* algebra/logic.spad.pamphlet: New file.

	* algebra/boolean.spad.pamphlet (Logic): Move there.
	(BooleanLogic): Likewise.
	(PropositionalLogic): Likewise.
	(PropositionalFormula): Likewise.
	(PropositionalFormulaFunctions1): Likewise.
	(PropositionalFormulaFunctions2): Likewise.
	(KleeneTrivalentLogic): Likewise.

1 files changed, 0 insertions, 481 deletions

diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet
index dcdf0562..3ad4b2ff 100644
--- a/src/algebra/boolean.spad.pamphlet
+++ b/src/algebra/boolean.spad.pamphlet
@@ -12,386 +12,6 @@
 \tableofcontents
 \eject
 
-\section{Categories an domains for logic}
-
-<<category BOOLE BooleanLogic>>=
-)abbrev category BOOLE BooleanLogic
-++ Author: Gabriel Dos Reis
-++ Date Created: April 04, 2010
-++ Date Last Modified: April 04, 2010
-++ Description:
-++   This is the category of Boolean logic structures.
-BooleanLogic(): Category == Logic with
-    not: % -> %
-      ++ \spad{not x} returns the complement or negation of \spad{x}.
-    and: (%,%) -> %
-      ++ \spad{x and y} returns the conjunction of \spad{x} and \spad{y}.
-    or: (%,%) -> %
-      ++ \spad{x or y} returns the disjunction of \spad{x} and \spad{y}.
-  add
-    not x == ~ x
-    x and y == x /\ y
-    x or y == x \/ y
-@
-
-<<category PROPLOG PropositionalLogic>>=
-)abbrev category PROPLOG PropositionalLogic
-++ Author: Gabriel Dos Reis
-++ Date Created: Januray 14, 2008
-++ Date Last Modified: May 27, 2009
-++ Description: This category declares the connectives of
-++ Propositional Logic.
-PropositionalLogic(): Category == Join(BooleanLogic,SetCategory) with
-  true: %
-    ++ true is a logical constant.
-  false: %
-    ++ false is a logical constant.
-  implies: (%,%) -> %
-    ++ implies(p,q) returns the logical implication of `q' by `p'.
-  equiv: (%,%) -> %
-    ++ equiv(p,q) returns the logical equivalence of `p', `q'.
-@
-
-\section{domain PROPFRML PropositionalFormula}
-<<domain PROPFRML PropositionalFormula>>=
-)set mess autoload on
-)abbrev domain PROPFRML PropositionalFormula
-++ Author: Gabriel Dos Reis
-++ Date Created: Januray 14, 2008
-++ Date Last Modified: February, 2011
-++ Description: This domain implements propositional formula build
-++ over a term domain, that itself belongs to PropositionalLogic
-PropositionalFormula(T: SetCategory): Public == Private where
-  Public == Join(PropositionalLogic, CoercibleFrom T) with
-    isAtom : % -> Maybe T
-      ++ \spad{isAtom f} returns a value \spad{v} such that
-      ++ \spad{v case T} holds if the formula \spad{f} is a term.
-
-    isNot : % -> Maybe %
-      ++ \spad{isNot f} returns a value \spad{v} such that
-      ++ \spad{v case %} holds if the formula \spad{f} is a negation.
-
-    isAnd : % -> Maybe Pair(%,%)
-      ++ \spad{isAnd f} returns a value \spad{v} such that 
-      ++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
-      ++ is a conjunction formula.
-
-    isOr : % -> Maybe Pair(%,%)
-      ++ \spad{isOr f} returns a value \spad{v} such that 
-      ++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
-      ++ is a disjunction formula.
-
-    isImplies : % -> Maybe Pair(%,%)
-      ++ \spad{isImplies f} returns a value \spad{v} such that 
-      ++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
-      ++ is an implication formula.
-
-    isEquiv : % -> Maybe Pair(%,%)
-      ++ \spad{isEquiv f} returns a value \spad{v} such that 
-      ++ \spad{v case Pair(%,%)} holds if the formula \spad{f}
-      ++ is an equivalence formula.
-
-    conjunction: (%,%) -> %
-      ++ \spad{conjunction(p,q)} returns a formula denoting the
-      ++ conjunction of \spad{p} and \spad{q}.
-
-    disjunction: (%,%) -> %
-      ++ \spad{disjunction(p,q)} returns a formula denoting the
-      ++ disjunction of \spad{p} and \spad{q}.
-
-  Private == add
-    Rep == Union(T, Kernel %)
-    import Kernel %
-    import BasicOperator
-    import KernelFunctions2(Identifier,%)
-    import List %
-
-    -- Local names for proposition logical operators
-    macro FALSE == '%false
-    macro TRUE == '%true
-    macro NOT == '%not
-    macro AND == '%and
-    macro OR == '%or
-    macro IMP == '%implies
-    macro EQV == '%equiv
-
-    -- Return the nesting level of a formula
-    level(f: %): NonNegativeInteger ==
-      f' := rep f
-      f' case T => 0
-      height f'
-
-    -- A term is a formula
-    coerce(t: T): % == 
-      per t
-
-    false == per constantKernel FALSE
-    true == per constantKernel TRUE
