Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: " is about our hobby." That is the first sentence of [MP93], the first report on our formal development of lambda calculus and type theory, written in autumn 1992.  have continued to pursue this hobby on and off ever since, and have developed a substantial body of formal knowledge, including Church-Rosser and standardization theorems for beta reduction, and the basic theory of Pure Type Systems (PTS) leading to the strengthening theorem and type checking algorithms for PTS. Some of this work is reported in [MP93, vBJMP94, Pol94b, Pol95]. In the present paper  survey this work, including some new proofs, and point out what  feel has been learned about the general issues of formalizing mathematics. On the technical side,  describe an abstract, and simplified, proof of standardization for beta reduction, not previously published, that does not mention redex positions or residuals. On the general issues,  emphasize the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts. The LEGO Proof Development System [LP92] was used to check the work in an implementation of the Extended Calculus of Constructions (ECC) with inductive types [Luo94]. LEGO is a refinement style proof checker, publicly available by ftp and WWW, with a User's Manual [LP92] and a large collection of examples. Section 1.3 contains information on accessing the formal development described in this paper. Other interesting examples formalized in LEGO include program specification and data refinement [Luo91], strong normalization of System F [Alt93], synthetic domain theory [Reu95, Reu96], and operational semantics for imperative programs [Sch97].
['James McKinna', 'Robert Pollack']
I am writing a research paper on a idea Some Lambda Calculus and Type Theory Formalized
[{"from": "human", "value": "I am writing a research paper on a idea Some Lambda Calculus and Type Theory Formalized"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: \" is about our hobby.\" That is the first sentence of [MP93], the first report on our formal development of lambda calculus and type theory, written in autumn 1992.  have continued to pursue this hobby on and off ever since, and have developed a substantial body of formal knowledge, including Church-Rosser and standardization theorems for beta reduction, and the basic theory of Pure Type Systems (PTS) leading to the strengthening theorem and type checking algorithms for PTS. Some of this work is reported in [MP93, vBJMP94, Pol94b, Pol95]. In the present paper  survey this work, including some new proofs, and point out what  feel has been learned about the general issues of formalizing mathematics. On the technical side,  describe an abstract, and simplified, proof of standardization for beta reduction, not previously published, that does not mention redex positions or residuals. On the general issues,  emphasize the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts. The LEGO Proof Development System [LP92] was used to check the work in an implementation of the Extended Calculus of Constructions (ECC) with inductive types [Luo94]. LEGO is a refinement style proof checker, publicly available by ftp and WWW, with a User's Manual [LP92] and a large collection of examples. Section 1.3 contains information on accessing the formal development described in this paper. Other interesting examples formalized in LEGO include program specification and data refinement [Luo91], strong normalization of System F [Alt93], synthetic domain theory [Reu95, Reu96], and operational semantics for imperative programs [Sch97]."}]