TILC: The Interactive Lambda-Calculus Tracer1
... Variables in lambda-terms may occur free when they are not bound by any λ-abstraction. Terms are considered identical modulo renaming of bound variables. By Λ1 [x 7→ Λ2 ] we denote the substitution of variable x occurring free in Λ1 by Λ2 ; this substitution can not capture variables occurring free ...
... Variables in lambda-terms may occur free when they are not bound by any λ-abstraction. Terms are considered identical modulo renaming of bound variables. By Λ1 [x 7→ Λ2 ] we denote the substitution of variable x occurring free in Λ1 by Λ2 ; this substitution can not capture variables occurring free ...
Predicate Logic
... Q: What problem may occur if the same symbol is used to represent more than one variable in a formula? ambigous when proving/writing equivalences Q: Soln? do a variable substitution, i.e., above, replace the second y with an ”a” and the second ”z” with a ”b”. ...
... Q: What problem may occur if the same symbol is used to represent more than one variable in a formula? ambigous when proving/writing equivalences Q: Soln? do a variable substitution, i.e., above, replace the second y with an ”a” and the second ”z” with a ”b”. ...
Introduction, Scheme basics (expressions, values)
... > (define percentage (* 100 (/ score total)) ...
... > (define percentage (* 100 (/ score total)) ...
Slides
... Let be an unsatisfiable formula Theorem 2: A proof P is complete with respect to if for every full assignment ...
... Let be an unsatisfiable formula Theorem 2: A proof P is complete with respect to if for every full assignment ...
notes
... Programs describe computation, but they are more than just lists of instructions. They are mathematical objects as well. A programming language is a logical formalism, just like first-order logic. Such formalisms typically consist of • Syntax, a strict set of rules telling how to distinguish well-fo ...
... Programs describe computation, but they are more than just lists of instructions. They are mathematical objects as well. A programming language is a logical formalism, just like first-order logic. Such formalisms typically consist of • Syntax, a strict set of rules telling how to distinguish well-fo ...
PLD VII Haddad
... – easier to reason about programs written in them • FPLs encourage thinking at higher levels of abstraction – support modifying and combining existing programs – thus, FPLs encourage programmers to work in units larger than statements of conventional languages: "programming in the large" • FPLs prov ...
... – easier to reason about programs written in them • FPLs encourage thinking at higher levels of abstraction – support modifying and combining existing programs – thus, FPLs encourage programmers to work in units larger than statements of conventional languages: "programming in the large" • FPLs prov ...
A short introduction to the Lambda Calculus
... where the mathematician and the computer programmer would write “sin(x)”, in the λcalculus we simply write “sin x”. If a function takes more than one argument, then these are simply lined up after the function. Thus “x + 3” becomes “+ x 3”, and “x2 ” becomes “∗ x x”. Brackets are employed only to en ...
... where the mathematician and the computer programmer would write “sin(x)”, in the λcalculus we simply write “sin x”. If a function takes more than one argument, then these are simply lined up after the function. Thus “x + 3” becomes “+ x 3”, and “x2 ” becomes “∗ x x”. Brackets are employed only to en ...
7. Introduction to the Lambda Calculus
... work only under a license identical to this one. • For any reuse or distribution, you must make clear to others the license terms of this work. • Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. ...
... work only under a license identical to this one. • For any reuse or distribution, you must make clear to others the license terms of this work. • Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. ...
Lecture Notes in Computer Science
... or natural deduction systems. This is not only of theoretical significance, but also bears upon computational issues. It was one purpose of the workshop to bring some of these recent developments together. In concentrating on the proof-theoretic approach, however, other extensions of logic programmi ...
... or natural deduction systems. This is not only of theoretical significance, but also bears upon computational issues. It was one purpose of the workshop to bring some of these recent developments together. In concentrating on the proof-theoretic approach, however, other extensions of logic programmi ...
Rhys Price Jones
... Moses Schönfinkel in the early 1920s, and was mostly developed by Haskell Curry. The idea was to reduce the notation of logic to the simplest terms possible. As such, combinatory logic consists only of combinators, combination operations, and no free variables •[ http://planetmath.org/encyclopedia/ ...
... Moses Schönfinkel in the early 1920s, and was mostly developed by Haskell Curry. The idea was to reduce the notation of logic to the simplest terms possible. As such, combinatory logic consists only of combinators, combination operations, and no free variables •[ http://planetmath.org/encyclopedia/ ...
