1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
; $Id: tensor.scm,v 1.4 2008/01/25 13:30:21 logik Exp $
; 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")))
|
