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(* Title: HOL/MiniML/MiniML.thy


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ID: $Id$


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Author: Dieter Nazareth and Tobias Nipkow


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Copyright 1995 TU Muenchen


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Mini_ML with type inference rules.


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*)


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MiniML = Type +


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(* expressions *)


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datatype

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expr = Var nat  Abs expr  App expr expr

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(* type inference rules *)


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consts

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has_type :: "(typ list * expr * typ)set"

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syntax

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"@has_type" :: [typ list, expr, typ] => bool

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("((_) / (_) :: (_))" [60,0,60] 60)

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translations


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"a  e :: t" == "(a,e,t):has_type"


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inductive has_type

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intrs

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VarI "[ n < length a ] ==> a  Var n :: nth n a"


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AbsI "[ t1#a  e :: t2 ] ==> a  Abs e :: t1 > t2"


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AppI "[ a  e1 :: t2 > t1; a  e2 :: t2 ]


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==> a  App e1 e2 :: t1"

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end


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