Lambda Calculus
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... to Share — to copy, distribute and transmit the work to Remix — to adapt the work Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Share Alike. ...
lec5 - Indian Institute of Technology Kharagpur
... – There is a single barber in town. Those and only those who do not shave themselves are shaved by the barber. Who shaves the ...
... – There is a single barber in town. Those and only those who do not shave themselves are shaved by the barber. Who shaves the ...
Functional Programming
... discussion is on the basic elements of (untyped) Lambda calculus and suggests the way the pure mathematical formalism of the calculus can be turned into a weak-typed functional programming language based on normal-order evaluation. ...
... discussion is on the basic elements of (untyped) Lambda calculus and suggests the way the pure mathematical formalism of the calculus can be turned into a weak-typed functional programming language based on normal-order evaluation. ...
comments on the logic of constructible falsity (strong negation)
... Görnemann’s result suggests the conjecture that a classical model theory for the logic I have described may be obtained by allowing the domain to “grow with time”. This is in fact true. We may define a Nelson model structure as a triple (K, R, D), where K is a non-empty set of “stages of investigat ...
... Görnemann’s result suggests the conjecture that a classical model theory for the logic I have described may be obtained by allowing the domain to “grow with time”. This is in fact true. We may define a Nelson model structure as a triple (K, R, D), where K is a non-empty set of “stages of investigat ...
PDF
... 1 Intuitionistic Logic and Constructive Mathematics It turns out that there is there is a deep connection between the type systems we have been exploring for the lambda calculus, and proof systems for a variety of logic known as intuitionistic logic. Intuitionistic logic is the basis of constructive ...
... 1 Intuitionistic Logic and Constructive Mathematics It turns out that there is there is a deep connection between the type systems we have been exploring for the lambda calculus, and proof systems for a variety of logic known as intuitionistic logic. Intuitionistic logic is the basis of constructive ...
ppt - Rensselaer Polytechnic Institute: Computer Science
... represents the same f function, except it is anonymous. To represent the function evaluation f(2) = 4, we use the following -calculus syntax: ...
... represents the same f function, except it is anonymous. To represent the function evaluation f(2) = 4, we use the following -calculus syntax: ...
Knowledge Representation
... • Symbols represent facts: P, Q, etc.. • These are joined by logical connectives (and, or, implication) e.g., P Q; Q R • Given some statements in the logic we can deduce new facts (e.g., from above deduce R) ...
... • Symbols represent facts: P, Q, etc.. • These are joined by logical connectives (and, or, implication) e.g., P Q; Q R • Given some statements in the logic we can deduce new facts (e.g., from above deduce R) ...
first order logic
... Ideally, we can come up with a “perfect” logical system, which is consistent (not having contradictions) and is powerful (can derive everything that is true). But Gödel proved that there is no perfect logical system. This is called the Gödel’s incompleteness theorem. It is an important and surprisin ...
... Ideally, we can come up with a “perfect” logical system, which is consistent (not having contradictions) and is powerful (can derive everything that is true). But Gödel proved that there is no perfect logical system. This is called the Gödel’s incompleteness theorem. It is an important and surprisin ...
ppt - Computer Science at RPI
... represents the same f function, except it is anonymous. To represent the function evaluation f(2) = 4, we use the following -calculus syntax: ...
... represents the same f function, except it is anonymous. To represent the function evaluation f(2) = 4, we use the following -calculus syntax: ...
Sequent calculus - Wikipedia, the free encyclopedia
... The above rules can be divided into two major groups: logical and structural ones. Each of the logical rules introduces a new logical formula either on the left or on the right of the turnstile . In contrast, the structural rules operate on the structure of the sequents, ignoring the exact shape of ...
... The above rules can be divided into two major groups: logical and structural ones. Each of the logical rules introduces a new logical formula either on the left or on the right of the turnstile . In contrast, the structural rules operate on the structure of the sequents, ignoring the exact shape of ...
Functional Programming COMP2003
... 1. When the function definition is specific to a particular situation, and so can be defined and used in just one place. Usually the motive for forming the computation into a function is that it is being passed in as argument to some other functions which will use that computation in various ways, p ...
... 1. When the function definition is specific to a particular situation, and so can be defined and used in just one place. Usually the motive for forming the computation into a function is that it is being passed in as argument to some other functions which will use that computation in various ways, p ...