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; $Id: tensor.scm 2156 2008-01-25 13:25:12Z schimans $
; This is an attempt to build integers and rationals by means of a
; parametrized free algebra tensor.
(display "loading tensor.scm ...") (newline)
(add-param-alg "tensor" 'tensor-typeop
'("Tensor" "alpha1=>alpha2=>tensor"))
; (type-to-string (py "alpha1 tensor alpha2"))
; (type-to-string (py "alpha1 tensor alpha2 tensor alpha3"))
; (type-to-string (py "alpha1 tensor (alpha2 tensor alpha3)"))
; Infix notation allowed (and type parameters omitted) for the binary
; constructor. n#m#k
(add-token
"#"
'pair-op
(lambda (x y)
(let* ((type1 (term-to-type x))
(type2 (term-to-type y)))
(mk-term-in-app-form
(make-term-in-const-form
(let* ((constr (constr-name-to-constr "Tensor"))
(tvars (const-to-tvars constr))
(subst (make-substitution tvars (list type1 type2))))
(const-substitute constr subst #f)))
x y))))
(add-display
(py "alpha1 tensor alpha2")
(lambda (x)
(let* ((op (term-in-app-form-to-final-op x))
(args (term-in-app-form-to-args x)))
(if (and (term-in-const-form? op)
(string=? "Tensor"
(const-to-name (term-in-const-form-to-const op)))
(= 2 (length args)))
(list 'pair-op "#"
(term-to-token-tree (car args))
(term-to-token-tree (cadr args)))
#f))))
; (term-to-string (pt "boole#boole#boole"))
; (term-to-string (pt "(boole#boole)#boole"))
; (formula-to-string (pf "boole#boole=boole#boole"))
; (formula-to-string (nf (pf "(boole#boole)=(boole#boole)")))
(add-program-constant
"tensorFst" (py "alpha1 tensor alpha2=>alpha1") 1 'const 1)
(add-token
"fst" 'prefix-op
(lambda (x) (make-term-in-app-form
(make-term-in-const-form
(let* ((const (pconst-name-to-pconst "tensorFst"))
(tvars (const-to-tvars const))
(tensortype (term-to-type x))
(types (alg-form-to-types tensortype))
(type1 (car types))
(type2 (cadr types))
(subst (make-substitution tvars (list type1 type2))))
(const-substitute const subst #f)))
x)))
(add-display
(py "alpha1")
(lambda (x)
(let* ((op (term-in-app-form-to-final-op x))
(args (term-in-app-form-to-args x)))
(if (and (term-in-const-form? op)
(string=? "tensorFst"
(const-to-name (term-in-const-form-to-const op)))
(= 1 (length args)))
(list 'prefix-op "fst"
(term-to-token-tree (car args)))
#f))))
; (term-to-string (nt (pt "fst(boole1#boole2)")))
(add-computation-rule
(pt "(tensorFst alpha1 alpha2)((Tensor alpha1 alpha2)alpha1 alpha2)")
(pt "alpha1"))
; ok, computation rule fst(alpha1#alpha2) -> alpha1 added
; (term-to-string (nt (pt "fst(boole1#boole2)")))
(add-program-constant
"tensorSnd" (py "alpha1 tensor alpha2=>alpha2") 1 'const 1)
(add-token
"snd" 'prefix-op
(lambda (x) (make-term-in-app-form
(make-term-in-const-form
(let* ((const (pconst-name-to-pconst "tensorSnd"))
(tvars (const-to-tvars const))
(tensortype (term-to-type x))
(types (alg-form-to-types tensortype))
(type1 (car types))
(type2 (cadr types))
(subst (make-substitution tvars (list type1 type2))))
(const-substitute const subst #f)))
x)))
(add-display
(py "alpha1")
(lambda (x)
(let* ((op (term-in-app-form-to-final-op x))
(args (term-in-app-form-to-args x)))
(if (and (term-in-const-form? op)
(string=? "tensorSnd"
(const-to-name (term-in-const-form-to-const op)))
(= 1 (length args)))
(list 'prefix-op "snd"
(term-to-token-tree (car args)))
#f))))
; (term-to-string (nt (pt "snd(boole1#boole2)")))
(add-computation-rule
(pt "(tensorSnd alpha1 alpha2)((Tensor alpha1 alpha2)alpha1 alpha2)")
(pt "alpha2"))
; ok, computation rule snd(alpha1#alpha2) -> alpha1 added
; (term-to-string (nt (pt "snd(boole1#boole2)")))
; (add-pvar-name "Q" (make-arity (py "boole tensor boole")))
; (add-var-name "p" (py "boole tensor boole"))
; (set-goal (pf "all boole1,boole2 Q (boole1#boole2) ->
; all p Q p"))
; (assume 1)
; (ind)
; (use 1)
; Added 04-05-04
(define (term-in-tensor-form? term)
(and (term-in-app-form? term)
(let ((op (term-in-app-form-to-final-op term))
(args (term-in-app-form-to-args term)))
(and (term-in-const-form? op)
(string=? "Tensor"
(const-to-name (term-in-const-form-to-const op)))
(= 2 (length args))))))
; (term-in-tensor-form? (pt "1#k"))
(define (term-in-tensor-form-to-fst term)
(let ((args (term-in-app-form-to-args term)))
(if (= 2 (length args))
(car args)
(myerror "term-in-tensor-form-to-fst" "two argumments expected"
(term-to-string term)))))
; (term-to-string (term-in-tensor-form-to-fst (pt "1#k")))
(define (term-in-tensor-form-to-snd term)
(let ((args (term-in-app-form-to-args term)))
(if (= 2 (length args))
(cadr args)
(myerror "term-in-tensor-form-to-snd" "two argumments expected"
(term-to-string term)))))
; (term-to-string (term-in-tensor-form-to-snd (pt "1#k")))
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