-
-    ~ p ==
-      per kernel(operator(NOT, 1::Arity), [p], 1 + level p)
-
-    conjunction(p,q) ==
-      per kernel(operator(AND, 2), [p, q], 1 + max(level p, level q))
-
-    p /\ q == conjunction(p,q)
-
-    disjunction(p,q) ==
-      per kernel(operator(OR, 2), [p, q], 1 + max(level p, level q))
-
-    p \/ q == disjunction(p,q)
-
-    implies(p,q) ==
-      per kernel(operator(IMP, 2), [p, q], 1 + max(level p, level q))
-
-    equiv(p,q) ==
-      per kernel(operator(EQV, 2), [p, q], 1 + max(level p, level q))
-
-    isAtom f ==
-      f' := rep f
-      f' case T => just(f'@T)
-      nothing
-
-    isNot f ==
-      f' := rep f
-      f' case Kernel(%) and is?(f', NOT) => just(first argument f')
-      nothing
-
-    isBinaryOperator(f: Kernel %, op: Symbol): Maybe Pair(%, %) ==
-      not is?(f, op) => nothing
-      args := argument f
-      just pair(first args, second args)
-
-    isAnd f ==
-      f' := rep f
-      f' case Kernel % => isBinaryOperator(f', AND)
-      nothing
-
-    isOr f ==
-      f' := rep f
-      f' case Kernel % => isBinaryOperator(f', OR)
-      nothing
-
-    isImplies f ==
-      f' := rep f
-      f' case Kernel % => isBinaryOperator(f', IMP)
-      nothing
-
-
-    isEquiv f ==
-      f' := rep f
-      f' case Kernel % => isBinaryOperator(f', EQV)
-      nothing
-
-    -- Unparsing grammar.
-    --
-    -- Ideally, the following syntax would the external form
-    -- Formula:
-    --   EquivFormula
-    --
-    -- EquivFormula:
-    --   ImpliesFormula
-    --   ImpliesFormula <=> EquivFormula
-    --
-    -- ImpliesFormula:
-    --   OrFormula
-    --   OrFormula => ImpliesFormula
-    --
-    -- OrFormula:
-    --   AndFormula
-    --   AndFormula or OrFormula 
-    -- 
-    -- AndFormula
-    --   NotFormula
-    --   NotFormula and AndFormula
-    --
-    -- NotFormula:
-    --   PrimaryFormula
-    --   not NotFormula
-    --
-    -- PrimaryFormula:
-    --   Term
-    --   ( Formula )
-    --
-    -- Note: Since the token '=>' already means a construct different
-    --       from what we would like to have as a notation for
-    --       propositional logic, we will output the formula `p => q'
-    --       as implies(p,q), which looks like a function call.
-    --       Similarly, we do not have the token `<=>' for logical
-    --       equivalence; so we unparser `p <=> q' as equiv(p,q).
-    --
-    --       So, we modify the nonterminal PrimaryFormula to read
-    --       PrimaryFormula:
-    --         Term
-    --         implies(Formula, Formula)
-    --         equiv(Formula, Formula)
-    formula: % -> OutputForm
-    coerce(p: %): OutputForm ==
-      formula p
-
-    primaryFormula(p: %): OutputForm ==
-      p' := rep p
-      p' case T => p'@T::OutputForm
-      case constantIfCan p' is
-        c@Identifier => c::OutputForm
-        otherwise =>
-          is?(p', IMP) or is?(p', EQV) =>
-            args := argument p'
-            elt(operator(p')::OutputForm, 
-                  [formula first args, formula second args])$OutputForm
-          paren(formula p)$OutputForm
-
-    notFormula(p: %): OutputForm ==
-      case isNot p is
-        f@% => elt(outputForm 'not, [notFormula f])$OutputForm
-        otherwise => primaryFormula p
-
-    andFormula(f: %): OutputForm ==
-      case isAnd f is
-	p@Pair(%,%) =>
-          -- ??? idealy, we should be using `and$OutputForm' but
-          -- ??? a bug in the compiler currently prevents that.
-          infix(outputForm 'and, notFormula first p,
-             andFormula second p)$OutputForm
-        otherwise => notFormula f
-
-    orFormula(f: %): OutputForm ==
-      case isOr f is
-        p@Pair(%,%) => 
-          -- ??? idealy, we should be using `or$OutputForm' but
-          -- ??? a bug in the compiler currently prevents that.
-          infix(outputForm 'or, andFormula first p, 
-             orFormula second p)$OutputForm
-        otherwise => andFormula f
-
-    formula f ==
-      -- Note: this should be equivFormula, but see the explanation above.
-      orFormula f
-
-@
-
-<<package PROPFUN1 PropositionalFormulaFunctions1>>=
-)abbrev package PROPFUN1 PropositionalFormulaFunctions1
-++ Author: Gabriel Dos Reis
-++ Date Created: April 03, 2010
-++ Date Last Modified: April 03, 2010
-++ Description:
-++   This package collects unary functions operating on propositional
-++   formulae.
-PropositionalFormulaFunctions1(T): Public == Private where
