Computational lambda calculus: A combination of functional and

... calculus we can express it as a lambda abstraction AF. AH. ) which is LMNNO = A. AF. F which is a function of one argument that, when applied, returns as an output another function that accepts a second argument and then calculates a result in the same way as . This technique was invented by Mo ...

... calculus we can express it as a lambda abstraction AF. AH. ) which is LMNNO = A. AF. F which is a function of one argument that, when applied, returns as an output another function that accepts a second argument and then calculates a result in the same way as . This technique was invented by Mo ...

Functional Programming in CLEAN

... descriptions of the way a result can be computed, given some arguments. A natural way to write a computer program is therefore to define some functions and applying them to concrete values. We need not to constrain ourselves to numeric functions. Functions can also be defined that have, e.g., sequen ...

... descriptions of the way a result can be computed, given some arguments. A natural way to write a computer program is therefore to define some functions and applying them to concrete values. We need not to constrain ourselves to numeric functions. Functions can also be defined that have, e.g., sequen ...

Scala - Dave Reed

... ● Even numbers and functions are objects o Since numbers are objects they have methods ...

... ● Even numbers and functions are objects o Since numbers are objects they have methods ...

Termination of Higher-order Rewrite Systems

... computation are syntactic expressions in some formal language. A rewrite system consists of a collection of rules (the program). A computation step is performed by replacing a part of an expression by another expression, according to the rules. The resulting expression may be rewritten again and aga ...

... computation are syntactic expressions in some formal language. A rewrite system consists of a collection of rules (the program). A computation step is performed by replacing a part of an expression by another expression, according to the rules. The resulting expression may be rewritten again and aga ...

Types and Programming Languages

... x : U x: U x : U x : U T App x : U xx : T We can see that U must be of the form U T but this is not possible (unless we have recursive types, which are coming later). ...

... x : U x: U x : U x : U T App x : U xx : T We can see that U must be of the form U T but this is not possible (unless we have recursive types, which are coming later). ...

Declarative Programming in Escher

... program, that is, each axiom in the theory be true in the intended interpretation. This is because an implementation must guarantee that computed answers be correct in all models of the logic component of the program and hence be correct in the intended interpretation. Ultimately, the programmer is ...

... program, that is, each axiom in the theory be true in the intended interpretation. This is because an implementation must guarantee that computed answers be correct in all models of the logic component of the program and hence be correct in the intended interpretation. Ultimately, the programmer is ...

proof terms for classical derivations

... result (in that order) and disharged them in turn (also in that order). Seeing this, you may realise that there are two other proofs of the same formula. One where the conjuncts are formed in the other order (with term λyλxxy, xy) and the other, where the first discharged assumption of p is vacuous, ...

... result (in that order) and disharged them in turn (also in that order). Seeing this, you may realise that there are two other proofs of the same formula. One where the conjuncts are formed in the other order (with term λyλxxy, xy) and the other, where the first discharged assumption of p is vacuous, ...

Programming with Miranda

... storage locations, but instead has the ability to give names to the values of expressions; these names may then be used in other expressions or passed as parameters to functions. 2. The fact that in a functional language a name or an expression has a unique value that will never change is known as r ...

... storage locations, but instead has the ability to give names to the values of expressions; these names may then be used in other expressions or passed as parameters to functions. 2. The fact that in a functional language a name or an expression has a unique value that will never change is known as r ...

Higher Order Logic - Indiana University

... Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of comp ...

... Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of comp ...

Higher Order Logic - Theory and Logic Group

... Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of comp ...

... Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of comp ...

Functional Programming and Compiler Design

... Functions and other values begin with small letters … … types begin with capital letters. ...

... Functions and other values begin with small letters … … types begin with capital letters. ...

Probabilistic Modelling, Inference and Learning using Logical

... Example 3 The term (#Int 2 (#Int 3 []Int )) represents a list with the numbers 2 and 3 in it, obtained via a series of applications from the constants #Int , []Int , 2, and 3, each of which is a term. For convenience, we sometimes write [2, 3] to represent the same list. Example 4 Sets are identifie ...

... Example 3 The term (#Int 2 (#Int 3 []Int )) represents a list with the numbers 2 and 3 in it, obtained via a series of applications from the constants #Int , []Int , 2, and 3, each of which is a term. For convenience, we sometimes write [2, 3] to represent the same list. Example 4 Sets are identifie ...