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103 lines
2.9 KiB
Plaintext
103 lines
2.9 KiB
Plaintext
--# -path=.:englishExtended:common:prelude:abstract
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abstract Basic = open Conjunction in {
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cat Class;
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El Class;
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Ind Class;
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SubClassC (c1,c2 : Class) (Var c2 -> Formula);
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SubClass (c1,c2 : Class);
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Inherits Class Class ;
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[El Class];
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[Class];
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Formula;
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Desc Class;
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Var Class;
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Stmt ;
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-- inheritance between classes
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data
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inhz : (c : Class) -> Inherits c c;
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inhs : (c1, c2, c3 : Class) -> (p : Var c2 -> Formula) -> SubClassC c1 c2 p -> Inherits c2 c3 -> Inherits c1 c3;
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inhsC : (c1, c2, c3 : Class) -> SubClass c1 c2 -> Inherits c2 c3 -> Inherits c1 c3;
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-- coercion from Var to El
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data
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var : (c1 , c2 : Class) -> Inherits c1 c2 -> Var c1 -> El c2 ;
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-- coercion from Ind to El
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data
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el : (c1, c2 : Class) -> Inherits c1 c2 -> Ind c1 -> El c2;
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-- class-forming operations
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data
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both : Class -> Class -> Class ;
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either : Class -> Class -> Class ;
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-- first-order logic operations for Formula
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data
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not : Formula -> Formula;
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and : Formula -> Formula -> Formula;
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or : Formula -> Formula -> Formula;
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impl : Formula -> Formula -> Formula;
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equiv : Formula -> Formula -> Formula;
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-- quantification over instances of a Class
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data
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exists : (c : Class) -> (Var c -> Formula) -> Formula;
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forall : (c : Class) -> (Var c -> Formula) -> Formula;
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-- axioms for both
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data
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-- (both c1 c2) is subclass of c1 and of c2
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bothL : (c1, c2 : Class) -> Inherits (both c1 c2) c1 ;
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bothR : (c1, c2 : Class) -> Inherits (both c1 c2) c2 ;
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-- relationship with other subclasses
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bothC : (c1, c2, c3 : Class) -> Inherits c3 c1 -> Inherits c3 c2 -> Inherits c3 (both c1 c2);
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-- axioms for either
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data
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-- (either c1 c2) is superclass of c1 and of c2
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eitherL : (c1, c2 : Class) -> Inherits c1 (either c1 c2);
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eitherR : (c1, c2 : Class) -> Inherits c2 (either c1 c2);
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-- relationship with other subclasses
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eitherC : (c1,c2,c3 : Class) -> Inherits c1 c3 -> Inherits c2 c3 -> Inherits (either c1 c2) c3 ;
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-- Desc category
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data desc : (c1,c2 : Class) -> Inherits c1 c2 -> Desc c2 ;
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fun descClass : (c : Class) -> Desc c -> Class ;
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def descClass _ (desc c _ _) = c ;
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fun descInh : (c : Class) -> (p : Desc c) -> Inherits (descClass c p) c ;
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--def descInh c1 (desc c2 c1 i) = i ;
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fun desc2desc : (c1,c2 : Class) -> Inherits c1 c2 -> Desc c1 -> Desc c2 ;
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--def desc2desc _ _ inh dsc = desc ? ? (plusInh ? ? ? inh (descInh ? dsc)) ;
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--fun plusInh : (c1,c2,c3 : Class) -> Inherits c1 c2 -> Inherits c2 c3 -> Inherits c1 c3 ;
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--def plusInh _ _ _ inhz inh2 = inh2 ;
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-- plusInh _ _ _ (inhs _ _ _ sc inh1) inh2 = inhs ? ? ? sc (plusInh ? ? ? inh1 inh2) ;
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-- statements
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data
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subClassStm : (c1,c2 : Class) -> SubClass c1 c2 -> Stmt ;
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subClassCStm : (c1,c2 : Class) -> (p : Var c2 -> Formula) -> SubClassC c1 c2 p -> Stmt ;
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instStm : (c : Class) -> Ind c -> Stmt ;
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formStm : Formula -> Stmt ;
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}; |