M. Hofmann. A model of intensional Martin-Lof type theory in which unicity of identity proofs does not hold, Technical report, Dept. of Computer Science, University of Edinburgh, 1993. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
An Implementation of the Heine-Borel Covering Theorem in Type.. - Cederquist (Correct)
....recursive definitions on functional form, non linear inductive types cannot be defined, i.e. dependencies between the parameters cannot be introduced. It turned out that pattern matching together with nonlinear inductive definitions is a non conservative extension of Martin Lof s type theory (see [H]) The approach taken in Half is to allow only linear inductive definitions. As a consequense, the Id type a 2 A id(A; a) 2 Id (A; a; a) is not definable: without dependencies between the parameters there is no way of saying that the two elements are the same. Therefore, for abstract sets, ....
M. Hofmann. A model of intensional Martin-Lof type theory in which unicity of identity proofs does not hold, Technical report, Dept. of Computer Science, University of Edinburgh, 1993.
Type Theory and Programming - Coquand, Nordström, Smith, von Sydow (1994) (21 citations) (Correct)
....specially adapted to the particular proposition one wants to prove. Interestingly, the two disciplines are not proof theoretically equivalent. One can exhibit propositions that can be proved by pattern matching but are false in certain models of type theory with the standard elimination rules [24]. It is presently a research topic to gain a better understanding of this phenomenon. A programming example To indicate how type theory can be used as a programming logic, we give a simple example of the derivation of a program. The problem we consider is that of finding the minimal element in a ....
Martin Hofmann. A model of intensional martin-lof type theory in which unicity of identity proofs does not hold. Technical report, Dept. of Computer Science, University of Edinburgh, June 1993. Draft.
A Machine Assisted Proof of the Hahn-Banach Theorem - Cederquist (1997) (Correct)
....recursive definitions on functional form, non linear inductive types cannot be defined, i.e. dependencies between the parameters cannot be introduced. It turned out that pattern matching together with non linear inductive definitions is a non conservative extension of Martin Lof s type theory (see [8]) The approach taken in Half is to allow only linear inductive definitions. As a consequense, the Id type a 2 A id(A; a) 2 Id(A; a; a) is not definable: without dependencies between the parameters there is no way of saying that the two elements are the same. Therefore, for abstract sets, ....
M. Hofmann. A model of intensional Martin-Lof type theory in which unicity of identity proofs does not hold, Technical report, Dept. of Computer Science, University of Edinburgh, 1993.
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