ...
... Purity is not at odds with computations that require side effects like input-output, destructive updates, concurrency, exceptions, or language inter-operation. How is this possible? It is well-known that expressions in pure functional languages are referentially transparent so variables are immutabl ...
A short article for the Encyclopedia of Artificial Intelligence: Second
... individuals to the booleans. Using characteristic functions to represent predicates, this latter type is used as the type of predicates whose one argument is an individual. Similarly, an expression that is of the type o is defined to be a formula. Typed expressions are built by application (if M is ...
... individuals to the booleans. Using characteristic functions to represent predicates, this latter type is used as the type of predicates whose one argument is an individual. Similarly, an expression that is of the type o is defined to be a formula. Typed expressions are built by application (if M is ...
Haskell - CIS @ UPenn
... Add, subtract, and multiply are type (Num a) => a -> a -> a Divide is type (Fractional a) => a -> a -> a Exponentiation is type (Num a, Integral b) => a -> b -> a They have type (Integral a) => a -> Bool ...
... Add, subtract, and multiply are type (Num a) => a -> a -> a Divide is type (Fractional a) => a -> a -> a Exponentiation is type (Num a, Integral b) => a -> b -> a They have type (Integral a) => a -> Bool ...
LN10
... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...
... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...
Constructive logic and type theory (lecture notes 2009)
... on such theories. Proofs carried out within constructive logic may be considered as programs in a functional language, closely related to e.g. ML or Haskell. The importance of this is the possibility to extract from an existence proof (that, e.g., there are arbitrarily large prime numbers) a program ...
... on such theories. Proofs carried out within constructive logic may be considered as programs in a functional language, closely related to e.g. ML or Haskell. The importance of this is the possibility to extract from an existence proof (that, e.g., there are arbitrarily large prime numbers) a program ...
Biform Theories in Chiron
... language where T and F are the sets of terms and formulas of F , respectively. In the rest of this paper, let L = (E, F ) be a general language. A general logic is a set of general languages with a notion of logical consequence. In the rest of this paper, let K be a general logic. L is a language of ...
... language where T and F are the sets of terms and formulas of F , respectively. In the rest of this paper, let L = (E, F ) be a general language. A general logic is a set of general languages with a notion of logical consequence. In the rest of this paper, let K be a general logic. L is a language of ...
12 Towards a Theory of Document Structure
... If the document is built using a WYSIWYG structure editor, one is tempted to think that there is little need for abstract syntax. Only the concrete syntax of the document is presented and the editing is done by changing the concrete syntax. However, the editing commands (like navigation, insertions ...
... If the document is built using a WYSIWYG structure editor, one is tempted to think that there is little need for abstract syntax. Only the concrete syntax of the document is presented and the editing is done by changing the concrete syntax. However, the editing commands (like navigation, insertions ...
review of haskell
... GHC is the leading implementation of Haskell, and comprises a compiler and interpreter; The interactive nature of the interpreter makes it well suited for teaching and prototyping; GHC is freely available from: ...
... GHC is the leading implementation of Haskell, and comprises a compiler and interpreter; The interactive nature of the interpreter makes it well suited for teaching and prototyping; GHC is freely available from: ...
slides 4-up
... Curry’s fixed point combinator: Y = λf . (λx. f (x x)) (λx. f (x x)) how do we define length in the λ-calculus? Turing’s fixed point combinator: T = (λx. λy . y (x x y )) (λx. λy . y (x x y )) ...
... Curry’s fixed point combinator: Y = λf . (λx. f (x x)) (λx. f (x x)) how do we define length in the λ-calculus? Turing’s fixed point combinator: T = (λx. λy . y (x x y )) (λx. λy . y (x x y )) ...
Jun 2004 - University of Malta
... Define a function fromTo, which takes two integers and returns the list of integers starting from the first number and finishing with the second. For example, fromTo 2 5 would return [2,3,4,5]. Define a function dots which takes an integer parameter n and returns a string consisting of n dots. For e ...
... Define a function fromTo, which takes two integers and returns the list of integers starting from the first number and finishing with the second. For example, fromTo 2 5 would return [2,3,4,5]. Define a function dots which takes an integer parameter n and returns a string consisting of n dots. For e ...
