LYaPAS

Logical Language for the Representation of Synthesis Algorithms, or LYaPAS (ЛЯПАС), is a programming language that sprung out of 1964 Soviet Union. It is based on set-theoretical considerations oriented toward the programming of synthesis algorithms for finite-state and discrete devices. The language is self-extending and self-compiling with only a minimal translator written for the native machine environment.

Speciality keyboard mappings are highly recommended for entering in the many non-typical keyboard symbols found in the language.

Its use of octal numbers within the language specification is considered one of its interesting qualities.

LYaPAS-M is a further refinement of LYaPAS.

Operators

l-operators

First-level operators in the language.

Basic Computational Operators

Symbol	Name	Example
∨	Disjunction Operator	01001101 ∨ 10011000 = 11011101
∧	Conjunction Operator	01001101 ∧ 10011000 = 00001000
⊕	Exclusive Disjunction Operator	01000110 ⊕ 10001100 = 11001010
+	Addition Operator—Modulo 2p	01000110 + 10001100 = 11010010
-	Subtraction Operator—Modulo 2p	01000110 - 10001100 = 1011101
×	Multiplication Operator—Modulo 2p	01000110 × 10001100 = 01001000
×̅	Multiplication Operator with Round-Off	01000110 ×̄ 10001100 = 00100110
:	Division Operator	00001101:00000101 = 00000011 (remainder), я = 00000010 (integer part of quotient)
┐	Component-wise Inversion Operator	01001101 ┐ = 10110010
ɪ	Order Inversion Operator	01001101 ɪ = 10110010
⊢	Leftmost 1 Position-Locating Operator	00010110 ⊢ = 00000011 By convention, 00000000 ⊢ = 10000000 ⊢ = 00000000
⇤	Normalization Operator	00010110 ⇤ = 10110000, 00000000 ⇤ 00000000
<	Left-Shift Operator	01101010 < 00000100 = 10100000
>	Right-Shift Operator	01101010 > 00000101 = 00000011
←	Cyclic-Shift Operator	01101010 ← 00100100 = 10100110
▽	Weighting Operator	01101010 ▽ = 00000100 (number of ones)
⊻	Reflection Operator	(Requires a more in-depth explanation.)

Assignment Operators

Symbol	Name
⇒	Assignment Operator
⇔	Interchange Operator
⇐	Natural Assignment Operator
▵	Positive Element-Incrementation Operator
▵̅	Negative Element-Incrementation Operator
○	Null-Value-Assignment Operator
○̅	Maximum-Value-Assignment Operator

Implicit Variable τ

Implicit variable τ is a symbol that never appears in the program. The current value of τ is the result of the the realization of the current operator.

Control-Transfer Operators

Symbol	Name
→	Unconditional Transfer Operator
○→	Conditional Transfer-on-Zero Operator
↦	Conditional Transfer-on-One Operator
⇻	Exit Operator
!	Return Operator
↓	Transfer-to-Machine-Language Operator
Ẋ	Enumeration-of-Ones Operator
Ẍ	Random-Enumeration-of-Ones Operator

Exchanging Information with External Medium Operators

Symbol	Name
*	Print-One-Element Operator
⁑	Punch-One-Element Operator
↑	Input Operator
↗	Data-Transfer-to-External-Complex Operator
↙	Data-Transfer-from-External-Complex Operator

Other Operators

Symbol	Name
.	End-of-Algorithm Operator
⇇	Unlimited-Shift Operator

L-operators

Second-level operators in the language.

Example

genadj. Perform generalized adjunction (joining) of intervals of a set.

genadj ακ?, ßκ? /b, d/ (αß)
170 233 4 (αab)
○ a ⇒ bb_α ⇒ dc₀ ┐⇒ b

Test for generalized adjunction of intervals I_a and I_b, formation of the interval I_d—the result of the generalized adjunction—and setting of tags:

§1 △ a ⊕ d ○ → 4αa ⊕ αb∧ b ⇒ aßa
 ⊕ ßb ∧ a ⇒ a ⇤ ⊕ c0 ↦ 1αa
 ∨ αb ⊕ a ⇒ αd?ßα ∧ ßb ∨ a
 ∨ c0 ⇒ ßd?c0 ∨ αa ⇒ αac0 ∨ αb
 ⇒ αb ○ c ○ a

Test for presence of interval I_d in Int:

§2 αc ⊕ αd ⊕ b |→ 3ßc ⊕ ßd ∧ b
 ↦ 3c0 ∨ ßc ⇒ ßc ○̄ a

§3 △ c ⊕ d ↦ 2a ↦ 1 △ d → 1

§4 ○̄ a △ b ⊕ d ↦ 1d ⇒ bα ⇒ bß

External resources

• LYaPAS in the Encyclopedia of Programming Languages
• Library of Congress entry for LYaPAS: a programming language for logic and coding algorithms