-  T: SetCategory
-  Public == Type with
-    dual: PropositionalFormula T -> PropositionalFormula T
-      ++ \spad{dual f} returns the dual of the proposition \spad{f}.
-    atoms: PropositionalFormula T -> Set T
-      ++ \spad{atoms f} ++ returns the set of atoms appearing in
-      ++ the formula \spad{f}.
-    simplify: PropositionalFormula T -> PropositionalFormula T
-      ++ \spad{simplify f} returns a formula logically equivalent
-      ++ to \spad{f} where obvious tautologies have been removed.
-  Private == add
-    macro F == PropositionalFormula T
-    inline Pair(F,F)
-
-    dual f ==
-      f = true$F => false$F
-      f = false$F => true$F
-      isAtom f case T => f
-      (f1 := isNot f) case F => not dual f1
-      (f2 := isAnd f) case Pair(F,F) =>
-         disjunction(dual first f2, dual second f2)
-      (f2 := isOr f) case Pair(F,F) =>
-         conjunction(dual first f2, dual second f2)
-      error "formula contains `equiv' or `implies'"
-
-    atoms f ==
-      (t := isAtom f) case T => { t }
-      (f1 := isNot f) case F => atoms f1
-      (f2 := isAnd f) case Pair(F,F) =>
-         union(atoms first f2, atoms second f2)
-      (f2 := isOr f) case Pair(F,F) =>
-         union(atoms first f2, atoms second f2)
-      empty()$Set(T)
-
-    -- one-step simplification helper function
-    simplifyOneStep(f: F): F ==
-      (f1 := isNot f) case F =>
-        f1 = true$F => false$F
-        f1 = false$F => true$F
-        (f1' := isNot f1) case F => f1'         -- assume classical logic
-        f
-      (f2 := isAnd f) case Pair(F,F) =>
-        first f2 = false$F or second f2 = false$F => false$F
-        first f2 = true$F => second f2
-        second f2 = true$F => first f2
-        f
-      (f2 := isOr f) case Pair(F,F) =>
-        first f2 = false$F => second f2
-        second f2 = false$F => first f2
-        first f2 = true$F or second f2 = true$F => true$F
-        f
-      (f2 := isImplies f) case Pair(F,F) =>
-        first f2 = false$F or second f2 = true$F => true$F
-        first f2 = true$F => second f2
-        second f2 = false$F => not first f2
-        f
-      (f2 := isEquiv f) case Pair(F,F) =>
-        first f2 = true$F => second f2
-        second f2 = true$F => first f2
-        first f2 = false$F => not second f2
-        second f2 = false$F => not first f2
-        f
-      f
-
-    simplify f ==
-      (f1 := isNot f) case F => simplifyOneStep(not simplify f1)
-      (f2 := isAnd f) case Pair(F,F) =>
-        simplifyOneStep(conjunction(simplify first f2, simplify second f2))
-      (f2 := isOr f) case Pair(F,F) =>
-        simplifyOneStep(disjunction(simplify first f2, simplify second f2))
-      (f2 := isImplies f) case Pair(F,F) =>
-        simplifyOneStep(implies(simplify first f2, simplify second f2))
-      (f2 := isEquiv f) case Pair(F,F) =>
-        simplifyOneStep(equiv(simplify first f2, simplify second f2))
-      f
-@
-
-<<package PROPFUN2 PropositionalFormulaFunctions2>>=
-)abbrev package PROPFUN2 PropositionalFormulaFunctions2
-++ Author: Gabriel Dos Reis
-++ Date Created: April 03, 2010
-++ Date Last Modified: April 03, 2010
-++ Description:
-++   This package collects binary functions operating on propositional
-++   formulae.
-PropositionalFormulaFunctions2(S,T): Public == Private where
-  S: SetCategory
-  T: SetCategory
-  Public == Type with
-    map: (S -> T, PropositionalFormula S) -> PropositionalFormula T
-      ++ \spad{map(f,x)} returns a propositional formula where
-      ++ all atoms in \spad{x} have been replaced by the result
-      ++ of applying the function \spad{f} to them.
-  Private == add
-    macro FS == PropositionalFormula S
-    macro FT == PropositionalFormula T
-    map(f,x) ==
-      x = true$FS => true$FT
-      x = false$FS => false$FT
-      (t := isAtom x) case S => f(t)::FT
-      (f1 := isNot x) case FS => not map(f,f1)
-      (f2 := isAnd x) case Pair(FS,FS) =>
-         conjunction(map(f,first f2), map(f,second f2))
-      (f2 := isOr x) case Pair(FS,FS) =>
-         disjunction(map(f,first f2), map(f,second f2))
-      (f2 := isImplies x) case Pair(FS,FS) =>
-         implies(map(f,first f2), map(f,second f2))
-      (f2 := isEquiv x) case Pair(FS,FS) =>
-         equiv(map(f,first f2), map(f,second f2))
-      error "invalid propositional formula"
-
-@
-
 \section{domain REF Reference}
 <<domain REF Reference>>=
 )abbrev domain REF Reference
@@ -429,32 +49,6 @@ Reference(S:Type): SetCategory with
 
