J.H. Geuvers, The Church-Rosser property for - reduction in typed lambda calculi. In Proceedings of the seventh annual symposium on Logic in Computer Science, Santa Cruz, Cal., IEEE, pp 453--460.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... under the context , the term M has type T . Both judgments are defined by mutual induction with the rules written in figure 1. These rules include: Rules for well formed contexts (WF E) and (WF S) Logical rules (VAR) SORT) EXPPROD) IMPPROD) LAM) and (APP) 2 It is well known[4] that the reduction is not confluent on raw terms in a Church style PTS. 2 Rules for well formed contexts (WF E) T : s x = 2 Dom( x : T (WF S) Rules for well typed terms (x : T ) 2 x : T (VAR) s 1 ; s 1 ) 2 Axiom s 1 : s 2 (SORT) T : s 1 ;x : T U : s 2 (s 1 ....

J.H. Geuvers, The Church-Rosser property for - reduction in typed lambda calculi. In Proceedings of the seventh annual symposium on Logic in Computer Science, Santa Cruz, Cal., IEEE, pp 453--460.

....( x : A:M 2 )M 1 = M 2 [x : M 1 ] and ( x : A:Mx) M provided x 62 FV(M ) Remark 3. 1 The meta theory of LF is rather delicate because of the (conv) rule and the failure of the Church Rosser property for reduction on pseudo terms, anyway one can prove the following properties (see [HHP87, Geu92, Luo94]) it is decidable whether M : A is derivable 14 if M i : A (for i = 1; 2) is derivable, then M 1 = M 2 is decidable. It is convenient to separate the initial part of a context, which is intended to consist of constants, from the remaining part, consisting of variables. Therefore, we ....

H. Geuvers. The church-rosser property for -reduction in typed lambda calculi. In A. Scedrov, editor, Proc. 7th Symposium in Logic in Computer Science, Santa Cruz, 1992. I.E.E.E. Computer Society.

....the right hand side have a common reduct only if A and B do. This complication of was already known to the Automath community Nederpelt [1973] Con uence and Normalization for types systems from the Automath family was proved by Daalen [1980] For a study and proof of the general situation see Geuvers [1992], Geuvers [1993] For a study of type theory with terms without types attached to the bound variables, see Barthe and S orensen [n.d. where it is shown that the type checking (notably its undecidability) is not completely hopeless. In Magnusson [1994] an implementation of a proof assistant ....

Geuvers H. [1992], The Church-Rosser property for -reduction in typed lambda calculi, in `Proceedings of the seventh annual symposium on Logic in Computer Science, Santa Cruz, Cal.', IEEE, pp. 453-460.

.... y:B:y These terms have a common reduct only if A and B have. This complication of was already known to the Automath community Nederpelt [1973] Con uence and Normalization for types systems from the Automath family was proved by Daalen [1980] For a study and proof of the general situation see Geuvers [1992], Geuvers [1993] For a study of type theory with terms without types attached to the bound variables, see Barthe and S orensen [n.d. where it is shown that the type checking (notably its undecidability) is not completely hopeless. In Magnusson [1994] an implementation of a proof assistant ....

Geuvers, H. [1992]. The Church-Rosser property for -reduction in typed lambda calculi, Proceedings of the seventh annual symposium on Logic in Computer Science, Santa Cruz, Cal., IEEE, pp. 453-460.

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