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Constructive Category Theory
 IN PROCEEDINGS OF THE JOINT CLICSTYPES WORKSHOP ON CATEGORIES AND TYPE THEORY, GOTEBORG
, 1998
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Specifications, Algorithms, Axiomatisations and Proofs Commented Case Studies
 In the Coq Proof Assistant”, Summer School on Logic of Computation
, 1995
"... 1.1 An overview of the specification language Gallina.................... 5 ..."
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1.1 An overview of the specification language Gallina.................... 5
Axiomatisations, Proofs, and Formal Specifications of Algorithms: Commented Case Studies In the Coq Proof Assistant
"... this paper is but a tiny initial fragment of the theory of categories. However, it is quite promising, in that the power of dependent types and inductive types (or at least \Sigmatypes) is put to full use; note in particular the dependent equality between morphisms of possibly nonconvertible types ..."
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this paper is but a tiny initial fragment of the theory of categories. However, it is quite promising, in that the power of dependent types and inductive types (or at least \Sigmatypes) is put to full use; note in particular the dependent equality between morphisms of possibly nonconvertible types.
Gedanken: A tool for pondering the tractability of correct program technology
, 1994
"... syntax of elementary languages in Gedanken . . . . . . . . . . . 129 7.1 Match counting algorithm for patterns over PC k . . . . . . . . . . . . . 157 8.1 log 2 speed of Model Graphs after elimination . . . . . . . . . . . . . . . 187 8.2 log 2 speedup of Model Graphs after elimination . . . . . . ..."
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syntax of elementary languages in Gedanken . . . . . . . . . . . 129 7.1 Match counting algorithm for patterns over PC k . . . . . . . . . . . . . 157 8.1 log 2 speed of Model Graphs after elimination . . . . . . . . . . . . . . . 187 8.2 log 2 speedup of Model Graphs after elimination . . . . . . . . . . . . . 188 8.3 log 2 speed of Model Graphs after invalidation . . . . . . . . . . . . . . . 188 8.4 log 2 speedup of Model Graphs after invalidation . . . . . . . . . . . . . 189 ix Chapter 1 Summary One goal of computer science has been to develop a tool T to aid a programmer in building a program P that satisfies a specification S by helping the programmer build a proof in some logic of programs L that shows that P satisfies S. S typically is a pair of propositions (#, #) such that, for an input x to P , #(x) # #(P (x)) when P is defined on x. # is called the precondition or assumption, and # is called the postcondition or assertion. The problem of finding a suitable logic L of programs and specifications and verification tool T may be generically referred to as the "FloydHoare problem", formulated around 1967 [Flo67, Hoa69]. Around 1977, Davis and Schwartz proposed an extension of the FloydHoare problem in which there are multiple assumptions and assertions, referring to the state of a program as execution passes through di#erent places # in the program [DS77, Sch77]. A placed proposition is then a pair (#, #), where # is either a line of a program or the name of a function. A placed proposition (#, #) holds when, if execution reaches # and the value of the variables X in P is V , then #(V ) is valid. A program with assumptions and assertions or praa is then a triple R = (P, E, F ) where the assumptions E and assertions F are sets of placed propositions. T...