 @
 
-\section{category LOGIC Logic}
-
-<<category LOGIC Logic>>=
-)abbrev category LOGIC Logic
-++ Author: 
-++ Date Created:
-++ Date Last Changed: May 27, 2009
-++ Basic Operations: ~, /\, \/
-++ Related Constructors:
-++ Keywords: boolean
-++ Description:  
-++ `Logic' provides the basic operations for lattices,
-++ e.g., boolean algebra.
-
-
-Logic: Category == Type with
-       ~:        % -> %
-	++ ~(x) returns the logical complement of x.
-       /\:       (%, %) -> %
-	++ \spadignore { /\ }returns the logical `meet', e.g. `and'.
-       \/:       (%, %) -> %
-	++ \spadignore{ \/ } returns the logical `join', e.g. `or'.
-  add
-    x \/ y == ~(~x /\ ~y)
-
-@
 \section{domain BOOLEAN Boolean}
 <<domain BOOLEAN Boolean>>=
 )abbrev domain BOOLEAN Boolean
@@ -605,81 +199,6 @@ Bits(): Exports == Implementation where
 
 @
 
-
-\section{Kleene's Three-Valued Logic}
-<<domain KTVLOGIC KleeneTrivalentLogic>>=
-)abbrev domain KTVLOGIC KleeneTrivalentLogic
-++ Author: Gabriel Dos Reis
-++ Date Created: September 20, 2008
-++ Date Last Modified: January 14, 2012
-++ Description: 
-++   This domain implements Kleene's 3-valued propositional logic.
-KleeneTrivalentLogic(): Public == Private where
-  Public == Join(PropositionalLogic,Finite) with
-    unknown: %     ++ the indefinite `unknown' 
-    case: (%,[| false |]) -> Boolean
-      ++ x case false holds if the value of `x' is `false'
-    case: (%,[| unknown |]) -> Boolean
-      ++ x case unknown holds if the value of `x' is `unknown'
-    case: (%,[| true |]) -> Boolean
-      ++ s case true holds if the value of `x' is `true'.
-  Private == Maybe Boolean add
-    false == per just(false@Boolean)
-    unknown == per nothing
-    true == per just(true@Boolean)
-    x = y == rep x = rep y
-    x case true == x = true@%
-    x case false == x = false@%
-    x case unknown == x = unknown
-
-    not x ==
-      x case false => true
-      x case unknown => unknown
-      false
-
-    x and y ==
-      x case false => false
-      x case unknown =>
-        y case false => false
-        unknown
-      y
-
-    x or y ==
-      x case false => y
-      x case true => x
-      y case true => y
-      unknown
-
-    implies(x,y) ==
-      x case false => true
-      x case true => y
-      y case true => true
-      unknown
-
-    equiv(x,y) ==
-      x case unknown => x
-      x case true => y
-      not y
-
-    coerce(x: %): OutputForm ==
-      case rep x is
-        y@Boolean => y::OutputForm
-        otherwise => outputForm 'unknown
-
-    size() == 3
-
-    index n ==
-      n > 3 => error "index: argument out of bound"
-      n = 1 => false
-      n = 2 => unknown
-      true
-
-    lookup x ==
-      x = false => 1
-      x = unknown => 2
-      3
-@
-
 \section{License}
 
 <<license>>=