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Type Theory and Programming
, 1994
"... This paper gives an introduction to type theory, focusing on its recent use as a logical framework for proofs and programs. The first two sections give a background to type theory intended for the reader who is new to the subject. The following presents MartinLof's monomorphic type theory and an im ..."
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Cited by 21 (2 self)
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This paper gives an introduction to type theory, focusing on its recent use as a logical framework for proofs and programs. The first two sections give a background to type theory intended for the reader who is new to the subject. The following presents MartinLof's monomorphic type theory and an implementation, ALF, of this theory. Finally, a few small tutorial examples in ALF are given.
Optimized Encodings of Fragments of Type Theory in First Order Logic
 JLC: Journal of Logic and Computation
, 1994
"... The paper presents sound and complete translations of several fragments of MartinLof's monomorphic type theory to first order predicate calculus. The translations are optimised for the purpose of automated theorem proving in the mentioned fragments. The implementation of the theorem prover Gand ..."
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Cited by 7 (4 self)
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The paper presents sound and complete translations of several fragments of MartinLof's monomorphic type theory to first order predicate calculus. The translations are optimised for the purpose of automated theorem proving in the mentioned fragments. The implementation of the theorem prover Gandalf and several experimental results are described. 1 Introduction The subject of this paper is the problem of automated theorem proving in MartinLof's monomorphic type theory [19, 8], which is the underlying logic of the interactive proof development system ALF [2, 14]. In the scope of our paper the task of automated theorem proving in type theory is understood as demonstrating that a certain type is inhabited by constructing a term of that type. The problem of inhabitedness of a type A is understood in the following way: given a set of judgements \Gamma (these may be constant declarations, explicit definitions and defining equalities), find a term a such that a2A is derivable from \Gam...
A Machine Assisted Formalization of Pointfree Topology in Type Theory
, 1994
"... We will present a formalization of pointfree topology in MartinLöf's type theory. A notion of point will be introduced and we will show that the points of a Scott topology form a Scott domain. This work follows closely the intuitionistic approach to pointfree topology and domain theory, developed m ..."
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Cited by 6 (2 self)
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We will present a formalization of pointfree topology in MartinLöf's type theory. A notion of point will be introduced and we will show that the points of a Scott topology form a Scott domain. This work follows closely the intuitionistic approach to pointfree topology and domain theory, developed mainly by MartinLöf and Sambin. The important difference is that the definitions and proofs are machine checked by the proof assistant ALF.
A Machineassisted Proof that Well Typed Expressions Cannot Go Wrong
, 1998
"... This paper deals with the application of constructive type theory to the theory of programming languages. The main aim of this work is to investigate constructive formalisations of the mathematics of programs. Here, we consider a small typed functional language and prove some properties about it, ar ..."
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Cited by 3 (0 self)
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This paper deals with the application of constructive type theory to the theory of programming languages. The main aim of this work is to investigate constructive formalisations of the mathematics of programs. Here, we consider a small typed functional language and prove some properties about it, arriving at the property that establishes that well typed expressions cannot go wrong. First, we give the definitions and proofs in an informal style, and then we present and explain the formalisation of these definitions and proofs. For the formalisation, we use the proof editor ALF and its pattern matching facility.