An introduction to functional programming using Haskell
... Functions are values too! Hence you can pass functions as arguments to other functions (called higher order functions) ...
... Functions are values too! Hence you can pass functions as arguments to other functions (called higher order functions) ...
Dependent Types In Lambda Cube
... mathematician’s intuition. The intuitionism is sometimes mistaken for constructivism, but the intuitionism is just one kind of constructivism. On the other hand, it could be useful for our purposes not to distuinguish between these two philosophies. The main reason is that the true of a statement in ...
... mathematician’s intuition. The intuitionism is sometimes mistaken for constructivism, but the intuitionism is just one kind of constructivism. On the other hand, it could be useful for our purposes not to distuinguish between these two philosophies. The main reason is that the true of a statement in ...
Proof Theory in Type Theory
... the reference [1, 4], one should expect that it is not needed). This should come from an analysis of the given proof. For instance, it seems that we are really working in the fragment of (S0 ) with only positive sequents, and that we never really need to do an induction on a tree with uncountable br ...
... the reference [1, 4], one should expect that it is not needed). This should come from an analysis of the given proof. For instance, it seems that we are really working in the fragment of (S0 ) with only positive sequents, and that we never really need to do an induction on a tree with uncountable br ...
Notes - Cornell Computer Science
... easily able to see some of the deepest ideas in action. For example, you already know that in some sense, OCaml is a universal programming language. It is surprising how small the universal core of OCaml is. 3. We are studying the functional programming paradigm, algorithm design, and precise proble ...
... easily able to see some of the deepest ideas in action. For example, you already know that in some sense, OCaml is a universal programming language. It is surprising how small the universal core of OCaml is. 3. We are studying the functional programming paradigm, algorithm design, and precise proble ...
![Propositions as [Types] - Research Showcase @ CMU](http://s1.studyres.com/store/data/005730189_1-e85fa7d3c7cfa08d9a3b8e96a27d7888-300x300.png)
Propositions as [Types] - Research Showcase @ CMU
... types of Maietti [Mai98], in a suitable setting. Palmgren [Pal01] formulated a BHK interpretation of intuitionistic logic and used image factorizations, which are used in the semantics of our bracket types, to relate the BHK interpretation to the standard category-theoretic interpretation of proposi ...
... types of Maietti [Mai98], in a suitable setting. Palmgren [Pal01] formulated a BHK interpretation of intuitionistic logic and used image factorizations, which are used in the semantics of our bracket types, to relate the BHK interpretation to the standard category-theoretic interpretation of proposi ...
The superjump in Martin-Löf type theory
... Martin-Löf, in 1975 [11] and in his 1984 monograph [12] on an intuitionistic theory of types, gave a framework for a theory of constructive types or sets. The role of universes in this type theory is to allow for the formation of sets of sets which are themselves closed under certain set forming op ...
... Martin-Löf, in 1975 [11] and in his 1984 monograph [12] on an intuitionistic theory of types, gave a framework for a theory of constructive types or sets. The role of universes in this type theory is to allow for the formation of sets of sets which are themselves closed under certain set forming op ...
Tsinghua Software Day Program
... operational). After graduating from the Ecole Normale Sup□□ rieure of Paris, he worked with G□□ rard Berry on a mathematical account of the notion of sequential program, where programs as functions and programs as algorithms get closer. His most widely-known contributions are outcomes of this early ...
... operational). After graduating from the Ecole Normale Sup□□ rieure of Paris, he worked with G□□ rard Berry on a mathematical account of the notion of sequential program, where programs as functions and programs as algorithms get closer. His most widely-known contributions are outcomes of this early ...
A HIGHER-ORDER FINE-GRAINED LOGIC FOR INTENSIONAL
... Before defining our class of models, we first review the notions of a frame and a boolean prelattice, in terms of which these models will be specified. We take a (Henkin) frame to be a type-indexed family of sets S = hSA i such that SB A is a (possibly proper) subset of the set of functions from SA ...
... Before defining our class of models, we first review the notions of a frame and a boolean prelattice, in terms of which these models will be specified. We take a (Henkin) frame to be a type-indexed family of sets S = hSA i such that SB A is a (possibly proper) subset of the set of functions from SA ...
